- FindStat

Identifier

Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions

Images

[] => [] => [] => []

[[]] => [1,0] => [] => []

[[],[]] => [1,0,1,0] => [1] => [1]

[[[]]] => [1,1,0,0] => [] => []

[[],[],[]] => [1,0,1,0,1,0] => [2,1] => [2,1]

[[],[[]]] => [1,0,1,1,0,0] => [1,1] => [2]

[[[]],[]] => [1,1,0,0,1,0] => [2] => [1,1]

[[[],[]]] => [1,1,0,1,0,0] => [1] => [1]

[[[[]]]] => [1,1,1,0,0,0] => [] => []

[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [3,2,1] => [3,2,1]

[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [2,2,1] => [3,2]

[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [3,1,1] => [3,1,1]

[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [2,1,1] => [3,1]

[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,1,1] => [3]

[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [3,2] => [2,2,1]

[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [2,2] => [2,2]

[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [3,1] => [2,1,1]

[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [3] => [1,1,1]

[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [2,1] => [2,1]

[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [1,1] => [2]

[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [2] => [1,1]

[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [1] => [1]

[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [] => []

[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1]

[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [4,3,2]

[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [4,3,1,1]

[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [4,3,1]

[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [4,3]

[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [4,2,2,1]

[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [4,2,2]

[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [4,2,1,1]

[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1]

[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [4,2,1]

[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [4,2]

[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [4,1,1]

[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [4,1]

[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [4]

[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [3,3,2,1]

[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [3,3,2]

[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [3,3,1,1]

[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [3,3,1]

[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [3,3]

[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [3,2,2,1]

[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => [2,2,2,1]

[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [3,2,2]

[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => [2,2,2]

[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [3,2,1,1]

[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [3,1,1,1]

[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => [2,2,1,1]

[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => [2,1,1,1]

[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1]

[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [3,2,1]

[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [3,2]

[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [3,1,1]

[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [3,1]

[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [3]

[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => [2,2,1]

[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => [2,2]

[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => [2,1,1]

[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1]

[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => [2,1]

[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => [2]

[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [2] => [1,1]

[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [1] => [1]

[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [] => []

[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,4,3,2,1]

[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [5,4,3,2]

[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [5,4,3,1,1]

[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [5,4,3,1]

[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [5,4,3]

[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [5,4,2,2,1]

[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [5,4,2,2]

[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [5,4,2,1,1]

[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [5,4,1,1,1]

[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [5,4,2,1]

[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [5,4,2]

[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [5,4,1,1]

[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [5,4,1]

[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [5,4]

[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [5,3,3,2,1]

[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [5,3,3,2]

[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [5,3,3,1,1]

[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [5,3,3,1]

[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [5,3,3]

[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [5,3,2,2,1]

[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [5,2,2,2,1]

[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [5,3,2,2]

[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [5,2,2,2]

[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [5,3,2,1,1]

[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [5,3,1,1,1]

[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [5,2,2,1,1]

[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [5,2,1,1,1]

[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1]

[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [5,3,2,1]

[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [5,3,2]

[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [5,3,1,1]

[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [5,3,1]

[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [5,3]

[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [5,2,2,1]

[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [5,2,2]

[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [5,2,1,1]

>>> Load all 1494 entries. <<<

[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [5,1,1,1]

[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [5,2,1]

[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [5,2]

[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [5,1,1]

[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [5,1]

[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [5]

[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [4,4,3,2,1]

[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [4,4,3,2]

[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [4,4,3,1,1]

[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [4,4,3,1]

[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [4,4,3]

[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [4,4,2,2,1]

[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,4,2,2]

[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [4,4,2,1,1]

[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [4,4,1,1,1]

[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [4,4,2,1]

[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [4,4,2]

[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [4,4,1,1]

[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [4,4,1]

[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [4,4]

[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [4,3,3,2,1]

[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [3,3,3,2,1]

[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [4,3,3,2]

[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [3,3,3,2]

[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [4,3,3,1,1]

[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,3,3,1,1]

[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [4,3,3,1]

[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [4,3,3]

[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [3,3,3,1]

[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,3]

[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [4,3,2,2,1]

[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [4,2,2,2,1]

[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [3,3,2,2,1]

[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [3,2,2,2,1]

[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [2,2,2,2,1]

[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [4,3,2,2]

[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [4,2,2,2]

[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [3,3,2,2]

[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [3,2,2,2]

[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [2,2,2,2]

[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [4,3,2,1,1]

[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [4,3,1,1,1]

[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [4,2,2,1,1]

[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [4,2,1,1,1]

[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [4,1,1,1,1]

[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [3,3,2,1,1]

[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [3,3,1,1,1]

[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,2,2,1,1]

[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [2,2,2,1,1]

[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [3,2,1,1,1]

[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [3,1,1,1,1]

[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [2,2,1,1,1]

[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1]

[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1]

[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [4,3,2,1]

[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [4,3,2]

[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [4,3,1,1]

[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [4,3,1]

[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [4,3]

[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [4,2,2,1]

[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [4,2,2]

[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [4,2,1,1]

[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [4,1,1,1]

[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [4,2,1]

[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [4,2]

[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [4,1,1]

[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [4,1]

[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [4]

[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [3,3,2,1]

[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [3,3,2]

[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [3,3,1,1]

[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [3,3,1]

[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [3,3]

[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [3,2,2,1]

[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [2,2,2,1]

[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [3,2,2]

[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [2,2,2]

[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [3,2,1,1]

[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [3,1,1,1]

[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [2,2,1,1]

[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [2,1,1,1]

[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1]

[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [3,2,1]

[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [3,2]

[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [3,1,1]

[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [3,1]

[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [3]

[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [2,2,1]

[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [2,2]

[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [2,1,1]

[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1]

[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [2,1]

[[[[[],[[]]]]]] => [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] => [1,1]

[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1]

[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [] => []

[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1]

[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => [6,5,4,3,2]

[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => [6,5,4,3,1,1]

[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => [6,5,4,3,1]

[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => [6,5,4,3]

[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => [6,5,4,2,2,1]

[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => [6,5,4,2,2]

[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2,1] => [6,5,4,2,1,1]

[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => [6,5,4,1,1,1]

[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => [6,5,4,2,1]

[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => [6,5,4,2]

[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => [6,5,4,1,1]

[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => [6,5,4,1]

[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [6,5,4]

[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => [6,5,3,3,2,1]

[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => [6,5,3,3,2]

[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => [6,5,3,3,1,1]

[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2,1] => [6,5,3,3,1]

[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => [6,5,3,3]

[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2,1] => [6,5,3,2,2,1]

[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => [6,5,2,2,2,1]

[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2,1] => [6,5,3,2,2]

[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => [6,5,2,2,2]

[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2,1] => [6,5,3,2,1,1]

[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => [6,5,3,1,1,1]

[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => [6,5,2,2,1,1]

[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => [6,5,2,1,1,1]

[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => [6,5,1,1,1,1]

[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => [6,5,3,2,1]

[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => [6,5,3,2]

[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => [6,5,3,1,1]

[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => [6,5,3,1]

[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [6,5,3]

[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => [6,5,2,2,1]

[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => [6,5,2,2]

[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => [6,5,2,1,1]

[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => [6,5,1,1,1]

[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => [6,5,2,1]

[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => [6,5,2]

[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => [6,5,1,1]

[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [6,5,1]

[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [6,5]

[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => [6,4,4,3,2,1]

[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => [6,4,4,3,2]

[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => [6,4,4,3,1,1]

[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1,1] => [6,4,4,3,1]

[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => [6,4,4,3]

[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => [6,4,4,2,2,1]

[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => [6,4,4,2,2]

[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1,1] => [6,4,4,2,1,1]

[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => [6,4,4,1,1,1]

[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => [6,4,4,2,1]

[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => [6,4,4,2]

[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => [6,4,4,1,1]

[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => [6,4,4,1]

[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [6,4,4]

[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,1] => [6,4,3,3,2,1]

[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => [6,3,3,3,2,1]

[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1,1] => [6,4,3,3,2]

[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => [6,3,3,3,2]

[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1,1] => [6,4,3,3,1,1]

[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => [6,3,3,3,1,1]

[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => [6,4,3,3,1]

[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => [6,4,3,3]

[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => [6,3,3,3,1]

[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => [6,3,3,3]

[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,1] => [6,4,3,2,2,1]

[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => [6,4,2,2,2,1]

[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => [6,3,3,2,2,1]

[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => [6,3,2,2,2,1]

[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => [6,2,2,2,2,1]

[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => [6,4,3,2,2]

[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => [6,4,2,2,2]

[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => [6,3,3,2,2]

[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => [6,3,2,2,2]

[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => [6,2,2,2,2]

[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => [6,4,3,2,1,1]

[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => [6,4,3,1,1,1]

[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => [6,4,2,2,1,1]

[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => [6,4,2,1,1,1]

[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => [6,4,1,1,1,1]

[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => [6,3,3,2,1,1]

[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => [6,3,3,1,1,1]

[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => [6,3,2,2,1,1]

[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => [6,2,2,2,1,1]

[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [6,3,2,1,1,1]

[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [6,3,1,1,1,1]

[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [6,2,2,1,1,1]

[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [6,2,1,1,1,1]

[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [6,1,1,1,1,1]

[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => [6,4,3,2,1]

[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => [6,4,3,2]

[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => [6,4,3,1,1]

[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => [6,4,3,1]

[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [6,4,3]

[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => [6,4,2,2,1]

[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => [6,4,2,2]

[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [6,4,2,1,1]

[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => [6,4,1,1,1]

[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => [6,4,2,1]

[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [6,4,2]

[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [6,4,1,1]

[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1]

[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4]

[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => [6,3,3,2,1]

[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => [6,3,3,2]

[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => [6,3,3,1,1]

[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => [6,3,3,1]

[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [6,3,3]

[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => [6,3,2,2,1]

