Identifier
-
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
St001038: Dyck paths ⟶ ℤ
Values
[[],[]] => [1,0,1,0] => 2
[[[]]] => [1,1,0,0] => 1
[[],[],[]] => [1,0,1,0,1,0] => 3
[[],[[]]] => [1,0,1,1,0,0] => 1
[[[]],[]] => [1,1,0,0,1,0] => 1
[[[],[]]] => [1,1,0,1,0,0] => 1
[[[[]]]] => [1,1,1,0,0,0] => 2
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => 4
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => 1
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => 2
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => 1
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => 2
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => 1
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => 1
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => 1
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => 2
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => 1
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => 1
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => 1
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => 3
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => 2
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => 5
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => 2
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => 1
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => 2
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => 2
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => 1
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => 1
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => 3
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => 1
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => 2
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => 1
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => 3
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => 2
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => 1
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => 1
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => 1
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => 1
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => 1
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => 1
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => 2
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => 1
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => 1
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => 1
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => 1
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => 2
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => 3
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => 2
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => 1
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => 1
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => 1
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => 1
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => 1
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => 1
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => 2
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => 1
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => 1
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => 4
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => 2
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => 2
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => 2
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => 3
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 4
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
>>> Load all 1200 entries. <<<[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 1
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 2
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 3
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => 1
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => 4
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2
[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3
[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1
[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 5
[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1
[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1
[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 4
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 1
[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1
[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1
[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1
[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1
[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 1
[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 1
[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 1
[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 1
[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 1
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1
[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1
[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 1
[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3
[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 1
[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 1
[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1
[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1
[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1
[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 1
[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1
[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1
[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 1
[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 1
[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1
[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3
[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 4
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 4
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 1
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 1
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 1
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 1
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2
[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2
[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 2
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 2
[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 2
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 1
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 2
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 4
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 2
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 2
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 4
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 3
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 3
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[[],[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[[],[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[],[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[[],[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[[],[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[[],[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[[],[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[[],[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[[],[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[[],[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[[],[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2
