Identifier
-
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
St000381: Integer compositions ⟶ ℤ
Values
[[]] => [1,0] => [1] => 1
[[],[]] => [1,0,1,0] => [1,1] => 1
[[[]]] => [1,1,0,0] => [2] => 2
[[],[],[]] => [1,0,1,0,1,0] => [1,1,1] => 1
[[],[[]]] => [1,0,1,1,0,0] => [1,2] => 2
[[[]],[]] => [1,1,0,0,1,0] => [2,1] => 2
[[[],[]]] => [1,1,0,1,0,0] => [2,1] => 2
[[[[]]]] => [1,1,1,0,0,0] => [3] => 3
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [1,1,1,1] => 1
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [1,1,2] => 2
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [1,2,1] => 2
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [1,2,1] => 2
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,3] => 3
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [2,1,1] => 2
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [2,2] => 2
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [2,1,1] => 2
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [3,1] => 3
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [2,1,1] => 2
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [2,2] => 2
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [3,1] => 3
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [3,1] => 3
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [4] => 4
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => 1
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => 2
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => 2
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => 2
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 3
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => 2
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => 2
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => 2
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 3
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => 2
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [1,2,2] => 2
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [1,3,1] => 3
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [1,3,1] => 3
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,4] => 4
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => 2
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => 2
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 2
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [2,2,1] => 2
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [2,3] => 3
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => 2
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => 3
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [2,1,2] => 2
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [3,2] => 3
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => 2
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [2,2,1] => 2
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [3,1,1] => 3
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [3,1,1] => 3
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [4,1] => 4
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => 2
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [2,1,2] => 2
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [2,2,1] => 2
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [2,2,1] => 2
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [2,3] => 3
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [3,1,1] => 3
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [3,2] => 3
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [3,1,1] => 3
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [4,1] => 4
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [3,1,1] => 3
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [3,2] => 3
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [4,1] => 4
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [4,1] => 4
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [5] => 5
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => 1
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => 2
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => 2
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => 2
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 3
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => 2
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => 2
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => 2
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => 3
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => 2
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => 2
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => 3
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => 3
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 4
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => 2
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => 2
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => 2
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => 2
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => 3
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => 2
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => 3
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => 2
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => 3
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => 2
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => 2
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => 3
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => 3
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => 4
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => 2
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => 2
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => 2
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => 2
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => 3
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => 3
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => 3
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => 3
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => 4
>>> Load all 2062 entries. <<<[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => 3
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => 3
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => 4
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => 4
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 5
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => 2
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => 2
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => 2
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => 2
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 3
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => 2
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => 2
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => 2
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => 3
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => 2
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => 2
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => 3
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => 3
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => 4
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => 2
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => 3
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => 2
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => 3
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => 2
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => 3
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => 2
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => 3
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => 3
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => 3
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => 2
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => 2
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => 3
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => 3
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => 4
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => 2
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => 2
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => 3
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => 3
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => 4
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => 2
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => 2
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => 2
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => 2
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => 3
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => 3
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => 3
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => 3
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => 4
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => 3
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => 3
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => 4
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => 4
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => 5
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => 2
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,2] => 2
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => 2
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => 2
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => 3
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,1] => 2
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2] => 2
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,1] => 2
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => 3
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,1] => 2
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2] => 2
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => 3
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => 3
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,4] => 4
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => 3
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => 3
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => 3
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => 3
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => 3
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => 3
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => 4
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => 3
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,2] => 4
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => 3
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => 3
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => 4
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => 4
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => 5
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => 3
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => 3
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => 3
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => 3
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => 3
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => 4
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,2] => 4
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => 4
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => 5
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => 4
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,2] => 4
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => 5
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => 5
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6] => 6
[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => 1
[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => 2
[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => 2
[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,2,1] => 2
[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => 3
[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => 2
[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => 2
[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => 2
[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => 3
[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => 2
[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,2,2] => 2
[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,3,1] => 3
[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,3,1] => 3
[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => 4
[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => 2
[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => 2
[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => 2
[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,2,1] => 2
[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => 3
[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1] => 2
[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => 3
[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,2,1,2] => 2
[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => 3
[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1] => 2
[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,2,2,1] => 2
[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => 3
[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => 3
[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => 4
[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1] => 2
[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,2,1,2] => 2
[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,2,2,1] => 2
[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1] => 2
[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,2,3] => 3
[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => 3
[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => 3
[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => 3
[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,4,1] => 4
[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => 3
[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => 3
[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => 4
[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => 4
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => 5
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 2
[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => 2
[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => 2
[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,2,1] => 2
[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => 3
[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => 2
[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => 2
[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,2,1,1] => 2
[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => 3
[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,1] => 2
[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2] => 2
[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,3,1] => 3
[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => 3
[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => 4
[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 2
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => 3
[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,2] => 2
[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => 3
[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => 2
[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => 3
[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => 2
[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => 3
[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => 3
[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => 3
[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1] => 2
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,2,1,1] => 2
[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1] => 3
[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1] => 3
[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => 4
[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,2] => 2
[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2] => 2
[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => 3
[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => 3
[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => 4
[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1] => 2
[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => 2
[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,2,1,1] => 2
[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,2,1,1] => 2
[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => 3
[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1] => 3
[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => 3
[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1] => 3
[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => 4
[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1] => 3
[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => 3
[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => 4
[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => 4
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => 5
[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1] => 2
[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,2] => 2
[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => 2
[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => 2
[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => 3
[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,2,1,1] => 2
[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2] => 2
[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,2,1,1] => 2
[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => 3
[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,2,1,1] => 2
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2] => 2
[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => 3
[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => 3
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4] => 4
[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1] => 3
[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => 3
[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => 3
[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => 3
[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => 3
[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1] => 3
[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => 4
[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => 3
[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => 4