[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [6,2,2,2,1]

[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => [6,3,2,2]

[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [6,2,2,2]

[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [6,3,2,1,1]

[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [6,3,1,1,1]

[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [6,2,2,1,1]

[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [6,2,1,1,1]

[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [6,1,1,1,1]

[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [6,3,2,1]

[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [6,3,2]

[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [6,3,1,1]

[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [6,3,1]

[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3]

[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [6,2,2,1]

[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [6,2,2]

[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [6,2,1,1]

[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [6,1,1,1]

[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [6,2,1]

[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2]

[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1]

[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1]

[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6]

[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => [5,5,4,3,2,1]

[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => [5,5,4,3,2]

[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => [5,5,4,3,1,1]

[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2] => [5,5,4,3,1]

[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => [5,5,4,3]

[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => [5,5,4,2,2,1]

[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => [5,5,4,2,2]

[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2] => [5,5,4,2,1,1]

[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => [5,5,4,1,1,1]

[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => [5,5,4,2,1]

[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => [5,5,4,2]

[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [5,5,4,1,1]

[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [5,5,4,1]

[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [5,5,4]

[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => [5,5,3,3,2,1]

[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => [5,5,3,3,2]

[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => [5,5,3,3,1,1]

[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => [5,5,3,3,1]

[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => [5,5,3,3]

[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2] => [5,5,3,2,2,1]

[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => [5,5,2,2,2,1]

[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => [5,5,3,2,2]

[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => [5,5,2,2,2]

[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => [5,5,3,2,1,1]

[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => [5,5,3,1,1,1]

[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => [5,5,2,2,1,1]

[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => [5,5,2,1,1,1]

[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [5,5,1,1,1,1]

[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => [5,5,3,2,1]

[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => [5,5,3,2]

[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [5,5,3,1,1]

[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [5,5,3,1]

[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [5,5,3]

[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => [5,5,2,2,1]

[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => [5,5,2,2]

[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => [5,5,2,1,1]

[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [5,5,1,1,1]

[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => [5,5,2,1]

[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [5,5,2]

[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [5,5,1,1]

[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [5,5,1]

[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [5,5]

[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => [5,4,4,3,2,1]

[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => [4,4,4,3,2,1]

[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1] => [5,4,4,3,2]

[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [4,4,4,3,2]

[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1] => [5,4,4,3,1,1]

[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => [4,4,4,3,1,1]

[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => [5,4,4,3,1]

[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [5,4,4,3]

[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [4,4,4,3,1]

[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [4,4,4,3]

[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1] => [5,4,4,2,2,1]

[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => [4,4,4,2,2,1]

[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => [5,4,4,2,2]

[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [4,4,4,2,2]

[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => [5,4,4,2,1,1]

[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [5,4,4,1,1,1]

[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => [4,4,4,2,1,1]

[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [4,4,4,1,1,1]

[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => [5,4,4,2,1]

[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [5,4,4,2]

[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => [5,4,4,1,1]

[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [5,4,4,1]

[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [5,4,4]

[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [4,4,4,2,1]

[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [4,4,4,2]

[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [4,4,4,1,1]

[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [4,4,4,1]

[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [4,4,4]

[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1] => [5,4,3,3,2,1]

[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => [5,3,3,3,2,1]

[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => [4,4,3,3,2,1]

[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => [4,3,3,3,2,1]

[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [3,3,3,3,2,1]

[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => [5,4,3,3,2]

[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => [5,3,3,3,2]

[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => [4,4,3,3,2]

[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [4,3,3,3,2]

[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [3,3,3,3,2]

[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => [5,4,3,3,1,1]

[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => [5,3,3,3,1,1]

[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => [4,4,3,3,1,1]

[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => [4,3,3,3,1,1]

[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [3,3,3,3,1,1]

[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => [5,4,3,3,1]

[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [5,4,3,3]

[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => [5,3,3,3,1]

[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [5,3,3,3]

[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [4,4,3,3,1]

[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [4,4,3,3]

[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [4,3,3,3,1]

[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [4,3,3,3]

[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [3,3,3,3,1]

[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [3,3,3,3]

[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [5,4,3,2,2,1]

[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => [5,4,2,2,2,1]

[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [5,3,3,2,2,1]

[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [5,3,2,2,2,1]

[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [5,2,2,2,2,1]

[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => [4,4,3,2,2,1]

[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => [4,4,2,2,2,1]

[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => [4,3,3,2,2,1]

[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [3,3,3,2,2,1]

[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [4,3,2,2,2,1]

[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [4,2,2,2,2,1]

[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [3,3,2,2,2,1]

[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [3,2,2,2,2,1]

[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [2,2,2,2,2,1]

[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => [5,4,3,2,2]

[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => [5,4,2,2,2]

[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => [5,3,3,2,2]

[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [5,3,2,2,2]

[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [5,2,2,2,2]

[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [4,4,3,2,2]

[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => [4,4,2,2,2]

[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [4,3,3,2,2]

[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [3,3,3,2,2]

[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [4,3,2,2,2]

[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [4,2,2,2,2]

[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [3,3,2,2,2]

[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [3,2,2,2,2]

[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [2,2,2,2,2]

[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => [5,4,3,2,1,1]

[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [5,4,3,1,1,1]

[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => [5,4,2,2,1,1]

[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [5,4,2,1,1,1]

[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [5,4,1,1,1,1]

[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => [5,3,3,2,1,1]

[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [5,3,3,1,1,1]

[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => [5,3,2,2,1,1]

[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => [5,2,2,2,1,1]

[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [5,3,2,1,1,1]

[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [5,3,1,1,1,1]

[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [5,2,2,1,1,1]

[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [5,2,1,1,1,1]

[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [5,1,1,1,1,1]

[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => [4,4,3,2,1,1]

[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [4,4,3,1,1,1]

[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [4,4,2,2,1,1]

[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [4,4,2,1,1,1]

[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [4,4,1,1,1,1]

[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [4,3,3,2,1,1]

[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [3,3,3,2,1,1]

[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [4,3,3,1,1,1]

[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [3,3,3,1,1,1]

[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [4,3,2,2,1,1]

[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [4,2,2,2,1,1]

[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [3,3,2,2,1,1]

[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [3,2,2,2,1,1]

[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [2,2,2,2,1,1]

[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [4,3,2,1,1,1]

[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [4,3,1,1,1,1]

[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [4,2,2,1,1,1]

[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [4,2,1,1,1,1]

[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [4,1,1,1,1,1]

[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [3,3,2,1,1,1]

[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [3,3,1,1,1,1]

[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,2,2,1,1,1]

[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [2,2,2,1,1,1]

[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [3,2,1,1,1,1]

[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [3,1,1,1,1,1]

[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [2,2,1,1,1,1]

[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1]

[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [1,1,1,1,1,1]

[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [5,4,3,2,1]

[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [5,4,3,2]

[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [5,4,3,1,1]

[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [5,4,3,1]

[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [5,4,3]

[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [5,4,2,2,1]

[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [5,4,2,2]

[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [5,4,2,1,1]

[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [5,4,1,1,1]

[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [5,4,2,1]

[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [5,4,2]

[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [5,4,1,1]

[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [5,4,1]

[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [5,4]

[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [5,3,3,2,1]

[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [5,3,3,2]

[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [5,3,3,1,1]

[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [5,3,3,1]

[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [5,3,3]

[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [5,3,2,2,1]

[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [5,2,2,2,1]

[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [5,3,2,2]

[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [5,2,2,2]

[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [5,3,2,1,1]

[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [5,3,1,1,1]

[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [5,2,2,1,1]

[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [5,2,1,1,1]

[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1]

[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [5,3,2,1]

[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [5,3,2]

[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [5,3,1,1]

[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [5,3,1]

[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [5,3]

[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [5,2,2,1]

[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [5,2,2]

[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [5,2,1,1]

[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [5,1,1,1]

[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [5,2,1]

[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [5,2]

[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [5,1,1]

[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [5,1]

[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [5]

[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [4,4,3,2,1]

[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [4,4,3,2]

[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [4,4,3,1,1]

[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [4,4,3,1]

[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [4,4,3]

[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [4,4,2,2,1]

[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [4,4,2,2]

[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [4,4,2,1,1]

[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [4,4,1,1,1]

[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [4,4,2,1]

[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [4,4,2]

[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [4,4,1,1]

[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [4,4,1]

[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [4,4]

[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [4,3,3,2,1]

[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [3,3,3,2,1]

[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [4,3,3,2]

[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [3,3,3,2]

[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [4,3,3,1,1]

[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,3,3,1,1]

[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [4,3,3,1]

[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [4,3,3]

[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [3,3,3,1]

[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [3,3,3]

[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [4,3,2,2,1]

[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [4,2,2,2,1]

[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [3,3,2,2,1]

[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [3,2,2,2,1]

[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [2,2,2,2,1]

[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [4,3,2,2]

[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [4,2,2,2]

[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [3,3,2,2]

[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [3,2,2,2]

[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [2,2,2,2]

[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [4,3,2,1,1]

[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [4,3,1,1,1]

[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [4,2,2,1,1]

[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [4,2,1,1,1]

[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [4,1,1,1,1]

[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [3,3,2,1,1]

[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [3,3,1,1,1]

[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,2,2,1,1]

[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [2,2,2,1,1]

[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [3,2,1,1,1]

[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [3,1,1,1,1]

[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [2,2,1,1,1]

[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [2,1,1,1,1]

[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1]

[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [4,3,2,1]

[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [4,3,2]

[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [4,3,1,1]

[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [4,3,1]

[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [4,3]

[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [4,2,2,1]

[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [4,2,2]

[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [4,2,1,1]

[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [4,1,1,1]

[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [4,2,1]

[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [4,2]

[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [4,1,1]

[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [4,1]

[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [4]

[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [3,3,2,1]

[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [3,3,2]

[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [3,3,1,1]

[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [3,3,1]

[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [3,3]

[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [3,2,2,1]

[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [2,2,2,1]

