Identifier
-
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
St000306: Dyck paths ⟶ ℤ (values match St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: )
Values
[[]] => [1,0] => 0
[[],[]] => [1,0,1,0] => 1
[[[]]] => [1,1,0,0] => 0
[[],[],[]] => [1,0,1,0,1,0] => 2
[[],[[]]] => [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] => 0
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => 3
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => 2
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => 2
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => 2
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => 1
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => 2
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => 1
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => 2
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => 1
[[[],[],[]]] => [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] => 1
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => 0
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => 4
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => 3
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => 3
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => 3
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => 2
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => 3
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => 2
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => 3
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => 2
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => 2
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => 2
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => 2
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => 2
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => 1
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => 3
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => 2
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => 2
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => 2
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => 1
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => 3
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => 2
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => 2
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => 1
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => 2
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => 2
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => 2
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => 2
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => 1
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => 2
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => 1
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => 2
[[[],[[],[]]]] => [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] => 1
[[[[],[]],[]]] => [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] => 1
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => 1
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => 1
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => 1
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => 0
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[],[],[[[]]],[]] => [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] => 3
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 3
[[],[],[[[],[]]]] => [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] => 4
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[],[[]],[[[]]]] => [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] => 4
[[],[[[]]],[],[]] => [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] => 3
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[[],[[[[]]]],[]] => [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] => 3
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[],[[],[[],[]]]] => [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] => 2
[[],[[[]],[[]]]] => [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] => 2
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
>>> Load all 795 entries. <<<[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[[],[[[],[[]]]]] => [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] => 2
[[],[[[[],[]]]]] => [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] => 1
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[[]],[[[[]]]]] => [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] => 4
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[[[]]],[[]],[]] => [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] => 3
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[[[[],[]]],[],[]] => [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] => 2
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[[[[]]]],[[]]] => [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] => 3
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[[[[]],[[]]],[]] => [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] => 2
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[[[[[]],[]]],[]] => [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] => 1
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[[[],[],[[[]]]]] => [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] => 2
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[[[],[[],[[]]]]] => [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] => 2
[[[],[[[],[]]]]] => [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] => 2
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[[[[[]]],[],[]]] => [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] => 1
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[[[[[]],[]],[]]] => [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] => 1
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[[],[],[[[]]],[],[]] => [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] => 4
[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[[],[],[[[],[]]],[]] => [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] => 3
[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[[],[],[[[[]],[]]]] => [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] => 3
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[[],[[]],[[[[]]]]] => [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] => 5
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[[],[[[]]],[[[]]]] => [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] => 4
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[[],[[[],[]]],[],[]] => [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] => 3
[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 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] => 3
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[[],[[],[[],[[]]]]] => [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] => 3