[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1] => 3
[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => 3
[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => 4
[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => 4
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => 5
[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1] => 3
[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => 3
[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => 3
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => 3
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => 3
[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => 4
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => 4
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => 4
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => 5
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => 4
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => 4
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => 5
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => 5
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => 6
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 2
[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 2
[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 2
[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => 2
[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 3
[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 2
[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 2
[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 2
[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 3
[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 2
[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 2
[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => 3
[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 3
[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => 4
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 2
[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => 2
[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => 2
[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => 2
[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => 3
[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => 2
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => 3
[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => 2
[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => 3
[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => 2
[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => 2
[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,1] => 3
[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => 3
[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => 4
[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => 2
[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => 2
[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => 2
[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => 2
[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => 3
[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => 3
[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => 3
[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => 3
[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => 4
[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => 3
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => 3
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => 4
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => 4
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => 5
[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 2
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 3
[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 2
[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 3
[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 2
[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 3
[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => 2
[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 3
[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => 3
[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 3
[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 2
[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => 3
[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 2
[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => 3
[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 2
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 3
[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,1] => 3
[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => 3
[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 2
[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 2
[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => 3
[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 3
[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => 4
[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 3
[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => 3
[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,3,1] => 3
[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => 3
[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => 4
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 2
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 2
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => 3
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => 3
[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 4
[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => 2
[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => 2
[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => 3
[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => 3
[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => 4
[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => 2
[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => 2
[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => 3
[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => 3
[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => 4
[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => 2
[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => 3
[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => 2
[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => 3
[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => 3
[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => 3
[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => 3
[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => 3
[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => 4
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => 4
[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => 2
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => 2
[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => 2
[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => 2
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => 3
[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => 3
[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => 3
[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => 3
[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => 4
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => 3
[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => 3
[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => 4
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => 4
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => 5
[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => 2
[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => 2
[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => 2
[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => 2
[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => 3
[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => 3
[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => 3
[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => 3
[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => 4
[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => 3
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => 3
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => 4
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => 4
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => 5
[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => 2
[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => 2
[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => 2
[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => 2
[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => 3
[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => 2
[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => 2
[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => 2
[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => 3
[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => 2
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => 2
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => 3
[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => 3
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => 4
[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => 3
[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => 3
[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => 3
[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => 3
[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => 3
[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => 3
[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => 4
[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => 3
[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => 4
[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => 3
[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => 3
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => 4
[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => 4
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => 5
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => 3
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => 3
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => 3
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => 3
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => 3
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => 4
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => 4
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => 4
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => 5
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => 4
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => 4
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => 5
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => 5
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => 6
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1] => 2
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,2] => 2
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,2,1] => 2
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,2,1] => 2
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,3] => 3
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,2,1,1] => 2
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,2,2] => 2
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,2,1,1] => 2
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,3,1] => 3
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,1] => 2
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2] => 2
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,3,1] => 3
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,3,1] => 3
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4] => 4
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => 2
[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,1,2] => 2
[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,1] => 2
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,1] => 2
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,3] => 3
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1] => 2
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,1] => 3
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,2,1,2] => 2
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,2] => 3
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1] => 2
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,2,2,1] => 2
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,1] => 3
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,1] => 3
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1] => 4
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1] => 2
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1,2] => 2
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,1] => 2
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,1] => 2
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,3] => 3
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,1] => 3
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,2] => 3
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,1,1] => 3
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1] => 4
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,1] => 3
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,2] => 3
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1] => 4
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,1] => 4
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,5] => 5
[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => 3
[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,2] => 3
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,2,1] => 3
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,1] => 3
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => 3
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,1,1] => 3
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2] => 3
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,1] => 3
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,3,1] => 3
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 3
[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2] => 3
[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,3,1] => 3
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,3,1] => 3
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4] => 4
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => 3
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1] => 4
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2] => 3
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2] => 4
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,2,1] => 3
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,2,1] => 4
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,2,1] => 3
[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => 3
[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,2,1] => 4
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3] => 4
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1] => 3
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,1] => 3
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1] => 4
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1] => 4
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => 5
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,2] => 3
[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,2] => 3
[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,2] => 4
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,1,2] => 4
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,2] => 5
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1] => 3
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,2,1] => 3
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,2,1,1] => 3
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,1,1] => 3
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,3,1] => 3
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1] => 4
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,2,1] => 4
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1] => 4
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => 5
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1] => 4
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,2,1] => 4
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => 5
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => 5
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1] => 6
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => 3
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,2] => 3
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,2,1] => 3
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,2,1] => 3
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => 3
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,2,1,1] => 3
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2] => 3
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,2,1,1] => 3
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,3,1] => 3
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 3
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2] => 3
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,3,1] => 3
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,3,1] => 3
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4] => 4
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1] => 4
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,2] => 4
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,1] => 4
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,2,1] => 4
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3] => 4
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1] => 4
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => 5
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,2] => 4
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,2] => 5
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1] => 4
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,2,1] => 4
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => 5
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => 5
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1] => 6
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1] => 4
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,1,2] => 4
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,1] => 4
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,1] => 4
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,3] => 4
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => 5
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,2] => 5
