Identifier
-
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
St000676: Dyck paths ⟶ ℤ
Values
[] => [] => [] => 0
[[]] => [1,0] => [1,0] => 1
[[],[]] => [1,0,1,0] => [1,1,0,0] => 1
[[[]]] => [1,1,0,0] => [1,0,1,0] => 2
[[],[],[]] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 1
[[],[[]]] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 2
[[[]],[]] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
[[[],[]]] => [1,1,0,1,0,0] => [1,1,1,0,0,0] => 2
[[[[]]]] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 3
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 2
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 3
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 3
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0] => 2
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 3
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 3
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 4
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 2
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 3
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 2
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 3
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 4
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 2
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 3
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => 3
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 4
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 2
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 4
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 3
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 3
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 3
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 3
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 4
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 3
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => 3
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0] => 4
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 3
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 4
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => 4
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 4
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 2
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 3
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 3
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 3
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
>>> Load all 1200 entries. <<<[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 4
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 3
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 4
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 4
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 4
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 4
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 4
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 4
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 4
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 3
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 4
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 3
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 4
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 4
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 5
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 4
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 4
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 4
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 4
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 5
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 5
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 4
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 4
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 5
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 2
[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 2
[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3
[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3
[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3
[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3
[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4
[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 3
[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 4
[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 4
[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 4
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3
[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4
[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 3
[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5
[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3
[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3
[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 4
[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4
[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4
[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5
[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 2
[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 3
[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4
[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 4
[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 3
[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 4
[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 3
[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 3
[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 4
[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 3
[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 4
[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 4
[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 4
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5
[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 4
[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 4
[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 5
[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 5
[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3
[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 4
[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 4
[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5
[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 4
[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 4
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 4
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 5
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 4
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 5
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 4
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 5
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 5
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 5
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3
[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 5
[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 5
[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5
[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 5
[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 4
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 5
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 5
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4
[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 3
[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 4
[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 4
[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 4
[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5
[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5
[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5
[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3
[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 4
[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 3
[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 4
[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 5
[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 4
[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 4
[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3
[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 4
[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 4
[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 5
[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 5
[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4
[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 4
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 5
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3
[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 3
[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 3
[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 4
[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 3
[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 4
[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 3
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 4
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4
[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 5
[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 4
[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 4
[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 4
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 4
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 3
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 4
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 4
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 4
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 5
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 4
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 5
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 4
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 5
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 3
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 3
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 3
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 4
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 3
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 4
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 4
[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 4
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 4
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 5
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 3
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 4
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 5
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 3
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 4
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 4
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 4
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 5
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 4
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 4
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 4
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 5
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 4
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 5
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 4
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 5
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 5
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 4
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 4
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 4
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 4
[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 5
[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 5
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 5
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 4
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 5
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 4