[[],[[],[[[],[]]]]] => [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
[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[],[[[],[[],[]]]]] => [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] => 2
[[],[[[[]],[[]]]]] => [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] => 2
[[],[[[[],[],[]]]]] => [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] => 2
[[],[[[[[]],[]]]]] => [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] => 2
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[[[]],[[[[[]]]]]] => [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] => 5
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 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] => 3
[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 2
[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[[[[[[]]]]],[[]]] => [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] => 3
[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 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] => 2
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[[[[],[[],[]]]],[]] => [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] => 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] => 2
[[[[[],[],[]]]],[]] => [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] => 2
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 2
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 2
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 2
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 2
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 2
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 2
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[[[],[[[[],[]]]]]] => [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] => 2
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[[[[[[]]]],[],[]]] => [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
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[[[[[[]]],[]],[]]] => [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] => 2
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[[[[[[]],[]]],[]]] => [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] => 2
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[],[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[[],[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[[],[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[[],[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[],[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[[],[],[],[[]],[],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[[],[],[],[[[[]]],[]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[],[],[[]],[],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[[],[],[[]],[],[[],[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5
[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[[],[],[[],[[[]]]],[]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[[],[],[[[[]]],[]],[]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[[],[],[[[],[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[[],[],[[[],[[]]]],[]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 4
[[],[],[[[[]],[]]],[]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[[],[],[[[[],[]]]],[]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[[],[],[[],[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[],[],[[[[[]],[]]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[[],[],[[[[[],[]]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[[],[[],[]],[],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5
[[],[[],[]],[],[[],[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5
[[],[[[]]],[[[[]]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[[],[[],[[[]]]],[],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[[],[[[[]]],[]],[],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[[],[[[],[],[]]],[],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[[],[[[],[[]]]],[],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4
[[],[[[[]],[]]],[],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[[],[[[[],[]]]],[],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[],[[[[[[]]]]]],[]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[[],[[],[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[[],[[],[[],[[],[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[[],[[],[[[],[]],[]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[[],[[[],[]],[[],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[[],[[[],[[],[]]],[]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[[],[[[[],[]],[]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 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] => 2
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[[]],[],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[[]],[],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[[[]],[],[],[[]],[],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5
[[[]],[],[],[[],[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[[]],[],[[],[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[[]],[[]],[[[],[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[[]],[[],[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[[]],[[[],[[]],[]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[[[]]],[],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[[[],[]],[],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[[[[]]],[],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[[[],[]],[],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[[[[]]],[],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[[[]]],[[[[]]]],[]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[[],[]],[[],[[],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[[],[]],[[[],[]],[]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[[[],[[]]],[],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[[[[],[]]],[[]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[[[[[]]]],[[]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[[[],[]]],[[[],[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[[[[],[]]],[[[[]]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[[[[[]]]],[[[],[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 2
[[[[[]]]],[[[[]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[[],[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[[],[],[[]]],[],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[[[[],[],[]]],[],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[[[],[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[[],[[],[]]],[[],[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[[[[],[]],[]],[[],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[[],[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[[[[]],[],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[[[[],[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[[[],[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[[[],[[[[]]]]],[[]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[[[],[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[[[[],[[]],[]]],[[]]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[[[[],[[[]]]]],[[]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[[[[[[]]],[]]],[[]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 2