[[],[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[[],[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[[],[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[],[],[],[[]],[],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[],[],[],[[]],[],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[[],[],[],[[]],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[[],[],[],[[]],[[],[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[[],[],[],[[]],[[[]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[],[],[],[[],[]],[],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[[],[],[],[[[]]],[],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[[],[],[],[[],[]],[[]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[[],[],[],[[[]]],[[]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[[],[],[],[[],[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[[],[],[],[[],[[]]],[]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[[],[],[],[[[]],[]],[]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[[],[],[],[[[],[]]],[]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[[],[],[],[[[[]]]],[]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[],[],[],[[],[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[[],[],[],[[],[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[[],[],[],[[],[[]],[]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[[],[],[],[[],[[],[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[[],[],[],[[],[[[]]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
[[],[],[],[[[]],[],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[[],[],[],[[[]],[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[[],[],[],[[[],[]],[]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[[],[],[],[[[[]]],[]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[[],[],[],[[[],[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[[],[],[],[[[],[[]]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[],[],[],[[[[]],[]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[[],[],[],[[[[],[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[[],[],[],[[[[[]]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[],[],[[]],[],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3
[[],[],[[]],[],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[[],[],[[]],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[[],[],[[]],[],[[],[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[[],[],[[]],[],[[[]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[],[],[[]],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[[],[],[[]],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[[],[],[[]],[[],[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[[],[],[[]],[[[]]],[]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[[],[],[[]],[[],[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[[],[],[[]],[[],[[]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[],[],[[]],[[[]],[]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[[],[],[[]],[[[],[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[[],[],[[]],[[[[]]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[],[],[[],[]],[],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[[],[],[[],[]],[],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[[],[],[[[]]],[],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[[],[],[[],[]],[[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[[],[],[[[]]],[[]],[]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[],[],[[],[]],[[],[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[[],[],[[],[]],[[[]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[[],[],[[[]]],[[],[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[[],[],[[[]]],[[[]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[[],[],[[],[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[[],[],[[],[[]]],[],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[[],[],[[[]],[]],[],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[[],[],[[[],[]]],[],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[[],[],[[[[]]]],[],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[],[],[[],[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[[],[],[[],[[]]],[[]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[[],[],[[[]],[]],[[]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[[],[],[[[],[]]],[[]]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[[],[],[[[[]]]],[[]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[],[],[[],[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[[],[],[[],[],[[]]],[]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[[],[],[[],[[]],[]],[]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[[],[],[[],[[],[]]],[]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[[],[],[[],[[[]]]],[]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[[],[],[[[]],[],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1
[[],[],[[[]],[[]]],[]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[[],[],[[[],[]],[]],[]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[[],[],[[[[]]],[]],[]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[[],[],[[[],[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 5
[[],[],[[[],[[]]]],[]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[[],[],[[[[]],[]]],[]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[[],[],[[[[],[]]]],[]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[[],[],[[],[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[[],[],[[],[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[[],[],[[],[],[[]],[]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[[],[],[[],[],[[],[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[[],[],[[],[],[[[]]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[[],[],[[],[[]],[],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[[],[],[[],[[]],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[[],[],[[],[[],[]],[]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[[],[],[[],[[[]]],[]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[[],[],[[],[[],[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[[],[],[[],[[],[[]]]]] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[[],[],[[],[[[]],[]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[[],[],[[],[[[],[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[[],[],[[],[[[[]]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[[],[],[[[]],[],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[[],[],[[[]],[],[[]]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[[],[],[[[]],[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1
[[],[],[[[]],[[],[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[],[],[[[]],[[[]]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[[],[],[[[],[]],[],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[[],[],[[[[]]],[],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[[],[],[[[],[]],[[]]]] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[[],[],[[[[]]],[[]]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[],[],[[[],[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[[],[],[[[],[[]]],[]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[[],[],[[[[]],[]],[]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1
[[],[],[[[[],[]]],[]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[[],[],[[[[[]]]],[]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[],[],[[[],[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[[],[],[[[],[],[[]]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[],[],[[[],[[]],[]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[[],[],[[[],[[],[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[[],[],[[[],[[[]]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[],[],[[[[]],[],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[[],[],[[[[]],[[]]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[[],[],[[[[],[]],[]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[[],[],[[[[[]]],[]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 4