[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [3,2,2]

[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [2,2,2]

[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [3,2,1,1]

[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [3,1,1,1]

[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [2,2,1,1]

[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [2,1,1,1]

[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1]

[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [3,2,1]

[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [3,2]

[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [3,1,1]

[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [3,1]

[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [3]

[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [2,2,1]

[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [2,2]

[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [2,1,1]

[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1]

[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [2,1]

[[[[[[],[[]]]]]]] => [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] => [1,1]

[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1]

[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => []

[[],[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]

[[],[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => [7,6,5,4,3,2]

[[],[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2,1] => [7,6,5,4,3,1,1]

[[],[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => [7,6,5,4,3,1]

[[],[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => [7,6,5,4,3]

[[],[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2,1] => [7,6,5,4,2,2,1]

[[],[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,6,4,4,3,2,1] => [7,6,5,4,2,2]

[[],[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,4,4,3,2,1] => [7,6,5,4,1,1,1]

[[],[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => [7,6,5,4,2,1]

[[],[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,5,4,4,3,2,1] => [7,6,5,4,2]

[[],[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => [7,6,5,4,1,1]

[[],[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => [7,6,5,4,1]

[[],[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => [7,6,5,4]

[[],[],[],[[]],[],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,3,2,1] => [7,6,5,3,3,2,1]

[[],[],[],[[]],[],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,6,5,3,3,2,1] => [7,6,5,3,3,2]

[[],[],[],[[]],[[[]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,5,5,3,3,2,1] => [7,6,5,3,3]

[[],[],[],[[[]]],[],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,3,3,2,1] => [7,6,5,2,2,2,1]

[[],[],[],[[[]]],[[]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,6,3,3,3,2,1] => [7,6,5,2,2,2]

[[],[],[],[[],[[]]],[]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,4,3,3,2,1] => [7,6,5,3,1,1,1]

[[],[],[],[[[[]]]],[]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3,2,1] => [7,6,5,1,1,1,1]

[[],[],[],[[],[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => [7,6,5,3,2,1]

[[],[],[],[[[]],[],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => [7,6,5,2,2,1]

[[],[],[],[[[],[]],[]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => [7,6,5,2,1,1]

[[],[],[],[[[[]]],[]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => [7,6,5,1,1,1]

[[],[],[],[[[[],[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,2,1] => [7,6,5,1]

[[],[],[],[[[[[]]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => [7,6,5]

[[],[],[[]],[],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,2,1] => [7,6,4,4,3,2,1]

[[],[],[[]],[],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,2,1] => [7,6,4,4,3,2]

[[],[],[[]],[],[[],[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,2,1] => [7,6,4,4,3,1]

[[],[],[[]],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,4,2,2,1] => [7,6,4,4,2,2,1]

[[],[],[[]],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,2,2,1] => [7,6,4,4,2,2]

[[],[],[[]],[[],[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,2,2,1] => [7,6,4,4,2,1]

[[],[],[[]],[[[[]]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,2,1] => [7,6,4,4]

[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2,1] => [7,6,3,3,3,2,1]

[[],[],[[[]]],[[[]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,2,2,1] => [7,6,3,3,3]

[[],[],[[],[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,2,1] => [7,6,4,3,2,2,1]

[[],[],[[],[[]]],[],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,2,1] => [7,6,4,2,2,2,1]

[[],[],[[[],[]]],[],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,2,2,1] => [7,6,3,2,2,2,1]

[[],[],[[[[]]]],[],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2,1] => [7,6,2,2,2,2,1]

[[],[],[[[[]]]],[[]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2,1] => [7,6,2,2,2,2]

[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2,1] => [7,6,1,1,1,1,1]

[[],[],[[],[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => [7,6,4,3,2,1]

[[],[],[[],[[[[]]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => [7,6,4]

[[],[],[[[]],[],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => [7,6,3,3,2,1]

[[],[],[[[],[]],[],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => [7,6,3,2,2,1]

[[],[],[[[[]]],[],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => [7,6,2,2,2,1]

[[],[],[[[],[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,2,1] => [7,6,3,2,1,1]

[[],[],[[[],[[]]],[]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,2,1] => [7,6,3,1,1,1]

[[],[],[[[[],[]]],[]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2,1] => [7,6,2,1,1,1]

[[],[],[[[[[]]]],[]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => [7,6,1,1,1,1]

[[],[],[[[],[],[[]]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2,1] => [7,6,3,2]

[[],[],[[[],[[],[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => [7,6,3,1]

[[],[],[[[],[[[]]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => [7,6,3]

[[],[],[[[[]],[[]]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => [7,6,2,2]

[[],[],[[[[],[]],[]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => [7,6,2,1,1]

[[],[],[[[[[]]],[]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => [7,6,1,1,1]

[[],[],[[[[],[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => [7,6,2,1]

[[],[],[[[[],[[]]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => [7,6,2]

[[],[],[[[[[]],[]]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => [7,6,1,1]

[[],[],[[[[[],[]]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => [7,6,1]

[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [7,6]

[[],[[]],[],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,1] => [7,5,5,4,3,2,1]

[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1,1] => [7,5,5,4,3,2]

[[],[[]],[],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,1,1] => [7,5,5,4,3,1,1]

[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1,1] => [7,5,5,4,3,1]

[[],[[]],[],[[[[]]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,1,1] => [7,5,5,4]

[[],[[]],[[]],[],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,3,1,1] => [7,5,5,3,3,2,1]

[[],[[]],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,5,3,3,1,1] => [7,5,5,3,3,1,1]

[[],[[]],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,5,5,3,3,1,1] => [7,5,5,3,3]

[[],[[]],[[[]]],[],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,3,3,1,1] => [7,5,5,2,2,2,1]

[[],[[]],[[[[]]]],[]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3,1,1] => [7,5,5,1,1,1,1]

[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => [7,5,5]

[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,1,1] => [7,4,4,4,3,2,1]

[[],[[],[]],[],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,1,1] => [7,5,4,4,3,2]

[[],[[],[]],[],[[],[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,1,1] => [7,5,4,4,3,1]

[[],[[[]]],[],[[],[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,1,1,1] => [7,4,4,4,3,1]

[[],[[[]]],[[]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,1,1,1] => [7,4,4,4,2,2]

[[],[[],[]],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,4,2,1,1] => [7,5,4,4,2,1,1]

[[],[[[]]],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,4,4,1,1,1] => [7,4,4,4,1,1,1]

[[],[[],[]],[[[[]]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,1,1] => [7,5,4,4]

[[],[[[]]],[[[[]]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1,1,1] => [7,4,4,4]

[[],[[],[[]]],[],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,1,1] => [7,5,3,3,3,2,1]

[[],[[[],[]]],[],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,1,1] => [7,4,3,3,3,2,1]

[[],[[[[]]]],[],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,1,1,1] => [7,3,3,3,3,2,1]

[[],[[[]],[]],[[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,1,1,1] => [7,4,4,3,3,1,1]

[[],[[[],[]]],[[[]]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,1,1,1] => [7,4,3,3,3]

[[],[[[[]]]],[[[]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1,1,1] => [7,3,3,3,3]

[[],[[],[],[[]]],[],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,1,1] => [7,5,4,2,2,2,1]

[[],[[[],[],[]]],[],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,1,1] => [7,4,3,2,2,2,1]

[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1,1] => [7,2,2,2,2,2,1]

[[],[[[[],[]]]],[[]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1,1] => [7,3,2,2,2,2]

[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => [7,2,2,2,2,2]

[[],[[],[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,1] => [7,5,4,3,2,1,1]

[[],[[],[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,4,3,2,1,1] => [7,5,4,3,1,1,1]

[[],[[],[[],[]],[]],[]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,2,1,1] => [7,5,3,2,2,1,1]

[[],[[],[[[[]]]]],[]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => [7,5,1,1,1,1,1]

[[],[[[]],[[]],[]],[]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,3,1,1,1] => [7,4,4,2,2,1,1]

[[],[[[],[[]]],[]],[]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1,1,1] => [7,4,2,2,2,1,1]

[[],[[[[[]]]],[]],[]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => [7,2,2,2,2,1,1]

[[],[[[],[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,1,1] => [7,4,3,2,1,1,1]

[[],[[[],[[],[]]]],[]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => [7,4,2,1,1,1,1]

[[],[[[],[[[]]]]],[]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => [7,4,1,1,1,1,1]

[[],[[[[]],[[]]]],[]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => [7,3,3,1,1,1,1]

[[],[[[[],[]],[]]],[]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => [7,3,2,2,1,1,1]

[[],[[[[[]]],[]]],[]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => [7,2,2,2,1,1,1]

[[],[[[[],[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1] => [7,3,2,1,1,1,1]

[[],[[[[],[[]]]]],[]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => [7,3,1,1,1,1,1]

[[],[[[[[]],[]]]],[]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => [7,2,2,1,1,1,1]

[[],[[[[[],[]]]]],[]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => [7,2,1,1,1,1,1]

[[],[[[[[[]]]]]],[]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => [7,1,1,1,1,1,1]

[[],[[],[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => [7,5,4,3,2,1]

[[],[[],[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1,1] => [7,5,4,3,2]

[[],[[],[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1,1] => [7,5,4,3,1,1]

[[],[[],[],[[]],[],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1,1] => [7,5,4,2,2,1]

[[],[[],[],[[[],[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => [7,5,4,1]

[[],[[],[],[[[[]]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => [7,5,4]

[[],[[],[[]],[],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1,1] => [7,5,3,3,2,1]

[[],[[],[[[],[]]],[]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => [7,5,2,1,1,1]

[[],[[],[[[[]]]],[]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => [7,5,1,1,1,1]

[[],[[],[[],[],[[]]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => [7,5,3,2]

[[],[[],[[],[[]],[]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => [7,5,3,1,1]

[[],[[],[[],[[],[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => [7,5,3,1]

[[],[[],[[],[[[]]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => [7,5,3]

[[],[[],[[[]],[],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => [7,5,2,2,1]