[[[[[],[],[]]]],[[]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 2
[[[[[],[[]]]]],[[]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 2
[[[[[[]],[]]]],[[]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 2
[[[[[[],[]]]]],[[]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 2
[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[[],[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[[[],[[],[[],[]]]],[]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[[[],[[[],[]],[]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[[[[]],[],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[[[[],[]],[[],[]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[[[[],[[],[]]],[]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[[[[],[]],[]],[]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[[[[],[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[[[[],[[[[]]]]]],[]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[[[[[[]]],[[]]]],[]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[[[[[],[],[[]]]]],[]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 2
[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 2
[[[[[[]],[[]]]]],[]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2
[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 2
[[[[[[],[[]]]]]],[]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 2
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 2
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[[],[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[[[],[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[[[],[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[[[],[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[[[],[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[[[],[],[],[[]],[],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[[[],[],[],[[],[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[[[],[],[[]],[],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[[[],[[]],[],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[[[]],[],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[[[[]],[[]],[],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[[[[],[]],[],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[[[],[],[]],[],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[[[[],[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 2
[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 1
[[[[[[],[],[]]]],[]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 2
[[[[[[],[[]]]]],[]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 2
[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 1
[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[[[[],[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[[[[],[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[[[[],[[]],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[[[[],[[]],[[[]]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[[[[],[[[[]]]],[]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[[[[],[[[]],[],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[[[[],[[[]],[[]]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[[[[],[[[[]]],[]]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 2
[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 1
[[[[[[]]],[[[]]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[[[[[],[],[[]]],[]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 2
[[[[[],[[[]]]],[]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 2
[[[[[[]],[[]]],[]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 1
[[[[[[],[[]]]],[]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[[[[[],[],[[],[]]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 1
[[[[[],[],[[[]]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 1
[[[[[],[[],[]],[]]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 1
[[[[[],[[[]]],[]]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 1
[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 1
[[[[[],[[[],[]]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 1
[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[[[[[[]],[[[]]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[[[[[[],[[]]],[]]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 1
[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 1
[[[[[[[],[]]],[]]]]] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 1
[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 1
[[[[[[],[[]],[]]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 1
[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 1
[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[[[[[[[],[]],[]]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[[[[[[[],[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 1
[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[[],[[],[[],[[],[[],[]]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[[],[[],[[],[[[],[]],[]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 3
[[],[[],[[[],[]],[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 3
[[],[[],[[[],[[],[]]],[]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 3
[[],[[],[[[[],[]],[]],[]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 3
[[],[[[],[]],[[],[[],[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[[],[[[],[]],[[[],[]],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[[],[[[],[[],[]]],[[],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 3
[[],[[[[],[]],[]],[[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 3
[[],[[[],[[],[[],[]]]],[]]] => [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 3
[[],[[[],[[[],[]],[]]],[]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 3
[[],[[[[],[]],[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 3
[[],[[[[],[[],[]]],[]],[]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 3
[[],[[[[[],[]],[]],[]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 3
[[[],[]],[[],[[],[[],[]]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[[],[]],[[],[[[],[]],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[[[],[]],[[[],[]],[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[[[],[]],[[[],[[],[]]],[]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[[[],[]],[[[[],[]],[]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[[[],[[],[]]],[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[[],[[],[]]],[[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[[[[],[]],[]],[[],[[],[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[[[[],[]],[]],[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[[[],[[],[[],[]]]],[[],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 4