[[],[],[[[[],[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[[],[],[[[[],[[]]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[],[],[[[[[]],[]]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[[],[],[[[[[],[]]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[[],[[]],[],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[[],[[]],[],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[[],[[]],[],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[[],[[]],[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[[],[[]],[],[[]],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[[],[[]],[],[[],[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[[],[[]],[],[[[]]],[]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[[],[[]],[],[[],[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[[],[[]],[],[[],[[]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2
[[],[[]],[],[[[]],[]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[[],[[]],[],[[[],[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[[],[[]],[],[[[[]]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[],[[]],[[]],[],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[[],[[]],[[]],[],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[[],[[]],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[[],[[]],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 1
[[],[[]],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[[],[[]],[[],[]],[],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[[],[[]],[[[]]],[],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[[],[[]],[[],[]],[[]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1
[[],[[]],[[[]]],[[]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[[],[[]],[[],[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[[],[[]],[[],[[]]],[]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[[],[[]],[[[]],[]],[]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2
[[],[[]],[[[],[]]],[]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[[],[[]],[[[[]]]],[]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[],[[]],[[],[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[[],[[]],[[],[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[[],[[]],[[],[[]],[]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 1
[[],[[]],[[],[[],[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[[],[[]],[[],[[[]]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[],[[]],[[[]],[],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 1
[[],[[]],[[[]],[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[[],[[]],[[[],[]],[]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 1
[[],[[]],[[[[]]],[]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 1
[[],[[]],[[[],[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[[],[[]],[[[],[[]]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[],[[]],[[[[]],[]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[[],[[]],[[[[],[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[],[[],[]],[],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[[],[[],[]],[],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[[],[[[]]],[],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[[],[[],[]],[],[[]],[]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[[],[[[]]],[],[[]],[]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[[],[[],[]],[],[[],[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[[],[[],[]],[],[[[]]]] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[[],[[[]]],[],[[],[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[[],[[[]]],[],[[[]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[[],[[],[]],[[]],[],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[[],[[[]]],[[]],[],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[[],[[],[]],[[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1
[[],[[[]]],[[]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[[],[[],[]],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1
[[],[[],[]],[[[]]],[]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[[],[[[]]],[[],[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[[],[[[]]],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[[],[[],[]],[[],[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[[],[[],[]],[[],[[]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[[],[[],[]],[[[]],[]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1
[[],[[],[]],[[[],[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[[],[[],[]],[[[[]]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[[],[[[]]],[[],[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[[],[[[]]],[[],[[]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[[],[[[]]],[[[]],[]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 1
[[],[[[]]],[[[],[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[[],[[[]]],[[[[]]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[[],[[],[],[]],[],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[[],[[],[[]]],[],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[[],[[[]],[]],[],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[[],[[[],[]]],[],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[],[[[[]]]],[],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[[],[[],[],[]],[],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[[],[[],[[]]],[],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[[],[[[]],[]],[],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[[],[[[],[]]],[],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[[],[[[[]]]],[],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[[],[[],[],[]],[[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[[],[[],[[]]],[[]],[]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[[],[[[]],[]],[[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[[],[[[],[]]],[[]],[]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[[],[[[[]]]],[[]],[]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[],[[],[],[]],[[],[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[[],[[],[],[]],[[[]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[[],[[],[[]]],[[],[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[[],[[],[[]]],[[[]]]] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 2
[[],[[[]],[]],[[],[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 1
[[],[[[]],[]],[[[]]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[[],[[[],[]]],[[],[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[[],[[[],[]]],[[[]]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[[],[[[[]]]],[[],[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[[],[[[[]]]],[[[]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[[],[[],[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[[],[[],[],[[]]],[],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[[],[[],[[]],[]],[],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[[],[[],[[],[]]],[],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2
[[],[[],[[[]]]],[],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2
[[],[[[]],[],[]],[],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[[],[[[]],[[]]],[],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[[],[[[],[]],[]],[],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[[],[[[[]]],[]],[],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[[],[[[],[],[]]],[],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5