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => 5
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1] => 6
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => 5
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,2] => 5
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1] => 6
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,1] => 6
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => 7
[[],[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => 1
[[],[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => 2
[[],[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => 2
[[],[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,2,1] => 2
[[],[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => 3
[[],[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => 2
[[],[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => 2
[[],[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1] => 2
[[],[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => 3
[[],[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1] => 2
[[],[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,2,2] => 2
[[],[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,3,1] => 3
[[],[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,3,1] => 3
[[],[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => 4
[[],[],[],[[]],[],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => 2
[[],[],[],[[]],[],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => 2
[[],[],[],[[]],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => 2
[[],[],[],[[]],[[],[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,2,1] => 2
[[],[],[],[[]],[[[]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => 3
[[],[],[],[[],[]],[],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1] => 2
[[],[],[],[[[]]],[],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => 3
[[],[],[],[[],[]],[[]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,2,1,2] => 2
[[],[],[],[[[]]],[[]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => 3
[[],[],[],[[],[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,2,1,1,1] => 2
[[],[],[],[[],[[]]],[]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,2,2,1] => 2
[[],[],[],[[[]],[]],[]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,3,1,1] => 3
[[],[],[],[[[],[]]],[]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1] => 3
[[],[],[],[[[[]]]],[]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => 4
[[],[],[],[[],[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1] => 2
[[],[],[],[[],[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,2] => 2
[[],[],[],[[],[[]],[]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,2,2,1] => 2
[[],[],[],[[],[[],[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,2,2,1] => 2
[[],[],[],[[],[[[]]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,2,3] => 3
[[],[],[],[[[]],[],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1] => 3
[[],[],[],[[[]],[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,3,2] => 3
[[],[],[],[[[],[]],[]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1] => 3
[[],[],[],[[[[]]],[]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,4,1] => 4
[[],[],[],[[[],[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1] => 3
[[],[],[],[[[],[[]]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,3,2] => 3
[[],[],[],[[[[]],[]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,4,1] => 4
[[],[],[],[[[[],[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,4,1] => 4
[[],[],[],[[[[[]]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => 5
[[],[],[[]],[],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 2
[[],[],[[]],[],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 2
[[],[],[[]],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 2
[[],[],[[]],[],[[],[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 2
[[],[],[[]],[],[[[]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => 3
[[],[],[[]],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => 2
[[],[],[[]],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => 2
[[],[],[[]],[[],[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,2,1,1] => 2
[[],[],[[]],[[[]]],[]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => 3
[[],[],[[]],[[],[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,2,1,1] => 2
[[],[],[[]],[[],[[]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,2,2] => 2
[[],[],[[]],[[[]],[]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,3,1] => 3
[[],[],[[]],[[[],[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,3,1] => 3
[[],[],[[]],[[[[]]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => 4
[[],[],[[],[]],[],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 2
[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => 3
[[],[],[[],[]],[],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 2
[[],[],[[[]]],[],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => 3
[[],[],[[],[]],[[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 2
[[],[],[[[]]],[[]],[]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 3
[[],[],[[],[]],[[],[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 2
[[],[],[[],[]],[[[]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,2,1,3] => 3
[[],[],[[[]]],[[],[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,2,1] => 3
[[],[],[[[]]],[[[]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => 3
[[],[],[[],[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1] => 2
[[],[],[[],[[]]],[],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,2,2,1,1] => 2
[[],[],[[[]],[]],[],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,3,1,1,1] => 3
[[],[],[[[],[]]],[],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,3,1,1,1] => 3
[[],[],[[[[]]]],[],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => 4
[[],[],[[],[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,2,1,1,2] => 2
[[],[],[[],[[]]],[[]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,2,2] => 2
[[],[],[[[]],[]],[[]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,2] => 3
[[],[],[[[],[]]],[[]]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,3,1,2] => 3
[[],[],[[[[]]]],[[]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => 4
[[],[],[[],[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1] => 2
[[],[],[[],[],[[]]],[]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,2,1,2,1] => 2
[[],[],[[],[[]],[]],[]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,2,2,1,1] => 2
[[],[],[[],[[],[]]],[]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,2,2,1,1] => 2
[[],[],[[],[[[]]]],[]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,2,3,1] => 3
[[],[],[[[]],[],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1] => 3
[[],[],[[[]],[[]]],[]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,3,2,1] => 3
[[],[],[[[],[]],[]],[]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,3,1,1,1] => 3
[[],[],[[[[]]],[]],[]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,4,1,1] => 4
[[],[],[[[],[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1] => 3
[[],[],[[[],[[]]]],[]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,3,2,1] => 3
[[],[],[[[[]],[]]],[]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,4,1,1] => 4
[[],[],[[[[],[]]]],[]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,4,1,1] => 4
[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => 5
[[],[],[[],[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1] => 2
[[],[],[[],[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,2] => 2
[[],[],[[],[],[[]],[]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,2,1,2,1] => 2
[[],[],[[],[],[[],[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,2,1] => 2
[[],[],[[],[],[[[]]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,2,1,3] => 3
[[],[],[[],[[]],[],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,2,2,1,1] => 2
[[],[],[[],[[]],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,2,2,2] => 2
[[],[],[[],[[],[]],[]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,2,2,1,1] => 2
[[],[],[[],[[[]]],[]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,3,1] => 3
[[],[],[[],[[],[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1] => 2
[[],[],[[],[[],[[]]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,2,2,2] => 2
[[],[],[[],[[[]],[]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,2,3,1] => 3
[[],[],[[],[[[],[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,3,1] => 3
[[],[],[[],[[[[]]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,2,4] => 4
[[],[],[[[]],[],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1] => 3
[[],[],[[[]],[],[[]]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,3,1,2] => 3
[[],[],[[[]],[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,3,2,1] => 3
[[],[],[[[]],[[],[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,3,2,1] => 3
[[],[],[[[]],[[[]]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,3,3] => 3
[[],[],[[[],[]],[],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1] => 3
[[],[],[[[[]]],[],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1] => 4
[[],[],[[[],[]],[[]]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,3,1,2] => 3
[[],[],[[[[]]],[[]]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,4,2] => 4
[[],[],[[[],[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,3,1,1,1] => 3
[[],[],[[[],[[]]],[]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,3,2,1] => 3
[[],[],[[[[]],[]],[]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,4,1,1] => 4
[[],[],[[[[],[]]],[]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,4,1,1] => 4
[[],[],[[[[[]]]],[]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,5,1] => 5
[[],[],[[[],[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1] => 3
[[],[],[[[],[],[[]]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,2] => 3
[[],[],[[[],[[]],[]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,3,2,1] => 3
[[],[],[[[],[[],[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,3,2,1] => 3
[[],[],[[[],[[[]]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,3,3] => 3
[[],[],[[[[]],[],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,4,1,1] => 4
[[],[],[[[[]],[[]]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,4,2] => 4
[[],[],[[[[],[]],[]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,4,1,1] => 4
[[],[],[[[[[]]],[]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,5,1] => 5
[[],[],[[[[],[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,4,1,1] => 4
[[],[],[[[[],[[]]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,4,2] => 4
[[],[],[[[[[]],[]]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,5,1] => 5
[[],[],[[[[[],[]]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,5,1] => 5
[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => 6
[[],[[]],[],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 2
[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 2
[[],[[]],[],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 2
[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 2
[[],[[]],[],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 3
[[],[[]],[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 2
[[],[[]],[],[[]],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 2
[[],[[]],[],[[],[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 2
[[],[[]],[],[[[]]],[]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 3
[[],[[]],[],[[],[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 2
[[],[[]],[],[[],[[]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 2
[[],[[]],[],[[[]],[]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => 3
[[],[[]],[],[[[],[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 3
[[],[[]],[],[[[[]]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 4
[[],[[]],[[]],[],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 2
[[],[[]],[[]],[],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 2
[[],[[]],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 2
[[],[[]],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => 2
[[],[[]],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => 3
[[],[[]],[[],[]],[],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => 2
[[],[[]],[[[]]],[],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => 3
[[],[[]],[[],[]],[[]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => 2
[[],[[]],[[[]]],[[]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => 3
[[],[[]],[[],[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => 2
[[],[[]],[[],[[]]],[]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => 2
[[],[[]],[[[]],[]],[]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,1,1] => 3
[[],[[]],[[[],[]]],[]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,1,1] => 3
[[],[[]],[[[[]]]],[]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => 4
[[],[[]],[[],[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => 2
[[],[[]],[[],[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => 2
[[],[[]],[[],[[]],[]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => 2
[[],[[]],[[],[[],[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => 2
[[],[[]],[[],[[[]]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,2,3] => 3
[[],[[]],[[[]],[],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,1,1] => 3
[[],[[]],[[[]],[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,2] => 3
[[],[[]],[[[],[]],[]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,1] => 3
[[],[[]],[[[[]]],[]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,1] => 4
[[],[[]],[[[],[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,1,1] => 3
[[],[[]],[[[],[[]]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,2] => 3
[[],[[]],[[[[]],[]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,1] => 4
[[],[[]],[[[[],[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,1] => 4
[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => 5
[[],[[],[]],[],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 2
[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[],[]],[],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 2
[[],[[[]]],[],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => 3
[[],[[],[]],[],[[]],[]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 2
[[],[[[]]],[],[[]],[]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 3
[[],[[],[]],[],[[],[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 2
[[],[[],[]],[],[[[]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 3
[[],[[[]]],[],[[],[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,2,1] => 3
[[],[[[]]],[],[[[]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 3
[[],[[],[]],[[]],[],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 2
[[],[[[]]],[[]],[],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => 3
[[],[[],[]],[[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 2
[[],[[[]]],[[]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => 3
[[],[[],[]],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 2
[[],[[],[]],[[[]]],[]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 3
[[],[[[]]],[[],[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,2,1,1] => 3
[[],[[[]]],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 3
[[],[[],[]],[[],[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 2
[[],[[],[]],[[],[[]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 2
[[],[[],[]],[[[]],[]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => 3
[[],[[],[]],[[[],[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 3
[[],[[],[]],[[[[]]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 4
[[],[[[]]],[[],[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,2,1,1] => 3
[[],[[[]]],[[],[[]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,2,2] => 3
[[],[[[]]],[[[]],[]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,3,1] => 3
[[],[[[]]],[[[],[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,3,1] => 3
[[],[[[]]],[[[[]]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => 4
[[],[[],[],[]],[],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 2
[[],[[],[[]]],[],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 2
[[],[[[]],[]],[],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[[],[]]],[],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[[[]]]],[],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 4
[[],[[],[],[]],[],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 2
[[],[[],[[]]],[],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 2
[[],[[[]],[]],[],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => 3
[[],[[[],[]]],[],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => 3
[[],[[[[]]]],[],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 4
[[],[[],[],[]],[[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 2
[[],[[],[[]]],[[]],[]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 2
[[],[[[]],[]],[[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 3
[[],[[[],[]]],[[]],[]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 3
[[],[[[[]]]],[[]],[]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 4
[[],[[],[],[]],[[],[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 2
[[],[[],[],[]],[[[]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,3] => 3
[[],[[],[[]]],[[],[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => 2
[[],[[],[[]]],[[[]]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,2,2,3] => 3
[[],[[[]],[]],[[],[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 3
[[],[[[]],[]],[[[]]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,3,1,3] => 3
[[],[[[],[]]],[[],[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 3
[[],[[[],[]]],[[[]]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,3,1,3] => 3
[[],[[[[]]]],[[],[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,2,1] => 4
[[],[[[[]]]],[[[]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => 4
[[],[[],[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1] => 2
[[],[[],[],[[]]],[],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,2,1,2,1,1] => 2
[[],[[],[[]],[]],[],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => 2
[[],[[],[[],[]]],[],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,2,2,1,1,1] => 2
[[],[[],[[[]]]],[],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,1,1] => 3
[[],[[[]],[],[]],[],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[[]],[[]]],[],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,3,2,1,1] => 3