[[],[[],[[[]],[[]]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => [7,5,2,2]

[[],[[],[[[],[]],[]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => [7,5,2,1,1]

[[],[[],[[[[]]],[]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => [7,5,1,1,1]

[[],[[],[[[],[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => [7,5,2,1]

[[],[[],[[[],[[]]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => [7,5,2]

[[],[[],[[[[]],[]]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => [7,5,1,1]

[[],[[],[[[[],[]]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => [7,5,1]

[[],[[],[[[[[]]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [7,5]

[[],[[[]],[],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => [7,4,4,3,2,1]

[[],[[[]],[[],[[]]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => [7,4,4,2]

[[],[[[]],[[[]],[]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => [7,4,4,1,1]

[[],[[[]],[[[],[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => [7,4,4,1]

[[],[[[]],[[[[]]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => [7,4,4]

[[],[[[],[]],[],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => [7,4,3,3,2,1]

[[],[[[[]]],[],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => [7,3,3,3,2,1]

[[],[[[],[]],[[[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => [7,4,3,3]

[[],[[[[]]],[[],[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => [7,3,3,3,1]

[[],[[[[]]],[[[]]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => [7,3,3,3]

[[],[[[],[],[]],[],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1,1] => [7,4,3,2,2,1]

[[],[[[],[[]]],[],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1,1] => [7,4,2,2,2,1]

[[],[[[[],[]]],[],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => [7,3,2,2,2,1]

[[],[[[[[]]]],[],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => [7,2,2,2,2,1]

[[],[[[],[[]]],[[]]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => [7,4,2,2,2]

[[],[[[[]],[]],[[]]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => [7,3,3,2,2]

[[],[[[[],[]]],[[]]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => [7,3,2,2,2]

[[],[[[[[]]]],[[]]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => [7,2,2,2,2]

[[],[[[],[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1,1] => [7,4,3,2,1,1]

[[],[[[],[],[[]]],[]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => [7,4,3,1,1,1]

[[],[[[],[[]],[]],[]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => [7,4,2,2,1,1]

[[],[[[],[[],[]]],[]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => [7,4,2,1,1,1]

[[],[[[],[[[]]]],[]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => [7,4,1,1,1,1]

[[],[[[[]],[],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => [7,3,3,2,1,1]

[[],[[[[]],[[]]],[]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => [7,3,3,1,1,1]

[[],[[[[],[]],[]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => [7,3,2,2,1,1]

[[],[[[[[]]],[]],[]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => [7,2,2,2,1,1]

[[],[[[[],[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => [7,3,2,1,1,1]

[[],[[[[],[[]]]],[]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => [7,3,1,1,1,1]

[[],[[[[[]],[]]],[]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => [7,2,2,1,1,1]

[[],[[[[[],[]]]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => [7,2,1,1,1,1]

[[],[[[[[[]]]]],[]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => [7,1,1,1,1,1]

[[],[[[],[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => [7,4,3,2,1]

[[],[[[],[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => [7,4,3,2]

[[],[[[],[],[[]],[]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => [7,4,3,1,1]

[[],[[[],[],[[],[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => [7,4,3,1]

[[],[[[],[],[[[]]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => [7,4,3]

[[],[[[],[[]],[],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => [7,4,2,2,1]

[[],[[[],[[]],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => [7,4,2,2]

[[],[[[],[[],[]],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => [7,4,2,1,1]

[[],[[[],[[[]]],[]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => [7,4,1,1,1]

[[],[[[],[[],[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => [7,4,2,1]

[[],[[[],[[],[[]]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => [7,4,2]

[[],[[[],[[[]],[]]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => [7,4,1,1]

[[],[[[],[[[],[]]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => [7,4,1]

[[],[[[],[[[[]]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [7,4]

[[],[[[[]],[],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => [7,3,3,2,1]

[[],[[[[]],[],[[]]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => [7,3,3,2]

[[],[[[[]],[[]],[]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => [7,3,3,1,1]

[[],[[[[]],[[],[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => [7,3,3,1]

[[],[[[[]],[[[]]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => [7,3,3]

[[],[[[[],[]],[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => [7,3,2,2,1]

[[],[[[[[]]],[],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => [7,2,2,2,1]

[[],[[[[],[]],[[]]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => [7,3,2,2]

[[],[[[[[]]],[[]]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => [7,2,2,2]

[[],[[[[],[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => [7,3,2,1,1]

[[],[[[[],[[]]],[]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => [7,3,1,1,1]

[[],[[[[[]],[]],[]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => [7,2,2,1,1]

[[],[[[[[],[]]],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => [7,2,1,1,1]

[[],[[[[[[]]]],[]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => [7,1,1,1,1]

[[],[[[[],[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => [7,3,2,1]

[[],[[[[],[],[[]]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => [7,3,2]

[[],[[[[],[[]],[]]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => [7,3,1,1]

[[],[[[[],[[],[]]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [7,3,1]

[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [7,3]

[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => [7,2,2,1]

[[],[[[[[]],[[]]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => [7,2,2]

[[],[[[[[],[]],[]]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => [7,2,1,1]

[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [7,1,1,1]

[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [7,2,1]

[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [7,2]

[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [7,1,1]

[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [7,1]

[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [7]

[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => [6,6,5,4,3,2,1]

[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2] => [6,6,5,4,3,2]

[[[]],[],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2] => [6,6,5,4,3,1,1]

[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2] => [6,6,5,4,3,1]

[[[]],[],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2] => [6,6,5,4,3]

[[[]],[],[],[[]],[],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2] => [6,6,5,4,2,2,1]

[[[]],[],[],[[],[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2] => [6,6,5,4,2,1]

[[[]],[],[],[[[[]]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2] => [6,6,5,4]

[[[]],[],[[[[[]]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => [6,6,5]

[[[]],[[]],[],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,2] => [6,6,4,4,3,2,1]

[[[]],[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,4,2,2] => [6,6,4,4,2,2,1]

[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,2,2] => [6,6,4,4,2,2]

[[[]],[[]],[[[]]],[]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,4,4,2,2] => [6,6,4,4,1,1,1]

[[[]],[[]],[[[],[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4,2,2] => [6,6,4,4,1]

[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,2] => [6,6,4,4]

[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2] => [6,6,3,3,3,2,1]

[[[]],[[[[]]]],[],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => [6,6,2,2,2,2,1]

[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,2,2] => [6,6,3,2,2,2]

[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => [6,6,2,2,2,2]

[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => [6,6,1,1,1,1,1]

[[[]],[[],[],[[[]]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,2] => [6,6,4,3]

[[[]],[[],[[[],[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => [6,6,4,1]

[[[]],[[],[[[[]]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => [6,6,4]

[[[]],[[[[],[]]],[]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => [6,6,2,1,1,1]

[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => [6,6,1,1,1,1]

[[[]],[[[],[],[[]]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => [6,6,3,2]

[[[]],[[[],[[]],[]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => [6,6,3,1,1]

[[[]],[[[],[[],[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => [6,6,3,1]

[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => [6,6,3]

[[[]],[[[[]],[],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => [6,6,2,2,1]

[[[]],[[[[]],[[]]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => [6,6,2,2]

[[[]],[[[[],[]],[]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => [6,6,2,1,1]

[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => [6,6,1,1,1]

[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => [6,6,2,1]

[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => [6,6,2]

[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => [6,6,1,1]

[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => [6,6,1]

[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [6,6]

[[[],[]],[],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1] => [6,5,5,4,3,2,1]

[[[[]]],[],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3] => [5,5,5,4,3,2,1]

[[[],[]],[],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1] => [6,5,5,4,3,2]

[[[[]]],[],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3] => [5,5,5,4,3,2]

[[[],[]],[],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1] => [6,5,5,4,3,1]

[[[[]]],[],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3] => [5,5,5,4,3,1]

[[[[]]],[],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3] => [5,5,5,4,3]

[[[],[]],[],[[[[]]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,1] => [6,5,5,4]

[[[[]]],[],[[[[]]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => [5,5,5,4]

[[[],[]],[[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,5,3,3,1] => [6,5,5,3,3,1,1]

[[[],[]],[[[]],[]],[]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,3,3,1] => [6,5,5,2,2,1,1]

[[[[]]],[[[[]]]],[]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3] => [5,5,5,1,1,1,1]

[[[],[]],[[[]],[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,5,3,3,3,1] => [6,5,5,2,2]

[[[],[]],[[[],[[]]]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3,1] => [6,5,5,2]

[[[],[]],[[[[],[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => [6,5,5,1]

[[[],[]],[[[[[]]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => [6,5,5]

[[[[]]],[[[],[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3] => [5,5,5,2,1]

[[[[]]],[[[],[[]]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => [5,5,5,2]

[[[[]]],[[[[]],[]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => [5,5,5,1,1]

[[[[]]],[[[[],[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => [5,5,5,1]

[[[[]]],[[[[[]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [5,5,5]

[[[],[],[]],[],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1] => [6,5,4,4,3,2,1]

[[[],[[]]],[],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,1] => [6,4,4,4,3,2,1]

[[[[],[]]],[],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1] => [5,4,4,4,3,2,1]

[[[[[]]]],[],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4] => [4,4,4,4,3,2,1]

[[[[[]]]],[],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => [4,4,4,4,3,2]

[[[],[],[]],[],[[],[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,1] => [6,5,4,4,3,1]

[[[[],[]]],[],[[],[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,1] => [5,4,4,4,3,1]

[[[[[]]]],[],[[[]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [5,5,5,4] => [4,4,4,4,3]

[[[],[[]]],[[]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,1,1] => [6,4,4,4,2,2]

[[[[],[]]],[[]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,1] => [5,4,4,4,2,2]

[[[[[]]]],[[]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4] => [4,4,4,4,2,2]

[[[],[],[]],[[],[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,2,1] => [6,5,4,4,2,1]

[[[],[],[]],[[[[]]]]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,1] => [6,5,4,4]