[[],[[[],[[]]]],[],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[[],[[[[]],[]]],[],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[[],[[[[],[]]]],[],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[[],[[],[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[[],[[],[],[[]]],[[]]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[[],[[],[[]],[]],[[]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1
[[],[[],[[],[]]],[[]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[[],[[],[[[]]]],[[]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[[],[[[]],[],[]],[[]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[[],[[[]],[[]]],[[]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[[],[[[],[]],[]],[[]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1
[[],[[[[]]],[]],[[]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[[],[[[],[],[]]],[[]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[[],[[[],[[]]]],[[]]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[[],[[[[]],[]]],[[]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[[],[[[[],[]]]],[[]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[],[[],[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[[],[[],[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[[],[[],[],[[]],[]],[]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1
[[],[[],[],[[],[]]],[]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[[],[[],[],[[[]]]],[]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[[],[[],[[]],[],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 1
[[],[[],[[]],[[]]],[]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[[],[[],[[],[]],[]],[]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[[],[[],[[[]]],[]],[]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[[],[[],[[],[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2
[[],[[],[[],[[]]]],[]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[[],[[],[[[]],[]]],[]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[[],[[],[[[],[]]]],[]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2
[[],[[],[[[[]]]]],[]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[[],[[[]],[],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[[],[[[]],[],[[]]],[]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[[],[[[]],[[]],[]],[]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[[],[[[]],[[],[]]],[]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[[],[[[]],[[[]]]],[]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[[],[[[],[]],[],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1
[[],[[[[]]],[],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[[],[[[],[]],[[]]],[]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3
[[],[[[[]]],[[]]],[]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[[],[[[],[],[]],[]],[]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[[],[[[],[[]]],[]],[]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[[],[[[[]],[]],[]],[]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[[],[[[[],[]]],[]],[]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[[],[[[[[]]]],[]],[]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[[],[[[],[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 6
[[],[[[],[],[[]]]],[]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[[],[[[],[[]],[]]],[]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[[],[[[],[[],[]]]],[]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[[],[[[],[[[]]]]],[]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 4
[[],[[[[]],[],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[[],[[[[]],[[]]]],[]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 3
[[],[[[[],[]],[]]],[]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[[],[[[[[]]],[]]],[]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 4
[[],[[[[],[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[[],[[[[],[[]]]]],[]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[[],[[[[[]],[]]]],[]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[[],[[[[[],[]]]]],[]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 4
[[],[[[[[[]]]]]],[]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[[],[[],[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[[],[[],[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[[],[[],[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[[],[[],[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[[],[[],[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[[],[[],[],[[]],[],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[[],[[],[],[[]],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[[],[[],[],[[],[]],[]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[[],[[],[],[[[]]],[]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[[],[[],[],[[],[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[[],[[],[],[[],[[]]]]] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[[],[[],[],[[[]],[]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[[],[[],[],[[[],[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[[],[[],[],[[[[]]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[[],[[],[[]],[],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[[],[[],[[]],[],[[]]]] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 2
[[],[[],[[]],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1
[[],[[],[[]],[[],[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2
[[],[[],[[]],[[[]]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 2
[[],[[],[[],[]],[],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[[],[[],[[[]]],[],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[[],[[],[[],[]],[[]]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 2
[[],[[],[[[]]],[[]]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 2
[[],[[],[[],[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[[],[[],[[],[[]]],[]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1
[[],[[],[[[]],[]],[]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1
[[],[[],[[[],[]]],[]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[[],[[],[[[[]]]],[]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[[],[[],[[],[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[[],[[],[[],[],[[]]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 2
[[],[[],[[],[[]],[]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2
[[],[[],[[],[[],[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[[],[[],[[],[[[]]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[[],[[],[[[]],[],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[[],[[],[[[]],[[]]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 2
[[],[[],[[[],[]],[]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[[],[[],[[[[]]],[]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[[],[[],[[[],[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[[],[[],[[[],[[]]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[[],[[],[[[[]],[]]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[[],[[],[[[[],[]]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[[],[[],[[[[[]]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[[],[[[]],[],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[[],[[[]],[],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[[],[[[]],[],[[]],[]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 1
[[],[[[]],[],[[],[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2
[[],[[[]],[],[[[]]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[[],[[[]],[[]],[],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 1