[[[],[[[],[]],[]]],[[],[]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 4
[[[[],[]],[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[[[[],[[],[]]],[]],[[],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[[[[[],[]],[]],[]],[[],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[[[],[[],[[],[[],[]]]]],[]] => [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 3
[[[],[[],[[[],[]],[]]]],[]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 3
[[[],[[[],[]],[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 3
[[[],[[[],[[],[]]],[]]],[]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 3
[[[],[[[[],[]],[]],[]]],[]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 3
[[[[],[]],[[],[[],[]]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[[[[],[]],[[[],[]],[]]],[]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[[[[],[[],[]]],[[],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 3
[[[[[],[]],[]],[[],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[[[[],[[],[[],[]]]],[]],[]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 3
[[[[],[[[],[]],[]]],[]],[]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 3
[[[[[],[]],[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[[[[],[[],[]]],[]],[]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 3
[[[[[[],[]],[]],[]],[]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[[],[[],[[],[[],[[],[[],[]]]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 3
[[],[[],[[],[[],[[[],[]],[]]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 3
[[],[[],[[],[[[],[]],[[],[]]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 3
[[],[[],[[],[[[],[[],[]]],[]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 3
[[],[[],[[],[[[[],[]],[]],[]]]]] => [1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 3
[[],[[],[[[],[]],[[],[[],[]]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[[],[[],[[[],[]],[[[],[]],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 4
[[],[[],[[[],[[],[]]],[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 3
[[],[[],[[[[],[]],[]],[[],[]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 3
[[],[[],[[[],[[],[[],[]]]],[]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 4
[[],[[],[[[],[[[],[]],[]]],[]]]] => [1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 3
[[],[[],[[[[],[]],[[],[]]],[]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 4
[[],[[],[[[[],[[],[]]],[]],[]]]] => [1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 3
[[],[[],[[[[[],[]],[]],[]],[]]]] => [1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 3
[[],[[[],[]],[[],[[],[[],[]]]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[[],[[[],[]],[[],[[[],[]],[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 4
[[],[[[],[]],[[[],[]],[[],[]]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 3
[[],[[[],[]],[[[],[[],[]]],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 4
[[],[[[],[]],[[[[],[]],[]],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 3
[[],[[[],[[],[]]],[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[],[[[],[[],[]]],[[[],[]],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[[],[[[[],[]],[]],[[],[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[],[[[[],[]],[]],[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[[],[[[],[[],[[],[]]]],[[],[]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 3
[[],[[[],[[[],[]],[]]],[[],[]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 4
[[],[[[[],[]],[[],[]]],[[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 3
[[],[[[[],[[],[]]],[]],[[],[]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 4
[[],[[[[[],[]],[]],[]],[[],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 3
[[],[[[],[[],[[],[[],[]]]]],[]]] => [1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 3
[[],[[[],[[],[[[],[]],[]]]],[]]] => [1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 3
[[],[[[],[[[],[]],[[],[]]]],[]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 4
[[],[[[],[[[],[[],[]]],[]]],[]]] => [1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 3
[[],[[[],[[[[],[]],[]],[]]],[]]] => [1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 4
[[],[[[[],[]],[[],[[],[]]]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 3
[[],[[[[],[]],[[[],[]],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 3
[[],[[[[],[[],[]]],[[],[]]],[]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 4
[[],[[[[[],[]],[]],[[],[]]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 3
[[],[[[[],[[],[[],[]]]],[]],[]]] => [1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 3
[[],[[[[],[[[],[]],[]]],[]],[]]] => [1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 3
[[],[[[[[],[]],[[],[]]],[]],[]]] => [1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 3
[[],[[[[[],[[],[]]],[]],[]],[]]] => [1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 3
[[],[[[[[[],[]],[]],[]],[]],[]]] => [1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 3
[[[],[]],[[],[[],[[],[[],[]]]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 4
[[[],[]],[[],[[],[[[],[]],[]]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 4
[[[],[]],[[],[[[],[]],[[],[]]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 4
[[[],[]],[[],[[[],[[],[]]],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 4
[[[],[]],[[],[[[[],[]],[]],[]]]] => [1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 4
[[[],[]],[[[],[]],[[],[[],[]]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[[],[]],[[[],[]],[[[],[]],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[[[],[]],[[[],[[],[]]],[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 4
[[[],[]],[[[[],[]],[]],[[],[]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 4
[[[],[]],[[[],[[],[[],[]]]],[]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 4
[[[],[]],[[[],[[[],[]],[]]],[]]] => [1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 4
[[[],[]],[[[[],[]],[[],[]]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 4
[[[],[]],[[[[],[[],[]]],[]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 4
[[[],[]],[[[[[],[]],[]],[]],[]]] => [1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 4
[[[],[[],[]]],[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[[],[[],[]]],[[],[[[],[]],[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[[[],[[],[]]],[[[],[]],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[[[],[[],[]]],[[[],[[],[]]],[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[[[],[[],[]]],[[[[],[]],[]],[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[[[[],[]],[]],[[],[[],[[],[]]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[[[],[]],[]],[[],[[[],[]],[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[[[[],[]],[]],[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 4