[[],[[[],[]],[]],[],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[[[]]],[]],[],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,4,1,1,1] => 4
[[],[[[],[],[]]],[],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[[],[[]]]],[],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,2,1,1] => 3
[[],[[[[]],[]]],[],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,4,1,1,1] => 4
[[],[[[[],[]]]],[],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,4,1,1,1] => 4
[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => 5
[[],[[],[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,2] => 2
[[],[[],[],[[]]],[[]]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,1,2,2] => 2
[[],[[],[[]],[]],[[]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => 2
[[],[[],[[],[]]],[[]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,2,2,1,2] => 2
[[],[[],[[[]]]],[[]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,2] => 3
[[],[[[]],[],[]],[[]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => 3
[[],[[[]],[[]]],[[]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,2,2] => 3
[[],[[[],[]],[]],[[]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => 3
[[],[[[[]]],[]],[[]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,4,1,2] => 4
[[],[[[],[],[]]],[[]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,2] => 3
[[],[[[],[[]]]],[[]]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,2,2] => 3
[[],[[[[]],[]]],[[]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,4,1,2] => 4
[[],[[[[],[]]]],[[]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,4,1,2] => 4
[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => 5
[[],[[],[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1] => 2
[[],[[],[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,2,1] => 2
[[],[[],[],[[]],[]],[]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,2,1,2,1,1] => 2
[[],[[],[],[[],[]]],[]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,2,1,2,1,1] => 2
[[],[[],[],[[[]]]],[]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,2,1,3,1] => 3
[[],[[],[[]],[],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => 2
[[],[[],[[]],[[]]],[]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => 2
[[],[[],[[],[]],[]],[]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,2,2,1,1,1] => 2
[[],[[],[[[]]],[]],[]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,2,3,1,1] => 3
[[],[[],[[],[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1] => 2
[[],[[],[[],[[]]]],[]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,2,2,2,1] => 2
[[],[[],[[[]],[]]],[]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,2,3,1,1] => 3
[[],[[],[[[],[]]]],[]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,2,3,1,1] => 3
[[],[[],[[[[]]]]],[]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,1] => 4
[[],[[[]],[],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[[]],[],[[]]],[]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 3
[[],[[[]],[[]],[]],[]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,3,2,1,1] => 3
[[],[[[]],[[],[]]],[]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,3,2,1,1] => 3
[[],[[[]],[[[]]]],[]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,3,3,1] => 3
[[],[[[],[]],[],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[[[]]],[],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,4,1,1,1] => 4
[[],[[[],[]],[[]]],[]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 3
[[],[[[[]]],[[]]],[]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,4,2,1] => 4
[[],[[[],[],[]],[]],[]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[[],[[]]],[]],[]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,3,2,1,1] => 3
[[],[[[[]],[]],[]],[]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,4,1,1,1] => 4
[[],[[[[],[]]],[]],[]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,4,1,1,1] => 4
[[],[[[[[]]]],[]],[]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,5,1,1] => 5
[[],[[[],[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1] => 3
[[],[[[],[],[[]]]],[]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,1] => 3
[[],[[[],[[]],[]]],[]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,3,2,1,1] => 3
[[],[[[],[[],[]]]],[]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,3,2,1,1] => 3
[[],[[[],[[[]]]]],[]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,3,3,1] => 3
[[],[[[[]],[],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1] => 4
[[],[[[[]],[[]]]],[]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,4,2,1] => 4
[[],[[[[],[]],[]]],[]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,4,1,1,1] => 4
[[],[[[[[]]],[]]],[]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,5,1,1] => 5
[[],[[[[],[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1] => 4
[[],[[[[],[[]]]]],[]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,4,2,1] => 4
[[],[[[[[]],[]]]],[]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,5,1,1] => 5
[[],[[[[[],[]]]]],[]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,5,1,1] => 5
[[],[[[[[[]]]]]],[]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => 6
[[],[[],[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1] => 2
[[],[[],[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,2] => 2
[[],[[],[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,2,1] => 2
[[],[[],[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,2,1] => 2
[[],[[],[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,3] => 3
[[],[[],[],[[]],[],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,2,1,1] => 2
[[],[[],[],[[]],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,2,2] => 2
[[],[[],[],[[],[]],[]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,2,1,2,1,1] => 2
[[],[[],[],[[[]]],[]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,3,1] => 3
[[],[[],[],[[],[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,2,1,1] => 2
[[],[[],[],[[],[[]]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,2,1,2,2] => 2
[[],[[],[],[[[]],[]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,1,3,1] => 3
[[],[[],[],[[[],[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => 3
[[],[[],[],[[[[]]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,1,4] => 4
[[],[[],[[]],[],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => 2
[[],[[],[[]],[],[[]]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => 2
[[],[[],[[]],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => 2
[[],[[],[[]],[[],[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => 2
[[],[[],[[]],[[[]]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,2,2,3] => 3
[[],[[],[[],[]],[],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,2,2,1,1,1] => 2
[[],[[],[[[]]],[],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,2,3,1,1] => 3
[[],[[],[[],[]],[[]]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,2,2,1,2] => 2
[[],[[],[[[]]],[[]]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,2,3,2] => 3
[[],[[],[[],[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,2,2,1,1,1] => 2
[[],[[],[[],[[]]],[]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,2,2,2,1] => 2
[[],[[],[[[]],[]],[]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,2,3,1,1] => 3
[[],[[],[[[],[]]],[]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1] => 3
[[],[[],[[[[]]]],[]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,2,4,1] => 4
[[],[[],[[],[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1] => 2
[[],[[],[[],[],[[]]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,2] => 2
[[],[[],[[],[[]],[]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,2,2,2,1] => 2
[[],[[],[[],[[],[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,2,2,2,1] => 2
[[],[[],[[],[[[]]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,2,2,3] => 3
[[],[[],[[[]],[],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,1,1] => 3
[[],[[],[[[]],[[]]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2] => 3
[[],[[],[[[],[]],[]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,2,3,1,1] => 3
[[],[[],[[[[]]],[]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,2,4,1] => 4
[[],[[],[[[],[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1] => 3
[[],[[],[[[],[[]]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => 3
[[],[[],[[[[]],[]]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,2,4,1] => 4
[[],[[],[[[[],[]]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,1] => 4
[[],[[],[[[[[]]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,5] => 5
[[],[[[]],[],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => 3
[[],[[[]],[],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => 3
[[],[[[]],[],[[]],[]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 3
[[],[[[]],[],[[],[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 3
[[],[[[]],[],[[[]]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,1,3] => 3
[[],[[[]],[[]],[],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,1,1] => 3
[[],[[[]],[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2] => 3
[[],[[[]],[[],[]],[]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,1,1] => 3
[[],[[[]],[[[]]],[]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,3,1] => 3
[[],[[[]],[[],[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,2,1,1] => 3
[[],[[[]],[[],[[]]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,2,2] => 3
[[],[[[]],[[[]],[]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,3,1] => 3
[[],[[[]],[[[],[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,3,1] => 3
[[],[[[]],[[[[]]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,4] => 4
[[],[[[],[]],[],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => 3
[[],[[[[]]],[],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1] => 4
[[],[[[],[]],[],[[]]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => 3
[[],[[[[]]],[],[[]]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,1,2] => 4
[[],[[[],[]],[[]],[]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 3
[[],[[[[]]],[[]],[]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,1] => 4
[[],[[[],[]],[[],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 3
[[],[[[],[]],[[[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,3,1,3] => 3
[[],[[[[]]],[[],[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,2,1] => 4
[[],[[[[]]],[[[]]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,3] => 4
[[],[[[],[],[]],[],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1,1] => 3
[[],[[[],[[]]],[],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,1,1] => 3
[[],[[[[]],[]],[],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,1,1,1] => 4
[[],[[[[],[]]],[],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,1,1,1] => 4
[[],[[[[[]]]],[],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,5,1,1] => 5
[[],[[[],[],[]],[[]]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,2] => 3
[[],[[[],[[]]],[[]]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,2,2] => 3
[[],[[[[]],[]],[[]]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,2] => 4
[[],[[[[],[]]],[[]]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,2] => 4
[[],[[[[[]]]],[[]]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,5,2] => 5
[[],[[[],[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1] => 3
[[],[[[],[],[[]]],[]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,1] => 3
[[],[[[],[[]],[]],[]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,1,1] => 3
[[],[[[],[[],[]]],[]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,1,1] => 3
[[],[[[],[[[]]]],[]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,3,1] => 3
[[],[[[[]],[],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1] => 4
[[],[[[[]],[[]]],[]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,1] => 4
[[],[[[[],[]],[]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1] => 4
[[],[[[[[]]],[]],[]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,5,1,1] => 5
[[],[[[[],[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1] => 4
[[],[[[[],[[]]]],[]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,1] => 4
[[],[[[[[]],[]]],[]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,5,1,1] => 5
[[],[[[[[],[]]]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,5,1,1] => 5
[[],[[[[[[]]]]],[]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,6,1] => 6
[[],[[[],[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1] => 3
[[],[[[],[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,2] => 3
[[],[[[],[],[[]],[]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => 3
[[],[[[],[],[[],[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => 3
[[],[[[],[],[[[]]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,1,3] => 3
[[],[[[],[[]],[],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,3,2,1,1] => 3
[[],[[[],[[]],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,2,2] => 3
[[],[[[],[[],[]],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,1] => 3
[[],[[[],[[[]]],[]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,3,1] => 3
[[],[[[],[[],[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1] => 3
[[],[[[],[[],[[]]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => 3
[[],[[[],[[[]],[]]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,3,1] => 3
[[],[[[],[[[],[]]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,3,1] => 3
[[],[[[],[[[[]]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4] => 4
[[],[[[[]],[],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1] => 4
[[],[[[[]],[],[[]]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,4,1,2] => 4
[[],[[[[]],[[]],[]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,4,2,1] => 4
[[],[[[[]],[[],[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,4,2,1] => 4
[[],[[[[]],[[[]]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => 4
[[],[[[[],[]],[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1] => 4
[[],[[[[[]]],[],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,5,1,1] => 5
[[],[[[[],[]],[[]]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,4,1,2] => 4
[[],[[[[[]]],[[]]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,5,2] => 5
[[],[[[[],[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1] => 4
[[],[[[[],[[]]],[]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,4,2,1] => 4
[[],[[[[[]],[]],[]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,5,1,1] => 5
[[],[[[[[],[]]],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1] => 5
[[],[[[[[[]]]],[]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,6,1] => 6
[[],[[[[],[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1] => 4
[[],[[[[],[],[[]]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,2] => 4
[[],[[[[],[[]],[]]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,4,2,1] => 4
[[],[[[[],[[],[]]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,2,1] => 4
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => 4
[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,5,1,1] => 5
[[],[[[[[]],[[]]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,5,2] => 5
[[],[[[[[],[]],[]]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1] => 5
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,6,1] => 6
[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1] => 5
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,5,2] => 5
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,6,1] => 6
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,6,1] => 6
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => 7
[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 2
[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 2
[[[]],[],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 2
[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 2
[[[]],[],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 3
[[[]],[],[],[[]],[],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 2
[[[]],[],[],[[]],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 2
[[[]],[],[],[[],[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 2
[[[]],[],[],[[[]]],[]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 3
[[[]],[],[],[[],[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 2
[[[]],[],[],[[],[[]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 2
[[[]],[],[],[[[]],[]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 3
[[[]],[],[],[[[],[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 3
[[[]],[],[],[[[[]]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 4
[[[]],[],[[]],[],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[[[]],[],[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 2
[[[]],[],[[]],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 2
[[[]],[],[[]],[[],[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 2
[[[]],[],[[]],[[[]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 3
[[[]],[],[[],[]],[],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[[[]],[],[[[]]],[],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 3
[[[]],[],[[],[]],[[]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 2
[[[]],[],[[[]]],[[]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 3
[[[]],[],[[],[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 2
[[[]],[],[[],[[]]],[]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 2
[[[]],[],[[[]],[]],[]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 3
[[[]],[],[[[],[]]],[]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 3
[[[]],[],[[[[]]]],[]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 4
[[[]],[],[[],[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 2
[[[]],[],[[],[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 2
[[[]],[],[[],[[]],[]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 2
[[[]],[],[[],[[],[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 2
[[[]],[],[[],[[[]]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 3
[[[]],[],[[[]],[],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 3
[[[]],[],[[[]],[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 3
[[[]],[],[[[],[]],[]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 3
[[[]],[],[[[[]]],[]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 4
[[[]],[],[[[],[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 3
[[[]],[],[[[],[[]]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 3
[[[]],[],[[[[]],[]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 4
[[[]],[],[[[[],[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 4
[[[]],[],[[[[[]]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 5