[[[],[[]]],[[[]],[]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4,1,1] => [6,4,4,4,1,1]

[[[],[[]]],[[[[]]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1,1] => [6,4,4,4]

[[[[]],[]],[[],[[]]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4,2] => [5,5,4,4,2]

[[[[]],[]],[[[[]]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => [5,5,4,4]

[[[[],[]]],[[[],[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4,1] => [5,4,4,4,1]

[[[[],[]]],[[[[]]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => [5,4,4,4]

[[[[[]]]],[[],[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4] => [4,4,4,4,2,1]

[[[[[]]]],[[],[[]]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => [4,4,4,4,2]

[[[[[]]]],[[[]],[]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => [4,4,4,4,1,1]

[[[[[]]]],[[[],[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => [4,4,4,4,1]

[[[[[]]]],[[[[]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [4,4,4,4]

[[[],[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1] => [6,5,4,3,3,2,1]

[[[],[],[[]]],[],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,1] => [6,5,3,3,3,2,1]

[[[],[[]],[]],[],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,1] => [6,4,4,3,3,2,1]

[[[],[[[]]]],[],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,1,1] => [6,3,3,3,3,2,1]

[[[[],[],[]]],[],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1] => [5,4,3,3,3,2,1]

[[[[[[]]]]],[],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5] => [3,3,3,3,3,2,1]

[[[],[[]],[]],[],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,6,5,3,1,1] => [6,4,4,3,3,2]

[[[[[[]]]]],[],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => [3,3,3,3,3,2]

[[[],[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,2,1] => [6,5,4,3,3,1,1]

[[[],[[]],[]],[[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,1,1] => [6,4,4,3,3,1,1]

[[[[],[]],[]],[[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,1] => [5,4,4,3,3,1,1]

[[[[[[]]]]],[[]],[]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => [3,3,3,3,3,1,1]

[[[],[[]],[]],[[[]]]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,5,5,3,1,1] => [6,4,4,3,3]

[[[[],[[]]]],[[[]]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => [5,3,3,3,3]

[[[[[]],[]]],[[[]]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => [4,4,3,3,3]

[[[[[],[]]]],[[],[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => [4,3,3,3,3,1]

[[[[[],[]]]],[[[]]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => [4,3,3,3,3]

[[[[[[]]]]],[[],[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [3,3,3,3,3,1]

[[[[[[]]]]],[[[]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [3,3,3,3,3]

[[[],[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1] => [6,5,4,3,2,2,1]

[[[],[],[],[[]]],[],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,1] => [6,5,4,2,2,2,1]

[[[],[],[[[]]]],[],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,1] => [6,5,2,2,2,2,1]

[[[],[[[[]]]]],[],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1] => [6,2,2,2,2,2,1]

[[[[[[]]]],[]],[],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,6,4] => [3,3,3,3,2,2,1]

[[[[],[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1] => [5,4,3,2,2,2,1]

[[[[],[[],[]]]],[],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => [5,3,2,2,2,2,1]

[[[[],[[[]]]]],[],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => [5,2,2,2,2,2,1]

[[[[[]],[[]]]],[],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2] => [4,4,2,2,2,2,1]

[[[[[],[]],[]]],[],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1] => [4,3,3,2,2,2,1]

[[[[[[]]],[]]],[],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => [3,3,3,2,2,2,1]

[[[[[],[],[]]]],[],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1] => [4,3,2,2,2,2,1]

[[[[[],[[]]]]],[],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1] => [4,2,2,2,2,2,1]

[[[[[[]],[]]]],[],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => [3,3,2,2,2,2,1]

[[[[[[],[]]]]],[],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => [3,2,2,2,2,2,1]

[[[[[[[]]]]]],[],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => [2,2,2,2,2,2,1]

[[[],[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,6,4,3,2,1] => [6,5,4,3,2,2]

[[[],[[]],[[]]],[[]]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,6,3,3,1,1] => [6,4,4,2,2,2]

[[[],[[[]],[]]],[[]]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1,1] => [6,3,3,2,2,2]

[[[],[[[],[]]]],[[]]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => [6,3,2,2,2,2]

[[[],[[[[]]]]],[[]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => [6,2,2,2,2,2]

[[[[[],[]]],[]],[[]]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => [4,3,3,3,2,2]

[[[[[[]]]],[]],[[]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => [3,3,3,3,2,2]

[[[[],[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,1] => [5,4,3,2,2,2]

[[[[],[],[[]]]],[[]]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => [5,4,2,2,2,2]

[[[[],[[]],[]]],[[]]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => [5,3,3,2,2,2]

[[[[],[[],[]]]],[[]]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => [5,3,2,2,2,2]

[[[[],[[[]]]]],[[]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => [5,2,2,2,2,2]

[[[[[]],[],[]]],[[]]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => [4,4,3,2,2,2]

[[[[[]],[[]]]],[[]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => [4,4,2,2,2,2]

[[[[[],[]],[]]],[[]]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => [4,3,3,2,2,2]

[[[[[[]]],[]]],[[]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => [3,3,3,2,2,2]

[[[[[],[],[]]]],[[]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => [4,3,2,2,2,2]

[[[[[],[[]]]]],[[]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => [4,2,2,2,2,2]

[[[[[[]],[]]]],[[]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [3,3,2,2,2,2]

[[[[[[],[]]]]],[[]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => [3,2,2,2,2,2]

[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [2,2,2,2,2,2]

[[[],[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1] => [6,5,4,3,2,1,1]

[[[],[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,4,3,2,1] => [6,5,4,3,1,1,1]

[[[],[],[],[[[]]]],[]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,2,1] => [6,5,4,1,1,1,1]

[[[],[],[[[],[]]]],[]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => [6,5,2,1,1,1,1]

[[[],[],[[[[]]]]],[]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => [6,5,1,1,1,1,1]

[[[],[[]],[[]],[]],[]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,3,1,1] => [6,4,4,2,2,1,1]

[[[],[[[],[]]],[]],[]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1,1] => [6,3,2,2,2,1,1]

[[[],[[[[]]]],[]],[]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1] => [6,2,2,2,2,1,1]

[[[],[[],[],[[]]]],[]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => [6,4,3,1,1,1,1]

[[[],[[],[[]],[]]],[]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => [6,4,2,2,1,1,1]

[[[],[[],[[],[]]]],[]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => [6,4,2,1,1,1,1]

[[[],[[],[[[]]]]],[]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => [6,4,1,1,1,1,1]

[[[],[[[]],[],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => [6,3,3,2,1,1,1]

[[[],[[[]],[[]]]],[]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => [6,3,3,1,1,1,1]

[[[],[[[],[]],[]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => [6,3,2,2,1,1,1]

[[[],[[[[]]],[]]],[]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => [6,2,2,2,1,1,1]

[[[],[[[],[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => [6,3,2,1,1,1,1]

[[[],[[[],[[]]]]],[]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => [6,3,1,1,1,1,1]

[[[],[[[[]],[]]]],[]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1] => [6,2,2,1,1,1,1]

[[[],[[[[],[]]]]],[]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1] => [6,2,1,1,1,1,1]

[[[],[[[[[]]]]]],[]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => [6,1,1,1,1,1,1]

[[[[]],[],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2] => [5,5,4,3,2,1,1]

[[[[]],[[],[[]]]],[]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => [5,5,3,1,1,1,1]

[[[[]],[[[]],[]]],[]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => [5,5,2,2,1,1,1]

[[[[]],[[[],[]]]],[]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => [5,5,2,1,1,1,1]

[[[[]],[[[[]]]]],[]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => [5,5,1,1,1,1,1]

[[[[],[]],[],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1] => [5,4,4,3,2,1,1]

[[[[[]]],[],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3] => [4,4,4,3,2,1,1]

[[[[],[]],[[[]]]],[]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => [5,4,4,1,1,1,1]

[[[[[]]],[[],[]]],[]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => [4,4,4,2,1,1,1]

[[[[[]]],[[[]]]],[]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => [4,4,4,1,1,1,1]

[[[[[],[]]],[],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1] => [4,3,3,3,2,1,1]

[[[[[[]]]],[],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => [3,3,3,3,2,1,1]

[[[[],[[]]],[[]]],[]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => [5,3,3,3,1,1,1]

[[[[[]],[]],[[]]],[]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => [4,4,3,3,1,1,1]

[[[[[],[]]],[[]]],[]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => [4,3,3,3,1,1,1]

[[[[[[]]]],[[]]],[]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => [3,3,3,3,1,1,1]

[[[[],[],[[]]],[]],[]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => [5,4,2,2,2,1,1]

[[[[],[[]],[]],[]],[]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,1] => [5,3,3,2,2,1,1]

[[[[],[[],[]]],[]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => [5,3,2,2,2,1,1]

[[[[],[[[]]]],[]],[]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => [5,2,2,2,2,1,1]

[[[[[]],[],[]],[]],[]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => [4,4,3,2,2,1,1]

[[[[[]],[[]]],[]],[]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2] => [4,4,2,2,2,1,1]

[[[[[],[]],[]],[]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => [4,3,3,2,2,1,1]

[[[[[[]]],[]],[]],[]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => [3,3,3,2,2,1,1]

[[[[[],[],[]]],[]],[]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => [4,3,2,2,2,1,1]

[[[[[],[[]]]],[]],[]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1] => [4,2,2,2,2,1,1]

[[[[[[]],[]]],[]],[]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => [3,3,2,2,2,1,1]

[[[[[[],[]]]],[]],[]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => [3,2,2,2,2,1,1]

[[[[[[[]]]]],[]],[]] => [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]

[[[[],[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1] => [5,4,3,2,1,1,1]

[[[[],[],[],[[]]]],[]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1] => [5,4,3,1,1,1,1]

[[[[],[],[[]],[]]],[]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1] => [5,4,2,2,1,1,1]

[[[[],[],[[],[]]]],[]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1] => [5,4,2,1,1,1,1]

[[[[],[],[[[]]]]],[]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => [5,4,1,1,1,1,1]