[[],[[[]],[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[[],[[[]],[[],[]],[]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 1
[[],[[[]],[[[]]],[]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 1
[[],[[[]],[[],[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[[],[[[]],[[],[[]]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2
[[],[[[]],[[[]],[]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 3
[[],[[[]],[[[],[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[[],[[[]],[[[[]]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[[],[[[],[]],[],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[[],[[[[]]],[],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[[],[[[],[]],[],[[]]]] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 2
[[],[[[[]]],[],[[]]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[[],[[[],[]],[[]],[]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[[],[[[[]]],[[]],[]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[[],[[[],[]],[[],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[[],[[[],[]],[[[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[[],[[[[]]],[[],[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[[],[[[[]]],[[[]]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2
[[],[[[],[],[]],[],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[[],[[[],[[]]],[],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[[],[[[[]],[]],[],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[[],[[[[],[]]],[],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[[],[[[[[]]]],[],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[[],[[[],[],[]],[[]]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[[],[[[],[[]]],[[]]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 2
[[],[[[[]],[]],[[]]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[[],[[[[],[]]],[[]]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 2
[[],[[[[[]]]],[[]]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2
[[],[[[],[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[[],[[[],[],[[]]],[]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[[],[[[],[[]],[]],[]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1
[[],[[[],[[],[]]],[]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[[],[[[],[[[]]]],[]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[[],[[[[]],[],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[[],[[[[]],[[]]],[]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 1
[[],[[[[],[]],[]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1
[[],[[[[[]]],[]],[]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[[],[[[[],[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[[],[[[[],[[]]]],[]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[[],[[[[[]],[]]],[]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[[],[[[[[],[]]]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[[],[[[[[[]]]]],[]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[[],[[[],[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[[],[[[],[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[[],[[[],[],[[]],[]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3
[[],[[[],[],[[],[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[[],[[[],[],[[[]]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[[],[[[],[[]],[],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 4
[[],[[[],[[]],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 2
[[],[[[],[[],[]],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[[],[[[],[[[]]],[]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 4
[[],[[[],[[],[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[[],[[[],[[],[[]]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[[],[[[],[[[]],[]]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[[],[[[],[[[],[]]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[[],[[[],[[[[]]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[[],[[[[]],[],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[[],[[[[]],[],[[]]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2
[[],[[[[]],[[]],[]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 3
[[],[[[[]],[[],[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2
[[],[[[[]],[[[]]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[[],[[[[],[]],[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[[],[[[[[]]],[],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 4
[[],[[[[],[]],[[]]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 2
[[],[[[[[]]],[[]]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 2
[[],[[[[],[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[[],[[[[],[[]]],[]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 3
[[],[[[[[]],[]],[]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[[],[[[[[],[]]],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 5
[[],[[[[[[]]]],[]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[[],[[[[],[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[[],[[[[],[],[[]]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[[],[[[[],[[]],[]]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[[],[[[[],[[],[]]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[[],[[[[[]],[[]]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 3
[[],[[[[[],[]],[]]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 4
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[[]],[],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[[[]],[],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[[]],[],[],[[]],[],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[[[]],[],[],[[]],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[[[]],[],[],[[],[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[[[]],[],[],[[[]]],[]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[[[]],[],[],[[],[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[[[]],[],[],[[],[[]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[[[]],[],[],[[[]],[]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[[[]],[],[],[[[],[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[[]],[],[],[[[[]]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[[[]],[],[[]],[],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[[[]],[],[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[[[]],[],[[]],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[[[]],[],[[]],[[],[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[[[]],[],[[]],[[[]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[[[]],[],[[],[]],[],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[[[]],[],[[[]]],[],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[[[]],[],[[],[]],[[]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[[[]],[],[[[]]],[[]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[[[]],[],[[],[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[[[]],[],[[],[[]]],[]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[[[]],[],[[[]],[]],[]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 1