[[[]],[[]],[],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 2
[[[]],[[]],[],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 2
[[[]],[[]],[],[[]],[]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[[[]],[[]],[],[[],[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[[[]],[[]],[],[[[]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 3
[[[]],[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 2
[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 2
[[[]],[[]],[[],[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => 2
[[[]],[[]],[[[]]],[]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 3
[[[]],[[]],[[],[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => 2
[[[]],[[]],[[],[[]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => 2
[[[]],[[]],[[[]],[]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => 3
[[[]],[[]],[[[],[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => 3
[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 4
[[[]],[[],[]],[],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 2
[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 3
[[[]],[[],[]],[],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 2
[[[]],[[[]]],[],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 3
[[[]],[[],[]],[[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[[[]],[[[]]],[[]],[]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 3
[[[]],[[],[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[[[]],[[],[]],[[[]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 3
[[[]],[[[]]],[[],[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => 3
[[[]],[[[]]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => 3
[[[]],[[],[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 2
[[[]],[[],[[]]],[],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => 2
[[[]],[[[]],[]],[],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => 3
[[[]],[[[],[]]],[],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => 3
[[[]],[[[[]]]],[],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => 4
[[[]],[[],[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 2
[[[]],[[],[[]]],[[]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => 2
[[[]],[[[]],[]],[[]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => 3
[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => 3
[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => 4
[[[]],[[],[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 2
[[[]],[[],[],[[]]],[]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 2
[[[]],[[],[[]],[]],[]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => 2
[[[]],[[],[[],[]]],[]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => 2
[[[]],[[],[[[]]]],[]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => 3
[[[]],[[[]],[],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => 3
[[[]],[[[]],[[]]],[]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => 3
[[[]],[[[],[]],[]],[]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => 3
[[[]],[[[[]]],[]],[]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,1] => 4
[[[]],[[[],[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => 3
[[[]],[[[],[[]]]],[]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => 3
[[[]],[[[[]],[]]],[]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,1] => 4
[[[]],[[[[],[]]]],[]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,4,1,1] => 4
[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => 5
[[[]],[[],[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 2
[[[]],[[],[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 2
[[[]],[[],[],[[]],[]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 2
[[[]],[[],[],[[],[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 2
[[[]],[[],[],[[[]]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 3
[[[]],[[],[[]],[],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => 2
[[[]],[[],[[]],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => 2
[[[]],[[],[[],[]],[]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => 2
[[[]],[[],[[[]]],[]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => 3
[[[]],[[],[[],[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => 2
[[[]],[[],[[],[[]]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => 2
[[[]],[[],[[[]],[]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => 3
[[[]],[[],[[[],[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => 3
[[[]],[[],[[[[]]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => 4
[[[]],[[[]],[],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => 3
[[[]],[[[]],[],[[]]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => 3
[[[]],[[[]],[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => 3
[[[]],[[[]],[[],[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => 3
[[[]],[[[]],[[[]]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,3] => 3
[[[]],[[[],[]],[],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => 3
[[[]],[[[[]]],[],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,1] => 4
[[[]],[[[],[]],[[]]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => 3
[[[]],[[[[]]],[[]]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,2] => 4
[[[]],[[[],[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => 3
[[[]],[[[],[[]]],[]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => 3
[[[]],[[[[]],[]],[]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,1] => 4
[[[]],[[[[],[]]],[]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1] => 4
[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,5,1] => 5
[[[]],[[[],[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => 3
[[[]],[[[],[],[[]]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => 3
[[[]],[[[],[[]],[]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => 3
[[[]],[[[],[[],[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => 3
[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,3] => 3
[[[]],[[[[]],[],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1] => 4
[[[]],[[[[]],[[]]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,2] => 4
[[[]],[[[[],[]],[]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,1,1] => 4
[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,5,1] => 5
[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,1,1] => 4
[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,2] => 4
[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,5,1] => 5
[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,5,1] => 5
[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => 6
[[[],[]],[],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 2
[[[[]]],[],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[],[]],[],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 2
[[[[]]],[],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[],[]],[],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 2
[[[[]]],[],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 3
[[[],[]],[],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 2
[[[],[]],[],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 3
[[[[]]],[],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 3
[[[[]]],[],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 3
[[[],[]],[],[[]],[],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 2
[[[[]]],[],[[]],[],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 3
[[[],[]],[],[[]],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 2
[[[[]]],[],[[]],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 3
[[[],[]],[],[[],[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 2
[[[],[]],[],[[[]]],[]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 3
[[[[]]],[],[[],[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 3
[[[[]]],[],[[[]]],[]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 3
[[[],[]],[],[[],[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 2
[[[],[]],[],[[],[[]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 2
[[[],[]],[],[[[]],[]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 3
[[[],[]],[],[[[],[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 3
[[[],[]],[],[[[[]]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 4
[[[[]]],[],[[],[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 3
[[[[]]],[],[[],[[]]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 3
[[[[]]],[],[[[]],[]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 3
[[[[]]],[],[[[],[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 3
[[[[]]],[],[[[[]]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => 4
[[[],[]],[[]],[],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[[[[]]],[[]],[],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 3
[[[],[]],[[]],[],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 2
[[[[]]],[[]],[],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 3
[[[],[]],[[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 2
[[[[]]],[[]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 3
[[[],[]],[[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 2
[[[],[]],[[]],[[[]]]] => [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 3
[[[[]]],[[]],[[],[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,1] => 3
[[[[]]],[[]],[[[]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 3
[[[],[]],[[],[]],[],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[[[],[]],[[[]]],[],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 3
[[[[]]],[[],[]],[],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 3
[[[[]]],[[[]]],[],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => 3
[[[],[]],[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 2
[[[],[]],[[[]]],[[]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 3
[[[[]]],[[],[]],[[]]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,2] => 3
[[[[]]],[[[]]],[[]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => 3
[[[],[]],[[],[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 2
[[[],[]],[[],[[]]],[]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 2
[[[],[]],[[[]],[]],[]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 3
[[[],[]],[[[],[]]],[]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 3
[[[],[]],[[[[]]]],[]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 4
[[[[]]],[[],[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 3
[[[[]]],[[],[[]]],[]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,2,1] => 3
[[[[]]],[[[]],[]],[]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,3,1,1] => 3
[[[[]]],[[[],[]]],[]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,3,1,1] => 3
[[[[]]],[[[[]]]],[]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 4
[[[],[]],[[],[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 2
[[[],[]],[[],[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 2
[[[],[]],[[],[[]],[]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 2
[[[],[]],[[],[[],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 2
[[[],[]],[[],[[[]]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 3
[[[],[]],[[[]],[],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 3
[[[],[]],[[[]],[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 3
[[[],[]],[[[],[]],[]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 3
[[[],[]],[[[[]]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 4
[[[],[]],[[[],[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 3
[[[],[]],[[[],[[]]]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 3
[[[],[]],[[[[]],[]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 4
[[[],[]],[[[[],[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 4
[[[],[]],[[[[[]]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 5
[[[[]]],[[],[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 3
[[[[]]],[[],[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,2] => 3
[[[[]]],[[],[[]],[]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,2,1] => 3
[[[[]]],[[],[[],[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 3
[[[[]]],[[],[[[]]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,3] => 3
[[[[]]],[[[]],[],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,3,1,1] => 3
[[[[]]],[[[]],[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,3,2] => 3
[[[[]]],[[[],[]],[]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,3,1,1] => 3
[[[[]]],[[[[]]],[]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1] => 4
[[[[]]],[[[],[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,3,1,1] => 3
[[[[]]],[[[],[[]]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => 3
[[[[]]],[[[[]],[]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => 4
[[[[]]],[[[[],[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => 4
[[[[]]],[[[[[]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => 5
[[[],[],[]],[],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 2
[[[],[[]]],[],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 2
[[[[]],[]],[],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[[],[]]],[],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[[[]]]],[],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[],[],[]],[],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 2
[[[],[[]]],[],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 2
[[[[]],[]],[],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[[],[]]],[],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[[[]]]],[],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => 4
[[[],[],[]],[],[[]],[]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 2
[[[],[[]]],[],[[]],[]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[[[[]],[]],[],[[]],[]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 3
[[[[],[]]],[],[[]],[]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 3
[[[[[]]]],[],[[]],[]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 4
[[[],[],[]],[],[[],[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 2
[[[],[],[]],[],[[[]]]] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 3
[[[],[[]]],[],[[],[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[[[],[[]]],[],[[[]]]] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 3
[[[[]],[]],[],[[],[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 3
[[[[]],[]],[],[[[]]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 3
[[[[],[]]],[],[[],[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 3
[[[[],[]]],[],[[[]]]] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 3
[[[[[]]]],[],[[],[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => 4
[[[[[]]]],[],[[[]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 4
[[[],[],[]],[[]],[],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 2
[[[],[[]]],[[]],[],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 2
[[[[]],[]],[[]],[],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 3
[[[[],[]]],[[]],[],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 3
[[[[[]]]],[[]],[],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 4
[[[],[],[]],[[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 2
[[[],[[]]],[[]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 2
[[[[]],[]],[[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 3
[[[[],[]]],[[]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 3
[[[[[]]]],[[]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 4
[[[],[],[]],[[],[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 2
[[[],[],[]],[[[]]],[]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 3
[[[],[[]]],[[],[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => 2
[[[],[[]]],[[[]]],[]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 3
[[[[]],[]],[[],[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 3
[[[[]],[]],[[[]]],[]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 3
[[[[],[]]],[[],[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 3
[[[[],[]]],[[[]]],[]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 3
[[[[[]]]],[[],[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 4
[[[[[]]]],[[[]]],[]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 4
[[[],[],[]],[[],[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 2
[[[],[],[]],[[],[[]]]] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 2
[[[],[],[]],[[[]],[]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 3
[[[],[],[]],[[[],[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 3
[[[],[],[]],[[[[]]]]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 4
[[[],[[]]],[[],[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => 2
[[[],[[]]],[[],[[]]]] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => 2
[[[],[[]]],[[[]],[]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => 3
[[[],[[]]],[[[],[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => 3
[[[],[[]]],[[[[]]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 4
[[[[]],[]],[[],[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 3
[[[[]],[]],[[],[[]]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 3
[[[[]],[]],[[[]],[]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 3
[[[[]],[]],[[[],[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 3
[[[[]],[]],[[[[]]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 4
[[[[],[]]],[[],[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 3
[[[[],[]]],[[],[[]]]] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 3
[[[[],[]]],[[[]],[]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 3
[[[[],[]]],[[[],[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 3
[[[[],[]]],[[[[]]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 4
[[[[[]]]],[[],[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,2,1,1] => 4
[[[[[]]]],[[],[[]]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,2,2] => 4
[[[[[]]]],[[[]],[]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,1] => 4
[[[[[]]]],[[[],[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => 4
[[[[[]]]],[[[[]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[[[],[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 2
[[[],[],[[]]],[],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[[[],[[]],[]],[],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 2
[[[],[[],[]]],[],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 2
[[[],[[[]]]],[],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 3
[[[[]],[],[]],[],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[[]],[[]]],[],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 3