[[[[],[[]],[],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1] => [5,3,3,2,1,1,1]

[[[[],[[]],[[]]]],[]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => [5,3,3,1,1,1,1]

[[[[],[[],[]],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => [5,3,2,2,1,1,1]

[[[[],[[[]]],[]]],[]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => [5,2,2,2,1,1,1]

[[[[],[[],[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => [5,3,2,1,1,1,1]

[[[[],[[],[[]]]]],[]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => [5,3,1,1,1,1,1]

[[[[],[[[]],[]]]],[]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1] => [5,2,2,1,1,1,1]

[[[[],[[[],[]]]]],[]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => [5,2,1,1,1,1,1]

[[[[],[[[[]]]]]],[]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => [5,1,1,1,1,1,1]

[[[[[]],[],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2] => [4,4,3,2,1,1,1]

[[[[[]],[],[[]]]],[]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => [4,4,3,1,1,1,1]

[[[[[]],[[]],[]]],[]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => [4,4,2,2,1,1,1]

[[[[[]],[[],[]]]],[]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => [4,4,2,1,1,1,1]

[[[[[]],[[[]]]]],[]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => [4,4,1,1,1,1,1]

[[[[[],[]],[],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => [4,3,3,2,1,1,1]

[[[[[[]]],[],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [3,3,3,2,1,1,1]

[[[[[],[]],[[]]]],[]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => [4,3,3,1,1,1,1]

[[[[[[]]],[[]]]],[]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [3,3,3,1,1,1,1]

[[[[[],[],[]],[]]],[]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => [4,3,2,2,1,1,1]

[[[[[],[[]]],[]]],[]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => [4,2,2,2,1,1,1]

[[[[[[]],[]],[]]],[]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => [3,3,2,2,1,1,1]

[[[[[[],[]]],[]]],[]] => [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]

[[[[[[[]]]],[]]],[]] => [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]

[[[[[],[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => [4,3,2,1,1,1,1]

[[[[[],[],[[]]]]],[]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [4,3,1,1,1,1,1]

[[[[[],[[]],[]]]],[]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => [4,2,2,1,1,1,1]

[[[[[],[[],[]]]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [4,2,1,1,1,1,1]

[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [4,1,1,1,1,1,1]

[[[[[[]],[],[]]]],[]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [3,3,2,1,1,1,1]

[[[[[[]],[[]]]]],[]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [3,3,1,1,1,1,1]

[[[[[[],[]],[]]]],[]] => [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]

[[[[[[[]]],[]]]],[]] => [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]

[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [3,2,1,1,1,1,1]

[[[[[[],[[]]]]]],[]] => [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]

[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [2,2,1,1,1,1,1]

[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1]

[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [1,1,1,1,1,1,1]

[[[],[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1]

[[[],[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => [6,5,4,3,2]

[[[],[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => [6,5,4,3,1,1]

[[[],[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => [6,5,4,3,1]

[[[],[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => [6,5,4,3]

[[[],[],[],[[]],[],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => [6,5,4,2,2,1]

[[[],[],[],[[]],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => [6,5,4,2,2]

[[[],[],[],[[],[]],[]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,1] => [6,5,4,2,1,1]

[[[],[],[],[[[]]],[]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => [6,5,4,1,1,1]

[[[],[],[],[[],[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => [6,5,4,2,1]

[[[],[],[],[[],[[]]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => [6,5,4,2]

[[[],[],[],[[[]],[]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => [6,5,4,1,1]

[[[],[],[],[[[],[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => [6,5,4,1]

[[[],[],[],[[[[]]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [6,5,4]

[[[],[],[[]],[],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => [6,5,3,3,2,1]

[[[],[],[[]],[],[[]]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => [6,5,3,3,2]

[[[],[],[[]],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => [6,5,3,3,1,1]

[[[],[],[[]],[[],[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2,1] => [6,5,3,3,1]

[[[],[],[[]],[[[]]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => [6,5,3,3]

[[[],[],[[],[]],[],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,1] => [6,5,3,2,2,1]

[[[],[],[[[]]],[],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => [6,5,2,2,2,1]

[[[],[],[[],[]],[[]]]] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2,1] => [6,5,3,2,2]

[[[],[],[[[]]],[[]]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => [6,5,2,2,2]

[[[],[],[[],[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,1] => [6,5,3,2,1,1]

[[[],[],[[],[[]]],[]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => [6,5,3,1,1,1]

[[[],[],[[[]],[]],[]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => [6,5,2,2,1,1]

[[[],[],[[[],[]]],[]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => [6,5,2,1,1,1]

[[[],[],[[[[]]]],[]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => [6,5,1,1,1,1]

[[[],[],[[],[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => [6,5,3,2,1]

[[[],[],[[],[],[[]]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => [6,5,3,2]

[[[],[],[[],[[]],[]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => [6,5,3,1,1]

[[[],[],[[],[[],[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => [6,5,3,1]

[[[],[],[[],[[[]]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [6,5,3]

[[[],[],[[[]],[],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => [6,5,2,2,1]

[[[],[],[[[]],[[]]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => [6,5,2,2]

[[[],[],[[[],[]],[]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => [6,5,2,1,1]

[[[],[],[[[[]]],[]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => [6,5,1,1,1]

[[[],[],[[[],[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => [6,5,2,1]

[[[],[],[[[],[[]]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => [6,5,2]

[[[],[],[[[[]],[]]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => [6,5,1,1]

[[[],[],[[[[],[]]]]]] => [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]

[[[],[],[[[[[]]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [6,5]

[[[],[[]],[],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => [6,4,4,3,2,1]

[[[],[[]],[],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => [6,4,4,3,2]

[[[],[[]],[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => [6,4,4,3,1,1]

[[[],[[]],[],[[],[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1,1] => [6,4,4,3,1]

[[[],[[]],[],[[[]]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => [6,4,4,3]

[[[],[[]],[[]],[],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => [6,4,4,2,2,1]

[[[],[[]],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => [6,4,4,2,2]

[[[],[[]],[[],[]],[]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1,1] => [6,4,4,2,1,1]

[[[],[[]],[[[]]],[]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => [6,4,4,1,1,1]

[[[],[[]],[[],[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => [6,4,4,2,1]

[[[],[[]],[[],[[]]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => [6,4,4,2]

[[[],[[]],[[[]],[]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => [6,4,4,1,1]

[[[],[[]],[[[],[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => [6,4,4,1]

[[[],[[]],[[[[]]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [6,4,4]

[[[],[[],[]],[],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1] => [6,4,3,3,2,1]

[[[],[[[]]],[],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => [6,3,3,3,2,1]

[[[],[[],[]],[],[[]]]] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1,1] => [6,4,3,3,2]

[[[],[[[]]],[],[[]]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => [6,3,3,3,2]

[[[],[[],[]],[[]],[]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1,1] => [6,4,3,3,1,1]

[[[],[[[]]],[[]],[]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => [6,3,3,3,1,1]

[[[],[[],[]],[[],[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => [6,4,3,3,1]

[[[],[[],[]],[[[]]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => [6,4,3,3]

[[[],[[[]]],[[],[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => [6,3,3,3,1]

[[[],[[[]]],[[[]]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => [6,3,3,3]

[[[],[[],[],[]],[],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1] => [6,4,3,2,2,1]

[[[],[[],[[]]],[],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => [6,4,2,2,2,1]

[[[],[[[]],[]],[],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => [6,3,3,2,2,1]

[[[],[[[],[]]],[],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => [6,3,2,2,2,1]

[[[],[[[[]]]],[],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => [6,2,2,2,2,1]

[[[],[[],[],[]],[[]]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => [6,4,3,2,2]

[[[],[[],[[]]],[[]]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => [6,4,2,2,2]

[[[],[[[]],[]],[[]]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => [6,3,3,2,2]

[[[],[[[],[]]],[[]]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => [6,3,2,2,2]

[[[],[[[[]]]],[[]]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => [6,2,2,2,2]

[[[],[[],[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => [6,4,3,2,1,1]

[[[],[[],[],[[]]],[]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => [6,4,3,1,1,1]

[[[],[[],[[]],[]],[]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => [6,4,2,2,1,1]

[[[],[[],[[],[]]],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => [6,4,2,1,1,1]

[[[],[[],[[[]]]],[]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => [6,4,1,1,1,1]

[[[],[[[]],[],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => [6,3,3,2,1,1]

[[[],[[[]],[[]]],[]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => [6,3,3,1,1,1]

[[[],[[[],[]],[]],[]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => [6,3,2,2,1,1]

[[[],[[[[]]],[]],[]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => [6,2,2,2,1,1]

[[[],[[[],[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [6,3,2,1,1,1]

[[[],[[[],[[]]]],[]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [6,3,1,1,1,1]

[[[],[[[[]],[]]],[]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [6,2,2,1,1,1]

[[[],[[[[],[]]]],[]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [6,2,1,1,1,1]

[[[],[[[[[]]]]],[]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [6,1,1,1,1,1]

[[[],[[],[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => [6,4,3,2,1]

[[[],[[],[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => [6,4,3,2]

[[[],[[],[],[[]],[]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => [6,4,3,1,1]

[[[],[[],[],[[],[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => [6,4,3,1]

[[[],[[],[],[[[]]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [6,4,3]

[[[],[[],[[]],[],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => [6,4,2,2,1]

[[[],[[],[[]],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => [6,4,2,2]

[[[],[[],[[],[]],[]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [6,4,2,1,1]

[[[],[[],[[[]]],[]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => [6,4,1,1,1]

[[[],[[],[[],[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => [6,4,2,1]

[[[],[[],[[],[[]]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [6,4,2]

[[[],[[],[[[]],[]]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [6,4,1,1]

[[[],[[],[[[],[]]]]]] => [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]

[[[],[[],[[[[]]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4]

[[[],[[[]],[],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => [6,3,3,2,1]