[[[[],[]],[]],[[[],[[],[]]],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[[[[],[]],[]],[[[[],[]],[]],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[[[],[[],[[],[]]]],[[],[[],[]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[[[],[[],[[],[]]]],[[[],[]],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[[[],[[[],[]],[]]],[[],[[],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[[[],[[[],[]],[]]],[[[],[]],[]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[[[[],[]],[[],[]]],[[],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[[[[],[]],[[],[]]],[[[],[]],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[[[[],[[],[]]],[]],[[],[[],[]]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[[[[],[[],[]]],[]],[[[],[]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[[[[[],[]],[]],[]],[[],[[],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[[[[[],[]],[]],[]],[[[],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[[[],[[],[[],[[],[]]]]],[[],[]]] => [1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 4
[[[],[[],[[[],[]],[]]]],[[],[]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 4
[[[],[[[],[]],[[],[]]]],[[],[]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 4
[[[],[[[],[[],[]]],[]]],[[],[]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 4
[[[],[[[[],[]],[]],[]]],[[],[]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 4
[[[[],[]],[[],[[],[]]]],[[],[]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 4
[[[[],[]],[[[],[]],[]]],[[],[]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 4
[[[[],[[],[]]],[[],[]]],[[],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[[[[[],[]],[]],[[],[]]],[[],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[[[[],[[],[[],[]]]],[]],[[],[]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[[[[],[[[],[]],[]]],[]],[[],[]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[[[[[],[]],[[],[]]],[]],[[],[]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 4
[[[[[],[[],[]]],[]],[]],[[],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[[[[[[],[]],[]],[]],[]],[[],[]]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[[[],[[],[[],[[],[[],[]]]]]],[]] => [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 3
[[[],[[],[[],[[[],[]],[]]]]],[]] => [1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 3
[[[],[[],[[[],[]],[[],[]]]]],[]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 3
[[[],[[],[[[],[[],[]]],[]]]],[]] => [1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 3
[[[],[[],[[[[],[]],[]],[]]]],[]] => [1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 3
[[[],[[[],[]],[[],[[],[]]]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 3
[[[],[[[],[]],[[[],[]],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 4
[[[],[[[],[[],[]]],[[],[]]]],[]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 3
[[[],[[[[],[]],[]],[[],[]]]],[]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 3
[[[],[[[],[[],[[],[]]]],[]]],[]] => [1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 4
[[[],[[[],[[[],[]],[]]],[]]],[]] => [1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 3
[[[],[[[[],[]],[[],[]]],[]]],[]] => [1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 4
[[[],[[[[],[[],[]]],[]],[]]],[]] => [1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 3
[[[],[[[[[],[]],[]],[]],[]]],[]] => [1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 3
[[[[],[]],[[],[[],[[],[]]]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 3
[[[[],[]],[[],[[[],[]],[]]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 4
[[[[],[]],[[[],[]],[[],[]]]],[]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 3
[[[[],[]],[[[],[[],[]]],[]]],[]] => [1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 4
[[[[],[]],[[[[],[]],[]],[]]],[]] => [1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 3
[[[[],[[],[]]],[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[[[[],[[],[]]],[[[],[]],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[[[[[],[]],[]],[[],[[],[]]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[[[[[],[]],[]],[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[[[[],[[],[[],[]]]],[[],[]]],[]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 3
[[[[],[[[],[]],[]]],[[],[]]],[]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 4
[[[[[],[]],[[],[]]],[[],[]]],[]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 3
[[[[[],[[],[]]],[]],[[],[]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[[[[[[],[]],[]],[]],[[],[]]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[[[[],[[],[[],[[],[]]]]],[]],[]] => [1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 3
[[[[],[[],[[[],[]],[]]]],[]],[]] => [1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 3
[[[[],[[[],[]],[[],[]]]],[]],[]] => [1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 4
[[[[],[[[],[[],[]]],[]]],[]],[]] => [1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 3
[[[[],[[[[],[]],[]],[]]],[]],[]] => [1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 4
[[[[[],[]],[[],[[],[]]]],[]],[]] => [1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 3
[[[[[],[]],[[[],[]],[]]],[]],[]] => [1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 3
[[[[[],[[],[]]],[[],[]]],[]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[[[[[[],[]],[]],[[],[]]],[]],[]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[[[[],[[],[[],[]]]],[]],[]],[]] => [1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 3
[[[[[],[[[],[]],[]]],[]],[]],[]] => [1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 3
[[[[[[],[]],[[],[]]],[]],[]],[]] => [1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 3
[[[[[[],[[],[]]],[]],[]],[]],[]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[[[[[[[],[]],[]],[]],[]],[]],[]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 3
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Generating function
click to show known generating functions
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 1,3,1 1,7,5,1 1,15,18,7,1 1,31,57,33,9,1
$F_{2} = 1$
$F_{3} = 1 + q$
$F_{4} = 1 + 3\ q + q^{2}$
$F_{5} = 1 + 7\ q + 5\ q^{2} + q^{3}$
$F_{6} = 1 + 15\ q + 18\ q^{2} + 7\ q^{3} + q^{4}$
$F_{7} = 1 + 31\ q + 57\ q^{2} + 33\ q^{3} + 9\ q^{4} + q^{5}$
Description
The bounce count of a Dyck path.
For a Dyck path $D$ of length $2n$, this is the number of points $(i,i)$ for $1 \leq i < n$ that are touching points of the bounce path of $D$.
For a Dyck path $D$ of length $2n$, this is the number of points $(i,i)$ for $1 \leq i < n$ that are touching points of the bounce path of $D$.
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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