[[[[],[]],[]],[],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[[[]]],[]],[],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[[],[],[]]],[],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[[],[[]]]],[],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 3
[[[[[]],[]]],[],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[[[],[]]]],[],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[[[[]]]]],[],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 5
[[[],[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 2
[[[],[],[[]]],[],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 2
[[[],[[]],[]],[],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 2
[[[],[[],[]]],[],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 2
[[[],[[[]]]],[],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 3
[[[[]],[],[]],[],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[[]],[[]]],[],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => 3
[[[[],[]],[]],[],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[[[]]],[]],[],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,1,1,2] => 4
[[[[],[],[]]],[],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[[],[[]]]],[],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => 3
[[[[[]],[]]],[],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => 4
[[[[[],[]]]],[],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => 4
[[[[[[]]]]],[],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => 5
[[[],[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 2
[[[],[],[[]]],[[]],[]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 2
[[[],[[]],[]],[[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[[[],[[],[]]],[[]],[]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[[[],[[[]]]],[[]],[]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 3
[[[[]],[],[]],[[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 3
[[[[]],[[]]],[[]],[]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => 3
[[[[],[]],[]],[[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 3
[[[[[]]],[]],[[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,1] => 4
[[[[],[],[]]],[[]],[]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 3
[[[[],[[]]]],[[]],[]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => 3
[[[[[]],[]]],[[]],[]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 4
[[[[[],[]]]],[[]],[]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 4
[[[[[[]]]]],[[]],[]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 5
[[[],[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 2
[[[],[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,3] => 3
[[[],[],[[]]],[[],[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 2
[[[],[],[[]]],[[[]]]] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,2,3] => 3
[[[],[[]],[]],[[],[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[[[],[[]],[]],[[[]]]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 3
[[[],[[],[]]],[[],[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[[[],[[],[]]],[[[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,2,1,3] => 3
[[[],[[[]]]],[[],[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => 3
[[[],[[[]]]],[[[]]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,3] => 3
[[[[]],[],[]],[[],[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 3
[[[[]],[],[]],[[[]]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 3
[[[[]],[[]]],[[],[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => 3
[[[[]],[[]]],[[[]]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,3] => 3
[[[[],[]],[]],[[],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 3
[[[[],[]],[]],[[[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 3
[[[[[]]],[]],[[],[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => 4
[[[[[]]],[]],[[[]]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,3] => 4
[[[[],[],[]]],[[],[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 3
[[[[],[],[]]],[[[]]]] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,3] => 3
[[[[],[[]]]],[[],[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => 3
[[[[],[[]]]],[[[]]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,2,3] => 3
[[[[[]],[]]],[[],[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 4
[[[[[]],[]]],[[[]]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => 4
[[[[[],[]]]],[[],[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 4
[[[[[],[]]]],[[[]]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => 4
[[[[[[]]]]],[[],[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => 5
[[[[[[]]]]],[[[]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => 5
[[[],[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => 2
[[[],[],[],[[]]],[],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1] => 2
[[[],[],[[]],[]],[],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[[[],[],[[],[]]],[],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[[[],[],[[[]]]],[],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1] => 3
[[[],[[]],[],[]],[],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 2
[[[],[[]],[[]]],[],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => 2
[[[],[[],[]],[]],[],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 2
[[[],[[[]]],[]],[],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => 3
[[[],[[],[],[]]],[],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1,1] => 2
[[[],[[],[[]]]],[],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,2,2,1,1] => 2
[[[],[[[]],[]]],[],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => 3
[[[],[[[],[]]]],[],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,3,1,1,1] => 3
[[[],[[[[]]]]],[],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,4,1,1] => 4
[[[[]],[],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[[]],[],[[]]],[],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 3
[[[[]],[[]],[]],[],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 3
[[[[]],[[],[]]],[],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => 3
[[[[]],[[[]]]],[],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,3,1,1] => 3
[[[[],[]],[],[]],[],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[[[]]],[],[]],[],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[[],[]],[[]]],[],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 3
[[[[[]]],[[]]],[],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,2,1,1] => 4
[[[[],[],[]],[]],[],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[[],[[]]],[]],[],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 3
[[[[[]],[]],[]],[],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[[[],[]]],[]],[],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[[[[]]]],[]],[],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1] => 5
[[[[],[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1] => 3
[[[[],[],[[]]]],[],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,2,1,1] => 3
[[[[],[[]],[]]],[],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => 3
[[[[],[[],[]]]],[],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,1,1] => 3
[[[[],[[[]]]]],[],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,3,1,1] => 3
[[[[[]],[],[]]],[],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[[[]],[[]]]],[],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,2,1,1] => 4
[[[[[],[]],[]]],[],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[[[[]]],[]]],[],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1] => 5
[[[[[],[],[]]]],[],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1] => 4
[[[[[],[[]]]]],[],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,2,1,1] => 4
[[[[[[]],[]]]],[],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,1,1] => 5
[[[[[[],[]]]]],[],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,1,1,1] => 5
[[[[[[[]]]]]],[],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => 6
[[[],[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => 2
[[[],[],[],[[]]],[[]]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,2,2] => 2
[[[],[],[[]],[]],[[]]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 2
[[[],[],[[],[]]],[[]]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,1,2,1,2] => 2
[[[],[],[[[]]]],[[]]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,2] => 3
[[[],[[]],[],[]],[[]]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 2
[[[],[[]],[[]]],[[]]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => 2
[[[],[[],[]],[]],[[]]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 2
[[[],[[[]]],[]],[[]]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => 3
[[[],[[],[],[]]],[[]]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,2,1,1,2] => 2
[[[],[[],[[]]]],[[]]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2] => 2
[[[],[[[]],[]]],[[]]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => 3
[[[],[[[],[]]]],[[]]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,3,1,2] => 3
[[[],[[[[]]]]],[[]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,2] => 4
[[[[]],[],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[[]],[],[[]]],[[]]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 3
[[[[]],[[]],[]],[[]]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => 3
[[[[]],[[],[]]],[[]]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => 3
[[[[]],[[[]]]],[[]]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,3,2] => 3
[[[[],[]],[],[]],[[]]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[[[]]],[],[]],[[]]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,1,2] => 4
[[[[],[]],[[]]],[[]]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 3
[[[[[]]],[[]]],[[]]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,2,2] => 4
[[[[],[],[]],[]],[[]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[[],[[]]],[]],[[]]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => 3
[[[[[]],[]],[]],[[]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => 4
[[[[[],[]]],[]],[[]]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => 4
[[[[[[]]]],[]],[[]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2] => 5
[[[[],[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,2] => 3
[[[[],[],[[]]]],[[]]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,1,2,2] => 3
[[[[],[[]],[]]],[[]]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => 3
[[[[],[[],[]]]],[[]]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,2,1,2] => 3
[[[[],[[[]]]]],[[]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,3,2] => 3
[[[[[]],[],[]]],[[]]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => 4
[[[[[]],[[]]]],[[]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => 4
[[[[[],[]],[]]],[[]]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => 4
[[[[[[]]],[]]],[[]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2] => 5
[[[[[],[],[]]]],[[]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,2] => 4
[[[[[],[[]]]]],[[]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => 4
[[[[[[]],[]]]],[[]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,2] => 5
[[[[[[],[]]]]],[[]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,2] => 5
[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => 6
[[[],[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => 2
[[[],[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,2,1] => 2
[[[],[],[],[[]],[]],[]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,2,1,1] => 2
[[[],[],[],[[],[]]],[]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1] => 2
[[[],[],[],[[[]]]],[]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,3,1] => 3
[[[],[],[[]],[],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 2
[[[],[],[[]],[[]]],[]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 2
[[[],[],[[],[]],[]],[]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1] => 2
[[[],[],[[[]]],[]],[]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,1,1] => 3
[[[],[],[[],[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => 2
[[[],[],[[],[[]]]],[]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,1] => 2
[[[],[],[[[]],[]]],[]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,1,1] => 3
[[[],[],[[[],[]]]],[]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => 3
[[[],[],[[[[]]]]],[]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,1] => 4
[[[],[[]],[],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 2
[[[],[[]],[],[[]]],[]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 2
[[[],[[]],[[]],[]],[]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => 2
[[[],[[]],[[],[]]],[]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => 2
[[[],[[]],[[[]]]],[]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => 3
[[[],[[],[]],[],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 2
[[[],[[[]]],[],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => 3
[[[],[[],[]],[[]]],[]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 2
[[[],[[[]]],[[]]],[]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => 3
[[[],[[],[],[]],[]],[]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1,1] => 2
[[[],[[],[[]]],[]],[]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,2,2,1,1] => 2
[[[],[[[]],[]],[]],[]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => 3
[[[],[[[],[]]],[]],[]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,3,1,1,1] => 3
[[[],[[[[]]]],[]],[]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1] => 4
[[[],[[],[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1] => 2
[[[],[[],[],[[]]]],[]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => 2
[[[],[[],[[]],[]]],[]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,2,2,1,1] => 2
[[[],[[],[[],[]]]],[]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,2,2,1,1] => 2
[[[],[[],[[[]]]]],[]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,2,3,1] => 3
[[[],[[[]],[],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => 3
[[[],[[[]],[[]]]],[]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => 3
[[[],[[[],[]],[]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,3,1,1,1] => 3
[[[],[[[[]]],[]]],[]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,4,1,1] => 4
[[[],[[[],[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1] => 3
[[[],[[[],[[]]]]],[]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,3,2,1] => 3
[[[],[[[[]],[]]]],[]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,4,1,1] => 4
[[[],[[[[],[]]]]],[]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,4,1,1] => 4
[[[],[[[[[]]]]]],[]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,5,1] => 5
[[[[]],[],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 3
[[[[]],[],[],[[]]],[]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 3
[[[[]],[],[[]],[]],[]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 3
[[[[]],[],[[],[]]],[]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 3
[[[[]],[],[[[]]]],[]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 3
[[[[]],[[]],[],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 3
[[[[]],[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => 3
[[[[]],[[],[]],[]],[]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => 3
[[[[]],[[[]]],[]],[]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,3,1,1] => 3
[[[[]],[[],[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => 3
[[[[]],[[],[[]]]],[]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => 3
[[[[]],[[[]],[]]],[]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,3,1,1] => 3
[[[[]],[[[],[]]]],[]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1] => 3
[[[[]],[[[[]]]]],[]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => 4
[[[[],[]],[],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 3
[[[[[]]],[],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 4
[[[[],[]],[],[[]]],[]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 3
[[[[[]]],[],[[]]],[]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,1] => 4
[[[[],[]],[[]],[]],[]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 3
[[[[[]]],[[]],[]],[]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,2,1,1] => 4
[[[[],[]],[[],[]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 3
[[[[],[]],[[[]]]],[]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 3
[[[[[]]],[[],[]]],[]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1] => 4
[[[[[]]],[[[]]]],[]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => 4
[[[[],[],[]],[],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 3
[[[[],[[]]],[],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 3
[[[[[]],[]],[],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 4
[[[[[],[]]],[],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 4
[[[[[[]]]],[],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => 5
[[[[],[],[]],[[]]],[]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 3
[[[[],[[]]],[[]]],[]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => 3
[[[[[]],[]],[[]]],[]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 4
[[[[[],[]]],[[]]],[]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 4
[[[[[[]]]],[[]]],[]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,2,1] => 5
[[[[],[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1] => 3
[[[[],[],[[]]],[]],[]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => 3
[[[[],[[]],[]],[]],[]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => 3
[[[[],[[],[]]],[]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,2,1,1,1] => 3
[[[[],[[[]]]],[]],[]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,3,1,1] => 3
[[[[[]],[],[]],[]],[]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => 4
[[[[[]],[[]]],[]],[]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,2,1,1] => 4
[[[[[],[]],[]],[]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => 4
[[[[[[]]],[]],[]],[]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => 5
[[[[[],[],[]]],[]],[]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => 4
[[[[[],[[]]]],[]],[]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1] => 4
[[[[[[]],[]]],[]],[]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => 5
[[[[[[],[]]]],[]],[]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => 5
[[[[[[[]]]]],[]],[]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => 6
[[[[],[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1] => 3
[[[[],[],[],[[]]]],[]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => 3
[[[[],[],[[]],[]]],[]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => 3
[[[[],[],[[],[]]]],[]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => 3
[[[[],[],[[[]]]]],[]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => 3
[[[[],[[]],[],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => 3