[[[],[[[]],[],[[]]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => [6,3,3,2]

[[[],[[[]],[[]],[]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => [6,3,3,1,1]

[[[],[[[]],[[],[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => [6,3,3,1]

[[[],[[[]],[[[]]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [6,3,3]

[[[],[[[],[]],[],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => [6,3,2,2,1]

[[[],[[[[]]],[],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [6,2,2,2,1]

[[[],[[[],[]],[[]]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => [6,3,2,2]

[[[],[[[[]]],[[]]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [6,2,2,2]

[[[],[[[],[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [6,3,2,1,1]

[[[],[[[],[[]]],[]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [6,3,1,1,1]

[[[],[[[[]],[]],[]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [6,2,2,1,1]

[[[],[[[[],[]]],[]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [6,2,1,1,1]

[[[],[[[[[]]]],[]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [6,1,1,1,1]

[[[],[[[],[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [6,3,2,1]

[[[],[[[],[],[[]]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [6,3,2]

[[[],[[[],[[]],[]]]]] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [6,3,1,1]

[[[],[[[],[[],[]]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [6,3,1]

[[[],[[[],[[[]]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3]

[[[],[[[[]],[],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [6,2,2,1]

[[[],[[[[]],[[]]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [6,2,2]

[[[],[[[[],[]],[]]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [6,2,1,1]

[[[],[[[[[]]],[]]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [6,1,1,1]

[[[],[[[[],[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [6,2,1]

[[[],[[[[],[[]]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2]

[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1]

[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1]

[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6]

[[[[]],[],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => [5,5,4,3,2,1]

[[[[]],[],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => [5,5,4,3,2]

[[[[]],[],[],[[]],[]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => [5,5,4,3,1,1]

[[[[]],[],[],[[],[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2] => [5,5,4,3,1]

[[[[]],[],[],[[[]]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => [5,5,4,3]

[[[[]],[],[[]],[],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => [5,5,4,2,2,1]

[[[[]],[],[[]],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => [5,5,4,2,2]

[[[[]],[],[[],[]],[]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2] => [5,5,4,2,1,1]

[[[[]],[],[[[]]],[]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => [5,5,4,1,1,1]

[[[[]],[],[[],[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => [5,5,4,2,1]

[[[[]],[],[[],[[]]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => [5,5,4,2]

[[[[]],[],[[[]],[]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => [5,5,4,1,1]

[[[[]],[],[[[],[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [5,5,4,1]

[[[[]],[],[[[[]]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [5,5,4]

[[[[]],[[]],[],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => [5,5,3,3,2,1]

[[[[]],[[]],[],[[]]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => [5,5,3,3,2]

[[[[]],[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => [5,5,3,3,1,1]

[[[[]],[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => [5,5,3,3,1]

[[[[]],[[]],[[[]]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => [5,5,3,3]

[[[[]],[[],[]],[],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2] => [5,5,3,2,2,1]

[[[[]],[[[]]],[],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => [5,5,2,2,2,1]

[[[[]],[[],[]],[[]]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => [5,5,3,2,2]

[[[[]],[[[]]],[[]]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => [5,5,2,2,2]

[[[[]],[[],[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => [5,5,3,2,1,1]

[[[[]],[[],[[]]],[]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => [5,5,3,1,1,1]

[[[[]],[[[]],[]],[]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => [5,5,2,2,1,1]

[[[[]],[[[],[]]],[]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => [5,5,2,1,1,1]

[[[[]],[[[[]]]],[]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [5,5,1,1,1,1]

[[[[]],[[],[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => [5,5,3,2,1]

[[[[]],[[],[],[[]]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => [5,5,3,2]

[[[[]],[[],[[]],[]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => [5,5,3,1,1]

[[[[]],[[],[[],[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => [5,5,3,1]

[[[[]],[[],[[[]]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [5,5,3]

[[[[]],[[[]],[],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => [5,5,2,2,1]

[[[[]],[[[]],[[]]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => [5,5,2,2]

[[[[]],[[[],[]],[]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => [5,5,2,1,1]

[[[[]],[[[[]]],[]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [5,5,1,1,1]

[[[[]],[[[],[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => [5,5,2,1]

[[[[]],[[[],[[]]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [5,5,2]

[[[[]],[[[[]],[]]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [5,5,1,1]

[[[[]],[[[[],[]]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [5,5,1]

[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [5,5]

[[[[],[]],[],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => [5,4,4,3,2,1]

[[[[[]]],[],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => [4,4,4,3,2,1]

[[[[],[]],[],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1] => [5,4,4,3,2]

[[[[[]]],[],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [4,4,4,3,2]

[[[[],[]],[],[[]],[]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1] => [5,4,4,3,1,1]

[[[[[]]],[],[[]],[]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => [4,4,4,3,1,1]

[[[[],[]],[],[[],[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => [5,4,4,3,1]

[[[[],[]],[],[[[]]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [5,4,4,3]

[[[[[]]],[],[[],[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [4,4,4,3,1]

[[[[[]]],[],[[[]]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [4,4,4,3]

[[[[],[]],[[]],[],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1] => [5,4,4,2,2,1]

[[[[[]]],[[]],[],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => [4,4,4,2,2,1]

[[[[],[]],[[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => [5,4,4,2,2]

[[[[[]]],[[]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [4,4,4,2,2]

[[[[],[]],[[],[]],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => [5,4,4,2,1,1]

[[[[],[]],[[[]]],[]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => [5,4,4,1,1,1]

[[[[[]]],[[],[]],[]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => [4,4,4,2,1,1]

[[[[[]]],[[[]]],[]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [4,4,4,1,1,1]

[[[[],[]],[[],[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => [5,4,4,2,1]

[[[[],[]],[[],[[]]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [5,4,4,2]

[[[[],[]],[[[]],[]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => [5,4,4,1,1]

[[[[],[]],[[[],[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [5,4,4,1]

[[[[],[]],[[[[]]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [5,4,4]

[[[[[]]],[[],[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [4,4,4,2,1]

[[[[[]]],[[],[[]]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [4,4,4,2]

[[[[[]]],[[[]],[]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [4,4,4,1,1]

[[[[[]]],[[[],[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [4,4,4,1]

[[[[[]]],[[[[]]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [4,4,4]

[[[[],[],[]],[],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1] => [5,4,3,3,2,1]

[[[[],[[]]],[],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => [5,3,3,3,2,1]

[[[[[]],[]],[],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2] => [4,4,3,3,2,1]

[[[[[],[]]],[],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1] => [4,3,3,3,2,1]

[[[[[[]]]],[],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [3,3,3,3,2,1]

[[[[],[],[]],[],[[]]]] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => [5,4,3,3,2]

[[[[],[[]]],[],[[]]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => [5,3,3,3,2]

[[[[[]],[]],[],[[]]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => [4,4,3,3,2]

[[[[[],[]]],[],[[]]]] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [4,3,3,3,2]

[[[[[[]]]],[],[[]]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [3,3,3,3,2]

[[[[],[],[]],[[]],[]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => [5,4,3,3,1,1]

[[[[],[[]]],[[]],[]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => [5,3,3,3,1,1]

[[[[[]],[]],[[]],[]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => [4,4,3,3,1,1]

[[[[[],[]]],[[]],[]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => [4,3,3,3,1,1]

[[[[[[]]]],[[]],[]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [3,3,3,3,1,1]

[[[[],[],[]],[[],[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => [5,4,3,3,1]

[[[[],[],[]],[[[]]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [5,4,3,3]

[[[[],[[]]],[[],[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => [5,3,3,3,1]

[[[[],[[]]],[[[]]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [5,3,3,3]

[[[[[]],[]],[[],[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [4,4,3,3,1]

[[[[[]],[]],[[[]]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [4,4,3,3]

[[[[[],[]]],[[],[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [4,3,3,3,1]

[[[[[],[]]],[[[]]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [4,3,3,3]

[[[[[[]]]],[[],[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [3,3,3,3,1]

[[[[[[]]]],[[[]]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [3,3,3,3]

[[[[],[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => [5,4,3,2,2,1]

[[[[],[],[[]]],[],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => [5,4,2,2,2,1]

[[[[],[[]],[]],[],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => [5,3,3,2,2,1]

[[[[],[[],[]]],[],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => [5,3,2,2,2,1]

[[[[],[[[]]]],[],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [5,2,2,2,2,1]

[[[[[]],[],[]],[],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => [4,4,3,2,2,1]

[[[[[]],[[]]],[],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => [4,4,2,2,2,1]

[[[[[],[]],[]],[],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => [4,3,3,2,2,1]

[[[[[[]]],[]],[],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [3,3,3,2,2,1]

[[[[[],[],[]]],[],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [4,3,2,2,2,1]

[[[[[],[[]]]],[],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [4,2,2,2,2,1]

[[[[[[]],[]]],[],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [3,3,2,2,2,1]

[[[[[[],[]]]],[],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [3,2,2,2,2,1]

[[[[[[[]]]]],[],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [2,2,2,2,2,1]

[[[[],[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => [5,4,3,2,2]

[[[[],[],[[]]],[[]]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => [5,4,2,2,2]

[[[[],[[]],[]],[[]]]] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => [5,3,3,2,2]

[[[[],[[],[]]],[[]]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => [5,3,2,2,2]

[[[[],[[[]]]],[[]]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => [5,2,2,2,2]

[[[[[]],[],[]],[[]]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [4,4,3,2,2]

[[[[[]],[[]]],[[]]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => [4,4,2,2,2]

[[[[[],[]],[]],[[]]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [4,3,3,2,2]

[[[[[[]]],[]],[[]]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [3,3,3,2,2]

[[[[[],[],[]]],[[]]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [4,3,2,2,2]

[[[[[],[[]]]],[[]]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [4,2,2,2,2]

[[[[[[]],[]]],[[]]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [3,3,2,2,2]

[[[[[[],[]]]],[[]]]] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [3,2,2,2,2]

[[[[[[[]]]]],[[]]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [2,2,2,2,2]