[[[]],[],[[[],[]]],[]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[[[]],[],[[[[]]]],[]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[[[]],[],[[],[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[[[]],[],[[],[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[[[]],[],[[],[[]],[]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[[[]],[],[[],[[],[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[[[]],[],[[],[[[]]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[[[]],[],[[[]],[],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[[[]],[],[[[]],[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[[[]],[],[[[],[]],[]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[[[]],[],[[[[]]],[]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[[[]],[],[[[],[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[[]],[],[[[],[[]]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[[[]],[],[[[[]],[]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[[[]],[],[[[[],[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[[[]],[],[[[[[]]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[[]],[[]],[],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[[[]],[[]],[],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[[[]],[[]],[],[[]],[]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[[[]],[[]],[],[[],[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[[[]],[[]],[],[[[]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[[[]],[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[[[]],[[]],[[],[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[[[]],[[]],[[[]]],[]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[[[]],[[]],[[],[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[[[]],[[]],[[],[[]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[[[]],[[]],[[[]],[]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[[[]],[[]],[[[],[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[[]],[[],[]],[],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[[[]],[[],[]],[],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[[[]],[[[]]],[],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[[[]],[[],[]],[[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[[[]],[[[]]],[[]],[]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[[[]],[[],[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[[[]],[[],[]],[[[]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[[[]],[[[]]],[[],[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[[[]],[[[]]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[[]],[[],[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[[[]],[[],[[]]],[],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[[[]],[[[]],[]],[],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1
[[[]],[[[],[]]],[],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[[[]],[[[[]]]],[],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[[[]],[[],[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[[[]],[[],[[]]],[[]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[[[]],[[[]],[]],[[]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[[]],[[],[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[[[]],[[],[],[[]]],[]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[[[]],[[],[[]],[]],[]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 1
[[[]],[[],[[],[]]],[]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[[[]],[[],[[[]]]],[]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[[[]],[[[]],[],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1
[[[]],[[[]],[[]]],[]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[[[]],[[[],[]],[]],[]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 1
[[[]],[[[[]]],[]],[]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1
[[[]],[[[],[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[[[]],[[[],[[]]]],[]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[[[]],[[[[]],[]]],[]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[[[]],[[[[],[]]]],[]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[[]],[[],[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[[[]],[[],[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[[[]],[[],[],[[]],[]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[[[]],[[],[],[[],[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[[[]],[[],[],[[[]]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[[[]],[[],[[]],[],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[[[]],[[],[[]],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[[[]],[[],[[],[]],[]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[[[]],[[],[[[]]],[]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[[[]],[[],[[],[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[[[]],[[],[[],[[]]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[[[]],[[],[[[]],[]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[[[]],[[],[[[],[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[[[]],[[],[[[[]]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[[[]],[[[]],[],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[[[]],[[[]],[],[[]]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[[[]],[[[]],[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1
[[[]],[[[]],[[],[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[[[]],[[[]],[[[]]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[[[]],[[[],[]],[],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[[[]],[[[[]]],[],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[[[]],[[[],[]],[[]]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[[[]],[[[[]]],[[]]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[[]],[[[],[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[[[]],[[[],[[]]],[]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[[[]],[[[[]],[]],[]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1
[[[]],[[[[],[]]],[]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[[[]],[[[],[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[[[]],[[[],[],[[]]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[[[]],[[[],[[]],[]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[[[]],[[[],[[],[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[[[]],[[[[]],[],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[[[]],[[[[]],[[]]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[[[]],[[[[],[]],[]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[[],[]],[],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[[[],[]],[],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[[[],[]],[],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[[[],[]],[],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[[[],[]],[],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[[[],[]],[],[[]],[],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[[[],[]],[],[[]],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[[[],[]],[],[[],[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[[[],[]],[],[[[]]],[]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[[[],[]],[],[[],[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[[[],[]],[],[[],[[]]]] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[[[],[]],[],[[[]],[]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[[[],[]],[],[[[],[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[[[],[]],[],[[[[]]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[[[],[]],[[]],[],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
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Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,1,1 8,4,1,1 24,12,4,1,1 75,38,13,4,1,1 243,125,42,13,4,1,1
$F_{3} = q + q^{2}$
$F_{4} = 3\ q + q^{2} + q^{3}$
$F_{5} = 8\ q + 4\ q^{2} + q^{3} + q^{4}$
$F_{6} = 24\ q + 12\ q^{2} + 4\ q^{3} + q^{4} + q^{5}$
$F_{7} = 75\ q + 38\ q^{2} + 13\ q^{3} + 4\ q^{4} + q^{5} + q^{6}$
$F_{8} = 243\ q + 125\ q^{2} + 42\ q^{3} + 13\ q^{4} + 4\ q^{5} + q^{6} + q^{7}$
Description
The minimal height of a column in the parallelogram polyomino associated with the Dyck path.
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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