[[[[],[[]],[[]]]],[]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => 3
[[[[],[[],[]],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,1,1] => 3
[[[[],[[[]]],[]]],[]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1] => 3
[[[[],[[],[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1] => 3
[[[[],[[],[[]]]]],[]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,2,2,1] => 3
[[[[],[[[]],[]]]],[]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,3,1,1] => 3
[[[[],[[[],[]]]]],[]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1] => 3
[[[[],[[[[]]]]]],[]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => 4
[[[[[]],[],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => 4
[[[[[]],[],[[]]]],[]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 4
[[[[[]],[[]],[]]],[]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,1,1] => 4
[[[[[]],[[],[]]]],[]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,2,1,1] => 4
[[[[[]],[[[]]]]],[]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => 4
[[[[[],[]],[],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => 4
[[[[[[]]],[],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,1,1] => 5
[[[[[],[]],[[]]]],[]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 4
[[[[[[]]],[[]]]],[]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,2,1] => 5
[[[[[],[],[]],[]]],[]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => 4
[[[[[],[[]]],[]]],[]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,1] => 4
[[[[[[]],[]],[]]],[]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,1,1] => 5
[[[[[[],[]]],[]]],[]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1] => 5
[[[[[[[]]]],[]]],[]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,1] => 6
[[[[[],[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1] => 4
[[[[[],[],[[]]]]],[]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => 4
[[[[[],[[]],[]]]],[]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,2,1,1] => 4
[[[[[],[[],[]]]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1] => 4
[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => 4
[[[[[[]],[],[]]]],[]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1] => 5
[[[[[[]],[[]]]]],[]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,2,1] => 5
[[[[[[],[]],[]]]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1] => 5
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1] => 6
[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1] => 5
[[[[[[],[[]]]]]],[]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,2,1] => 5
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1] => 6
[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1] => 6
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => 7
[[[],[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1] => 2
[[[],[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,2] => 2
[[[],[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,2,1] => 2
[[[],[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,2,1] => 2
[[[],[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,3] => 3
[[[],[],[],[[]],[],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1] => 2
[[[],[],[],[[]],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,2,2] => 2
[[[],[],[],[[],[]],[]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,2,1,1] => 2
[[[],[],[],[[[]]],[]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,3,1] => 3
[[[],[],[],[[],[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1] => 2
[[[],[],[],[[],[[]]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,2,2] => 2
[[[],[],[],[[[]],[]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,3,1] => 3
[[[],[],[],[[[],[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,3,1] => 3
[[[],[],[],[[[[]]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,4] => 4
[[[],[],[[]],[],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 2
[[[],[],[[]],[],[[]]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 2
[[[],[],[[]],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 2
[[[],[],[[]],[[],[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 2
[[[],[],[[]],[[[]]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,2,3] => 3
[[[],[],[[],[]],[],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1] => 2
[[[],[],[[[]]],[],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1] => 3
[[[],[],[[],[]],[[]]]] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,1,2,1,2] => 2
[[[],[],[[[]]],[[]]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,2] => 3
[[[],[],[[],[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,2,1,1,1] => 2
[[[],[],[[],[[]]],[]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,1,2,2,1] => 2
[[[],[],[[[]],[]],[]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,3,1,1] => 3
[[[],[],[[[],[]]],[]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,3,1,1] => 3
[[[],[],[[[[]]]],[]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,4,1] => 4
[[[],[],[[],[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1] => 2
[[[],[],[[],[],[[]]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,2] => 2
[[[],[],[[],[[]],[]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,1,2,2,1] => 2
[[[],[],[[],[[],[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,1] => 2
[[[],[],[[],[[[]]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,2,3] => 3
[[[],[],[[[]],[],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1] => 3
[[[],[],[[[]],[[]]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,1,3,2] => 3
[[[],[],[[[],[]],[]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1] => 3
[[[],[],[[[[]]],[]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,4,1] => 4
[[[],[],[[[],[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1] => 3
[[[],[],[[[],[[]]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,1,3,2] => 3
[[[],[],[[[[]],[]]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,1,4,1] => 4
[[[],[],[[[[],[]]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,4,1] => 4
[[[],[],[[[[[]]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,5] => 5
[[[],[[]],[],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 2
[[[],[[]],[],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 2
[[[],[[]],[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 2
[[[],[[]],[],[[],[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 2
[[[],[[]],[],[[[]]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 3
[[[],[[]],[[]],[],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => 2
[[[],[[]],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => 2
[[[],[[]],[[],[]],[]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => 2
[[[],[[]],[[[]]],[]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => 3
[[[],[[]],[[],[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => 2
[[[],[[]],[[],[[]]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => 2
[[[],[[]],[[[]],[]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => 3
[[[],[[]],[[[],[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => 3
[[[],[[]],[[[[]]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => 4
[[[],[[],[]],[],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 2
[[[],[[[]]],[],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => 3
[[[],[[],[]],[],[[]]]] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 2
[[[],[[[]]],[],[[]]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => 3
[[[],[[],[]],[[]],[]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 2
[[[],[[[]]],[[]],[]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => 3
[[[],[[],[]],[[],[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 2
[[[],[[],[]],[[[]]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,2,1,3] => 3
[[[],[[[]]],[[],[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => 3
[[[],[[[]]],[[[]]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,3] => 3
[[[],[[],[],[]],[],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1,1] => 2
[[[],[[],[[]]],[],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,2,2,1,1] => 2
[[[],[[[]],[]],[],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => 3
[[[],[[[],[]]],[],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1] => 3
[[[],[[[[]]]],[],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,1] => 4
[[[],[[],[],[]],[[]]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,2,1,1,2] => 2
[[[],[[],[[]]],[[]]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2] => 2
[[[],[[[]],[]],[[]]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => 3
[[[],[[[],[]]],[[]]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,1,2] => 3
[[[],[[[[]]]],[[]]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,4,2] => 4
[[[],[[],[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1] => 2
[[[],[[],[],[[]]],[]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,2,1,2,1] => 2
[[[],[[],[[]],[]],[]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,2,2,1,1] => 2
[[[],[[],[[],[]]],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,2,2,1,1] => 2
[[[],[[],[[[]]]],[]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,3,1] => 3
[[[],[[[]],[],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => 3
[[[],[[[]],[[]]],[]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => 3
[[[],[[[],[]],[]],[]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,1,1] => 3
[[[],[[[[]]],[]],[]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,4,1,1] => 4
[[[],[[[],[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1] => 3
[[[],[[[],[[]]]],[]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,2,1] => 3
[[[],[[[[]],[]]],[]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,4,1,1] => 4
[[[],[[[[],[]]]],[]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,4,1,1] => 4
[[[],[[[[[]]]]],[]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,5,1] => 5
[[[],[[],[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1] => 2
[[[],[[],[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,2] => 2
[[[],[[],[],[[]],[]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,2,1,2,1] => 2
[[[],[[],[],[[],[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,1] => 2
[[[],[[],[],[[[]]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,3] => 3
[[[],[[],[[]],[],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,2,2,1,1] => 2
[[[],[[],[[]],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2] => 2
[[[],[[],[[],[]],[]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,2,2,1,1] => 2
[[[],[[],[[[]]],[]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,2,3,1] => 3
[[[],[[],[[],[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1] => 2
[[[],[[],[[],[[]]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2] => 2
[[[],[[],[[[]],[]]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,2,3,1] => 3
[[[],[[],[[[],[]]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,2,3,1] => 3
[[[],[[],[[[[]]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,4] => 4
[[[],[[[]],[],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => 3
[[[],[[[]],[],[[]]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => 3
[[[],[[[]],[[]],[]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => 3
[[[],[[[]],[[],[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => 3
[[[],[[[]],[[[]]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,3] => 3
[[[],[[[],[]],[],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1] => 3
[[[],[[[[]]],[],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,4,1,1] => 4
[[[],[[[],[]],[[]]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,1,2] => 3
[[[],[[[[]]],[[]]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,4,2] => 4
[[[],[[[],[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1] => 3
[[[],[[[],[[]]],[]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,2,1] => 3
[[[],[[[[]],[]],[]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,4,1,1] => 4
[[[],[[[[],[]]],[]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1] => 4
[[[],[[[[[]]]],[]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,5,1] => 5
[[[],[[[],[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1] => 3
[[[],[[[],[],[[]]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,1,2] => 3
[[[],[[[],[[]],[]]]]] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,2,1] => 3
[[[],[[[],[[],[]]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,2,1] => 3
[[[],[[[],[[[]]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,3] => 3
[[[],[[[[]],[],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1] => 4
[[[],[[[[]],[[]]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,4,2] => 4
[[[],[[[[],[]],[]]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,4,1,1] => 4
[[[],[[[[[]]],[]]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,5,1] => 5
[[[],[[[[],[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1] => 4
[[[],[[[[],[[]]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,2] => 4
[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,5,1] => 5
[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,5,1] => 5
[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,6] => 6
[[[[]],[],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 3
[[[[]],[],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 3
[[[[]],[],[],[[]],[]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 3
[[[[]],[],[],[[],[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 3
[[[[]],[],[],[[[]]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 3
[[[[]],[],[[]],[],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 3
[[[[]],[],[[]],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 3
[[[[]],[],[[],[]],[]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 3
[[[[]],[],[[[]]],[]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 3
[[[[]],[],[[],[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 3
[[[[]],[],[[],[[]]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 3
[[[[]],[],[[[]],[]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 3
[[[[]],[],[[[],[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 3
[[[[]],[],[[[[]]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 4
[[[[]],[[]],[],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 3
[[[[]],[[]],[],[[]]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => 3
[[[[]],[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => 3
[[[[]],[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => 3
[[[[]],[[]],[[[]]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,2,3] => 3
[[[[]],[[],[]],[],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => 3
[[[[]],[[[]]],[],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,3,1,1] => 3
[[[[]],[[],[]],[[]]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => 3
[[[[]],[[[]]],[[]]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,3,2] => 3
[[[[]],[[],[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => 3
[[[[]],[[],[[]]],[]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => 3
[[[[]],[[[]],[]],[]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,3,1,1] => 3
[[[[]],[[[],[]]],[]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,3,1,1] => 3
[[[[]],[[[[]]]],[]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1] => 4
[[[[]],[[],[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 3
[[[[]],[[],[],[[]]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => 3
[[[[]],[[],[[]],[]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => 3
[[[[]],[[],[[],[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 3
[[[[]],[[],[[[]]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,3] => 3
[[[[]],[[[]],[],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,3,1,1] => 3
[[[[]],[[[]],[[]]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,2] => 3
[[[[]],[[[],[]],[]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,3,1,1] => 3
[[[[]],[[[[]]],[]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1] => 4
[[[[]],[[[],[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,3,1,1] => 3
[[[[]],[[[],[[]]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2] => 3
[[[[]],[[[[]],[]]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1] => 4
[[[[]],[[[[],[]]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,1] => 4
[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,5] => 5
[[[[],[]],[],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 3
[[[[[]]],[],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 4
[[[[],[]],[],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 3
[[[[[]]],[],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,1,2] => 4
[[[[],[]],[],[[]],[]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 3
[[[[[]]],[],[[]],[]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,1] => 4
[[[[],[]],[],[[],[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 3
[[[[],[]],[],[[[]]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 3
[[[[[]]],[],[[],[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,1] => 4
[[[[[]]],[],[[[]]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,3] => 4
[[[[],[]],[[]],[],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 3
[[[[[]]],[[]],[],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,2,1,1] => 4
[[[[],[]],[[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 3
[[[[[]]],[[]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,2,2] => 4
[[[[],[]],[[],[]],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 3
[[[[],[]],[[[]]],[]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 3
[[[[[]]],[[],[]],[]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 4
[[[[[]]],[[[]]],[]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,1] => 4
[[[[],[]],[[],[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 3
[[[[],[]],[[],[[]]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 3
[[[[],[]],[[[]],[]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 3
[[[[],[]],[[[],[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 3
[[[[],[]],[[[[]]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 4
[[[[[]]],[[],[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,2,1,1] => 4
[[[[[]]],[[],[[]]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,2,2] => 4
[[[[[]]],[[[]],[]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,1] => 4
[[[[[]]],[[[],[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,1] => 4
[[[[[]]],[[[[]]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4] => 4
[[[[],[],[]],[],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 3
[[[[],[[]]],[],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 3