[[[[],[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => [5,4,3,2,1,1]

[[[[],[],[],[[]]],[]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => [5,4,3,1,1,1]

[[[[],[],[[]],[]],[]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => [5,4,2,2,1,1]

[[[[],[],[[],[]]],[]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [5,4,2,1,1,1]

[[[[],[],[[[]]]],[]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [5,4,1,1,1,1]

[[[[],[[]],[],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => [5,3,3,2,1,1]

[[[[],[[]],[[]]],[]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [5,3,3,1,1,1]

[[[[],[[],[]],[]],[]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => [5,3,2,2,1,1]

[[[[],[[[]]],[]],[]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => [5,2,2,2,1,1]

[[[[],[[],[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [5,3,2,1,1,1]

[[[[],[[],[[]]]],[]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [5,3,1,1,1,1]

[[[[],[[[]],[]]],[]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [5,2,2,1,1,1]

[[[[],[[[],[]]]],[]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [5,2,1,1,1,1]

[[[[],[[[[]]]]],[]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [5,1,1,1,1,1]

[[[[[]],[],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => [4,4,3,2,1,1]

[[[[[]],[],[[]]],[]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [4,4,3,1,1,1]

[[[[[]],[[]],[]],[]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [4,4,2,2,1,1]

[[[[[]],[[],[]]],[]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [4,4,2,1,1,1]

[[[[[]],[[[]]]],[]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [4,4,1,1,1,1]

[[[[[],[]],[],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [4,3,3,2,1,1]

[[[[[[]]],[],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [3,3,3,2,1,1]

[[[[[],[]],[[]]],[]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [4,3,3,1,1,1]

[[[[[[]]],[[]]],[]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [3,3,3,1,1,1]

[[[[[],[],[]],[]],[]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [4,3,2,2,1,1]

[[[[[],[[]]],[]],[]]] => [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]

[[[[[[]],[]],[]],[]]] => [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]

[[[[[[],[]]],[]],[]]] => [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]

[[[[[[[]]]],[]],[]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [2,2,2,2,1,1]

[[[[[],[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [4,3,2,1,1,1]

[[[[[],[],[[]]]],[]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [4,3,1,1,1,1]

[[[[[],[[]],[]]],[]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [4,2,2,1,1,1]

[[[[[],[[],[]]]],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [4,2,1,1,1,1]

[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [4,1,1,1,1,1]

[[[[[[]],[],[]]],[]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [3,3,2,1,1,1]

[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [3,3,1,1,1,1]

[[[[[[],[]],[]]],[]]] => [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]

[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [2,2,2,1,1,1]

[[[[[[],[],[]]]],[]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [3,2,1,1,1,1]

[[[[[[],[[]]]]],[]]] => [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]

[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [2,2,1,1,1,1]

[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [2,1,1,1,1,1]

[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1]

[[[[],[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1]

[[[[],[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [5,4,3,2]

[[[[],[],[],[[]],[]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [5,4,3,1,1]

[[[[],[],[],[[],[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [5,4,3,1]

[[[[],[],[],[[[]]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [5,4,3]

[[[[],[],[[]],[],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [5,4,2,2,1]

[[[[],[],[[]],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [5,4,2,2]

[[[[],[],[[],[]],[]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [5,4,2,1,1]

[[[[],[],[[[]]],[]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [5,4,1,1,1]

[[[[],[],[[],[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [5,4,2,1]

[[[[],[],[[],[[]]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [5,4,2]

[[[[],[],[[[]],[]]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [5,4,1,1]

[[[[],[],[[[],[]]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [5,4,1]

[[[[],[],[[[[]]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [5,4]

[[[[],[[]],[],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [5,3,3,2,1]

[[[[],[[]],[],[[]]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [5,3,3,2]

[[[[],[[]],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [5,3,3,1,1]

[[[[],[[]],[[],[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [5,3,3,1]

[[[[],[[]],[[[]]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [5,3,3]

[[[[],[[],[]],[],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [5,3,2,2,1]

[[[[],[[[]]],[],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [5,2,2,2,1]

[[[[],[[],[]],[[]]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [5,3,2,2]

[[[[],[[[]]],[[]]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [5,2,2,2]

[[[[],[[],[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [5,3,2,1,1]

[[[[],[[],[[]]],[]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [5,3,1,1,1]

[[[[],[[[]],[]],[]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [5,2,2,1,1]

[[[[],[[[],[]]],[]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [5,2,1,1,1]

[[[[],[[[[]]]],[]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1]

[[[[],[[],[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [5,3,2,1]

[[[[],[[],[],[[]]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [5,3,2]

[[[[],[[],[[]],[]]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [5,3,1,1]

[[[[],[[],[[],[]]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [5,3,1]

[[[[],[[],[[[]]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [5,3]

[[[[],[[[]],[],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [5,2,2,1]

[[[[],[[[]],[[]]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [5,2,2]

[[[[],[[[],[]],[]]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [5,2,1,1]

[[[[],[[[[]]],[]]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [5,1,1,1]

[[[[],[[[],[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [5,2,1]

[[[[],[[[],[[]]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [5,2]

[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [5,1,1]

[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [5,1]

[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [5]

[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [4,4,3,2,1]

[[[[[]],[],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [4,4,3,2]

[[[[[]],[],[[]],[]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [4,4,3,1,1]

[[[[[]],[],[[],[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [4,4,3,1]

[[[[[]],[],[[[]]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [4,4,3]

[[[[[]],[[]],[],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [4,4,2,2,1]

[[[[[]],[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [4,4,2,2]

[[[[[]],[[],[]],[]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [4,4,2,1,1]

[[[[[]],[[[]]],[]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [4,4,1,1,1]

[[[[[]],[[],[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [4,4,2,1]

[[[[[]],[[],[[]]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [4,4,2]

[[[[[]],[[[]],[]]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [4,4,1,1]

[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [4,4,1]

[[[[[]],[[[[]]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [4,4]

[[[[[],[]],[],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [4,3,3,2,1]

[[[[[[]]],[],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [3,3,3,2,1]

[[[[[],[]],[],[[]]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [4,3,3,2]

[[[[[[]]],[],[[]]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [3,3,3,2]

[[[[[],[]],[[]],[]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [4,3,3,1,1]

[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,3,3,1,1]

[[[[[],[]],[[],[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [4,3,3,1]

[[[[[],[]],[[[]]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [4,3,3]

[[[[[[]]],[[],[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [3,3,3,1]

[[[[[[]]],[[[]]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3,3]

[[[[[],[],[]],[],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [4,3,2,2,1]

[[[[[],[[]]],[],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [4,2,2,2,1]

[[[[[[]],[]],[],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [3,3,2,2,1]

[[[[[[],[]]],[],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [3,2,2,2,1]

[[[[[[[]]]],[],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [2,2,2,2,1]

[[[[[],[],[]],[[]]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [4,3,2,2]

[[[[[],[[]]],[[]]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [4,2,2,2]

[[[[[[]],[]],[[]]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [3,3,2,2]

[[[[[[],[]]],[[]]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [3,2,2,2]

[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [2,2,2,2]

[[[[[],[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [4,3,2,1,1]

[[[[[],[],[[]]],[]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [4,3,1,1,1]

[[[[[],[[]],[]],[]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [4,2,2,1,1]

[[[[[],[[],[]]],[]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [4,2,1,1,1]

[[[[[],[[[]]]],[]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [4,1,1,1,1]

[[[[[[]],[],[]],[]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [3,3,2,1,1]

[[[[[[]],[[]]],[]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [3,3,1,1,1]

[[[[[[],[]],[]],[]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,2,2,1,1]

[[[[[[[]]],[]],[]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [2,2,2,1,1]

[[[[[[],[],[]]],[]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [3,2,1,1,1]

[[[[[[],[[]]]],[]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [3,1,1,1,1]

[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [2,2,1,1,1]

[[[[[[[],[]]]],[]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [2,1,1,1,1]

[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1]

[[[[[],[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1]

[[[[[],[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [4,3,2]

[[[[[],[],[[]],[]]]]] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [4,3,1,1]

[[[[[],[],[[],[]]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [4,3,1]

[[[[[],[],[[[]]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [4,3]

[[[[[],[[]],[],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [4,2,2,1]

[[[[[],[[]],[[]]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [4,2,2]

[[[[[],[[],[]],[]]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [4,2,1,1]

[[[[[],[[[]]],[]]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [4,1,1,1]

[[[[[],[[],[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [4,2,1]

[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [4,2]

[[[[[],[[[]],[]]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [4,1,1]

[[[[[],[[[],[]]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [4,1]

[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [4]

[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [3,3,2,1]

[[[[[[]],[],[[]]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [3,3,2]

[[[[[[]],[[]],[]]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [3,3,1,1]

[[[[[[]],[[],[]]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [3,3,1]

[[[[[[]],[[[]]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [3,3]

[[[[[[],[]],[],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [3,2,2,1]

[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [2,2,2,1]

[[[[[[],[]],[[]]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [3,2,2]

[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [2,2,2]

[[[[[[],[],[]],[]]]]] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [3,2,1,1]

[[[[[[],[[]]],[]]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [3,1,1,1]

[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [2,2,1,1]

[[[[[[[],[]]],[]]]]] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [2,1,1,1]

[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1]

[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [3,2,1]

[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [3,2]

[[[[[[],[[]],[]]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [3,1,1]

[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [3,1]

[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [3]

[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [2,2,1]

[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [2,2]

[[[[[[[],[]],[]]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [2,1,1]

[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1]

[[[[[[[],[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [2,1]

[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [2]

[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1]

[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1]

[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => []

[[[[[[],[]],[]],[]],[]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1] => [5,4,4,3,3,2,2,1,1]

[[[[[[[],[]],[]],[]],[]],[]],[]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [11,9,7,5,3,1] => [6,5,5,4,4,3,3,2,2,1,1]

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.

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

conjugate

Description

Return the conjugate partition of the partition.
The conjugate partition of the partition

$\lambda$ of

$n$ is the partition

$\lambda^*$ whose Ferrers diagram is obtained from the diagram of

$\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.