[[[[[]],[]],[],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 4
[[[[[],[]]],[],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 4
[[[[[[]]]],[],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1] => 5
[[[[],[],[]],[],[[]]]] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 3
[[[[],[[]]],[],[[]]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => 3
[[[[[]],[]],[],[[]]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => 4
[[[[[],[]]],[],[[]]]] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => 4
[[[[[[]]]],[],[[]]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2] => 5
[[[[],[],[]],[[]],[]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 3
[[[[],[[]]],[[]],[]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => 3
[[[[[]],[]],[[]],[]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 4
[[[[[],[]]],[[]],[]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 4
[[[[[[]]]],[[]],[]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,2,1] => 5
[[[[],[],[]],[[],[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 3
[[[[],[],[]],[[[]]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,3] => 3
[[[[],[[]]],[[],[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => 3
[[[[],[[]]],[[[]]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,2,3] => 3
[[[[[]],[]],[[],[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 4
[[[[[]],[]],[[[]]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,3] => 4
[[[[[],[]]],[[],[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 4
[[[[[],[]]],[[[]]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,3] => 4
[[[[[[]]]],[[],[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,2,1] => 5
[[[[[[]]]],[[[]]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,3] => 5
[[[[],[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1] => 3
[[[[],[],[[]]],[],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1] => 3
[[[[],[[]],[]],[],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => 3
[[[[],[[],[]]],[],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1] => 3
[[[[],[[[]]]],[],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,3,1,1] => 3
[[[[[]],[],[]],[],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => 4
[[[[[]],[[]]],[],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,2,1,1] => 4
[[[[[],[]],[]],[],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => 4
[[[[[[]]],[]],[],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1] => 5
[[[[[],[],[]]],[],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1] => 4
[[[[[],[[]]]],[],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,2,1,1] => 4
[[[[[[]],[]]],[],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,1,1] => 5
[[[[[[],[]]]],[],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,1,1,1] => 5
[[[[[[[]]]]],[],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1] => 6
[[[[],[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,2] => 3
[[[[],[],[[]]],[[]]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2] => 3
[[[[],[[]],[]],[[]]]] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => 3
[[[[],[[],[]]],[[]]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,2,1,2] => 3
[[[[],[[[]]]],[[]]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,3,2] => 3
[[[[[]],[],[]],[[]]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => 4
[[[[[]],[[]]],[[]]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,2,2] => 4
[[[[[],[]],[]],[[]]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => 4
[[[[[[]]],[]],[[]]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2] => 5
[[[[[],[],[]]],[[]]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,2] => 4
[[[[[],[[]]]],[[]]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,2,2] => 4
[[[[[[]],[]]],[[]]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,2] => 5
[[[[[[],[]]]],[[]]]] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,1,2] => 5
[[[[[[[]]]]],[[]]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,2] => 6
[[[[],[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1] => 3
[[[[],[],[],[[]]],[]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,2,1] => 3
[[[[],[],[[]],[]],[]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,1,2,1,1] => 3
[[[[],[],[[],[]]],[]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,1,1] => 3
[[[[],[],[[[]]]],[]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,3,1] => 3
[[[[],[[]],[],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => 3
[[[[],[[]],[[]]],[]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => 3
[[[[],[[],[]],[]],[]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,1,1,1] => 3
[[[[],[[[]]],[]],[]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,3,1,1] => 3
[[[[],[[],[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1] => 3
[[[[],[[],[[]]]],[]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,2,2,1] => 3
[[[[],[[[]],[]]],[]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,3,1,1] => 3
[[[[],[[[],[]]]],[]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,3,1,1] => 3
[[[[],[[[[]]]]],[]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,4,1] => 4
[[[[[]],[],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => 4
[[[[[]],[],[[]]],[]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 4
[[[[[]],[[]],[]],[]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,1,1] => 4
[[[[[]],[[],[]]],[]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,2,1,1] => 4
[[[[[]],[[[]]]],[]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,1] => 4
[[[[[],[]],[],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => 4
[[[[[[]]],[],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,1,1] => 5
[[[[[],[]],[[]]],[]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 4
[[[[[[]]],[[]]],[]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,2,1] => 5
[[[[[],[],[]],[]],[]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1] => 4
[[[[[],[[]]],[]],[]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,1,1] => 4
[[[[[[]],[]],[]],[]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1] => 5
[[[[[[],[]]],[]],[]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1] => 5
[[[[[[[]]]],[]],[]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,1] => 6
[[[[[],[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1] => 4
[[[[[],[],[[]]]],[]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,2,1] => 4
[[[[[],[[]],[]]],[]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,2,1,1] => 4
[[[[[],[[],[]]]],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,1,1] => 4
[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,3,1] => 4
[[[[[[]],[],[]]],[]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,1,1] => 5
[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,2,1] => 5
[[[[[[],[]],[]]],[]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,1,1,1] => 5
[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,1] => 6
[[[[[[],[],[]]]],[]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1] => 5
[[[[[[],[[]]]]],[]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,2,1] => 5
[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,1] => 6
[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1] => 6
[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1] => 7
[[[[],[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1] => 3
[[[[],[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,2] => 3
[[[[],[],[],[[]],[]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,2,1] => 3
[[[[],[],[],[[],[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,1] => 3
[[[[],[],[],[[[]]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,3] => 3
[[[[],[],[[]],[],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,2,1,1] => 3
[[[[],[],[[]],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,2,2] => 3
[[[[],[],[[],[]],[]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1] => 3
[[[[],[],[[[]]],[]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,3,1] => 3
[[[[],[],[[],[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1] => 3
[[[[],[],[[],[[]]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,2,2] => 3
[[[[],[],[[[]],[]]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,3,1] => 3
[[[[],[],[[[],[]]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,3,1] => 3
[[[[],[],[[[[]]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,4] => 4
[[[[],[[]],[],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 3
[[[[],[[]],[],[[]]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => 3
[[[[],[[]],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => 3
[[[[],[[]],[[],[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 3
[[[[],[[]],[[[]]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,2,3] => 3
[[[[],[[],[]],[],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1] => 3
[[[[],[[[]]],[],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1] => 3
[[[[],[[],[]],[[]]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,2] => 3
[[[[],[[[]]],[[]]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3,2] => 3
[[[[],[[],[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1] => 3
[[[[],[[],[[]]],[]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,2,2,1] => 3
[[[[],[[[]],[]],[]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1] => 3
[[[[],[[[],[]]],[]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1] => 3
[[[[],[[[[]]]],[]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,4,1] => 4
[[[[],[[],[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 3
[[[[],[[],[],[[]]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,2] => 3
[[[[],[[],[[]],[]]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,2,2,1] => 3
[[[[],[[],[[],[]]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 3
[[[[],[[],[[[]]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,2,3] => 3
[[[[],[[[]],[],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,3,1,1] => 3
[[[[],[[[]],[[]]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,2] => 3
[[[[],[[[],[]],[]]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1] => 3
[[[[],[[[[]]],[]]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,4,1] => 4
[[[[],[[[],[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1] => 3
[[[[],[[[],[[]]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 3
[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,1] => 4
[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,1] => 4
[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,5] => 5
[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => 4
[[[[[]],[],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => 4
[[[[[]],[],[[]],[]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 4
[[[[[]],[],[[],[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 4
[[[[[]],[],[[[]]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,1,3] => 4
[[[[[]],[[]],[],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,2,1,1] => 4
[[[[[]],[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2] => 4
[[[[[]],[[],[]],[]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 4
[[[[[]],[[[]]],[]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,1] => 4
[[[[[]],[[],[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,2,1,1] => 4
[[[[[]],[[],[[]]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,2,2] => 4
[[[[[]],[[[]],[]]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,1] => 4
[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,1] => 4
[[[[[]],[[[[]]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4] => 4
[[[[[],[]],[],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => 4
[[[[[[]]],[],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1] => 5
[[[[[],[]],[],[[]]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => 4
[[[[[[]]],[],[[]]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2] => 5
[[[[[],[]],[[]],[]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 4
[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,2,1] => 5
[[[[[],[]],[[],[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 4
[[[[[],[]],[[[]]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,3] => 4
[[[[[[]]],[[],[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,2,1] => 5
[[[[[[]]],[[[]]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,3] => 5
[[[[[],[],[]],[],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1] => 4
[[[[[],[[]]],[],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,2,1,1] => 4
[[[[[[]],[]],[],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1] => 5
[[[[[[],[]]],[],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1] => 5
[[[[[[[]]]],[],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,1] => 6
[[[[[],[],[]],[[]]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,2] => 4
[[[[[],[[]]],[[]]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,2,2] => 4
[[[[[[]],[]],[[]]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,2] => 5
[[[[[[],[]]],[[]]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,1,2] => 5
[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,2] => 6
[[[[[],[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1] => 4
[[[[[],[],[[]]],[]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,1,2,1] => 4
[[[[[],[[]],[]],[]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,2,1,1] => 4
[[[[[],[[],[]]],[]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1] => 4
[[[[[],[[[]]]],[]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,3,1] => 4
[[[[[[]],[],[]],[]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1] => 5
[[[[[[]],[[]]],[]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,1] => 5
[[[[[[],[]],[]],[]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,1,1,1] => 5
[[[[[[[]]],[]],[]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,1] => 6
[[[[[[],[],[]]],[]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1] => 5
[[[[[[],[[]]]],[]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,2,1] => 5
[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1] => 6
[[[[[[[],[]]]],[]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1] => 6
[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1] => 7
[[[[[],[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1] => 4
[[[[[],[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,2] => 4
[[[[[],[],[[]],[]]]]] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,2,1] => 4
[[[[[],[],[[],[]]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,2,1] => 4
[[[[[],[],[[[]]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,3] => 4
[[[[[],[[]],[],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1] => 4
[[[[[],[[]],[[]]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,2,2] => 4
[[[[[],[[],[]],[]]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 4
[[[[[],[[[]]],[]]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,3,1] => 4
[[[[[],[[],[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1] => 4
[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,2,2] => 4
[[[[[],[[[]],[]]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,3,1] => 4
[[[[[],[[[],[]]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,1] => 4
[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,4] => 4
[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1] => 5
[[[[[[]],[],[[]]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,1,2] => 5
[[[[[[]],[[]],[]]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,2,1] => 5
[[[[[[]],[[],[]]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,2,1] => 5
[[[[[[]],[[[]]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,3] => 5
[[[[[[],[]],[],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1] => 5
[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,1] => 6
[[[[[[],[]],[[]]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,2] => 5
[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,2] => 6
[[[[[[],[],[]],[]]]]] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1] => 5
[[[[[[],[[]]],[]]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,1] => 5
[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1] => 6
[[[[[[[],[]]],[]]]]] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1] => 6
[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1] => 7
[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1] => 5
[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,2] => 5
[[[[[[],[[]],[]]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,2,1] => 5
[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,2,1] => 5
[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,3] => 5
[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1] => 6
[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,2] => 6
[[[[[[[],[]],[]]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1] => 6
[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1] => 7
[[[[[[[],[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1] => 6
[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,2] => 6
[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1] => 7
[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,1] => 7
[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => 8
[[],[[[[],[]],[]],[[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,4,1,1,2,1] => 4
[[],[[[[[],[]],[]],[]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,5,1,1,1,1] => 5
[[[],[]],[[],[[[],[]],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,2,3,1,1] => 3
[[[[],[]],[]],[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,1,3,1,1] => 3
[[[],[[],[[],[[],[]]]]],[]] => [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [2,2,2,2,1,1] => 2
[[[[],[[],[]]],[[],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,2,1,1] => 3
[[[[],[[[],[]],[]]],[]],[]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [3,3,1,1,1,1] => 3
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,8,4,1 1,20,15,5,1 1,50,53,21,6,1 1,126,182,84,28,7,1 1,322,616,326,120,36,8,1
$F_{2} = q$
$F_{3} = q + q^{2}$
$F_{4} = q + 3\ q^{2} + q^{3}$
$F_{5} = q + 8\ q^{2} + 4\ q^{3} + q^{4}$
$F_{6} = q + 20\ q^{2} + 15\ q^{3} + 5\ q^{4} + q^{5}$
$F_{7} = q + 50\ q^{2} + 53\ q^{3} + 21\ q^{4} + 6\ q^{5} + q^{6}$
$F_{8} = q + 126\ q^{2} + 182\ q^{3} + 84\ q^{4} + 28\ q^{5} + 7\ q^{6} + q^{7}$
$F_{9} = q + 322\ q^{2} + 616\ q^{3} + 326\ q^{4} + 120\ q^{5} + 36\ q^{6} + 8\ q^{7} + q^{8}$
Description
The largest part of an integer composition.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path to the depth of the tree.
This sends the maximal height of the Dyck path to the depth of the tree.
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