[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 5
[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 5
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 6
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 4
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 4
[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 5
[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 5
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 5
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 3
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 4
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 4
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 5
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 5
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 4
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 5
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 5
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 5
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 4
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 4
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 5
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 4
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 5
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 4
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 5
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 5
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 5
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 6
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 5
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 5
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 6
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 4
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 5
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 6
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 4
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 5
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 5
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 5
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 5
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 5
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 6
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 6
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 5
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [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] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 6
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 6
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[[],[],[[[]]],[],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[[],[],[[[]]],[[]],[]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[[],[],[[[]]],[[],[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[[],[],[[[]]],[[[]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5
[[],[],[[[[]]]],[],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[[],[],[[[[]]]],[[]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5
[[],[],[[[[]]],[]],[]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[[],[],[[[[]]],[[]]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 5
[[],[],[[[[[]]]],[]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 5
[[],[],[[[[[]]],[]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 5
[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[[],[[]],[],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3
[[],[[]],[],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[[],[[]],[],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[[],[[]],[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[[],[[]],[],[[]],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[[],[[]],[],[[],[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[[],[[]],[],[[[]]],[]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[[],[[]],[],[[],[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[[],[[]],[],[[],[[]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[[],[[]],[],[[[]],[]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[[],[[]],[],[[[],[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[[],[[]],[],[[[[]]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[[],[[]],[[]],[],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[[],[[]],[[]],[],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[[],[[]],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[[],[[]],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[[],[[]],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 5
[[],[[]],[[],[]],[],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[[],[[]],[[[]]],[],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[[],[[]],[[],[]],[[]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[[],[[]],[[[]]],[[]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 5
[[],[[]],[[],[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[[],[[]],[[],[[]]],[]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[[],[[]],[[[]],[]],[]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[[],[[]],[[[],[]]],[]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 4
[[],[[]],[[[[]]]],[]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[[],[[]],[[],[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[[],[[]],[[],[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[[],[[]],[[],[[]],[]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[[],[[]],[[],[[],[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[[],[[]],[[],[[[]]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5
[[],[[]],[[[]],[],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[],[[]],[[[]],[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 5
[[],[[]],[[[],[]],[]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[[],[[]],[[[[]]],[]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[[],[[]],[[[],[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 4
[[],[[]],[[[],[[]]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[[],[[]],[[[[]],[]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 5
[[],[[]],[[[[],[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 5
[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[[],[[[]]],[],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[[],[[[]]],[],[[]],[]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[[],[[[]]],[],[[],[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[[],[[[]]],[],[[[]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[[],[[[]]],[[]],[],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[[],[[[]]],[[]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 5
[[],[[[]]],[[],[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[[],[[[]]],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[[],[[[]]],[[],[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[[],[[[]]],[[],[[]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5
[[],[[[]]],[[[]],[]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[[],[[[]]],[[[],[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5
[[],[[[]]],[[[[]]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[[],[[[]],[]],[],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[[],[[[[]]]],[],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[[],[[[]],[]],[],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[[],[[[[]]]],[],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[[],[[[]],[]],[[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[[],[[[[]]]],[[]],[]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[[],[[[]],[]],[[],[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 4
[[],[[[]],[]],[[[]]]] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[[],[[[[]]]],[[],[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[[],[[[[]]]],[[[]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[[],[[[]],[],[]],[],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[[],[[[]],[[]]],[],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[[],[[[[]]],[]],[],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[[],[[[[]],[]]],[],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[[],[[[]],[],[]],[[]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[[],[[[]],[[]]],[[]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 5
[[],[[[[]]],[]],[[]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[[],[[[[]],[]]],[[]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[[],[[[]],[],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[[],[[[]],[],[[]]],[]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[[],[[[]],[[]],[]],[]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[[],[[[]],[[],[]]],[]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 4
[[],[[[]],[[[]]]],[]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[[],[[[[]]],[],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[[],[[[[]]],[[]]],[]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[],[[[[]],[]],[]],[]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[[],[[[[[]]]],[]],[]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[[],[[[[]],[],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 4
[[],[[[[]],[[]]]],[]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 5
[[],[[[[[]]],[]]],[]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[[],[[[[[]],[]]]],[]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[[],[[[[[[]]]]]],[]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[[],[[[]],[],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[[],[[[]],[],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[[],[[[]],[],[[]],[]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 4
[[],[[[]],[],[[],[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4
[[],[[[]],[],[[[]]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 5
[[],[[[]],[[]],[],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 4
[[],[[[]],[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 5
[[],[[[]],[[],[]],[]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 4
[[],[[[]],[[[]]],[]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[],[[[]],[[],[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 4
[[],[[[]],[[],[[]]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 5
[[],[[[]],[[[]],[]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 5
[[],[[[]],[[[],[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 5
[[],[[[]],[[[[]]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[],[[[[]]],[],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[[],[[[[]]],[],[[]]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 5
[[],[[[[]]],[[]],[]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 5
[[],[[[[]]],[[],[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 5
[[],[[[[]]],[[[]]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 6
[[],[[[[]],[]],[],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[[],[[[[[]]]],[],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[[],[[[[]],[]],[[]]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 5
[[],[[[[[]]]],[[]]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6
[[],[[[[]],[],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[[],[[[[]],[[]]],[]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 5
[[],[[[[[]]],[]],[]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[[],[[[[[]],[]]],[]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 5
[[],[[[[[[]]]]],[]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[[],[[[[]],[],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[[],[[[[]],[],[[]]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[],[[[[]],[[]],[]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 5
[[],[[[[]],[[],[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 5
[[],[[[[]],[[[]]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 6
[[],[[[[[]]],[],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[],[[[[[]]],[[]]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 6
[[],[[[[[]],[]],[]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[[],[[[[[[]]]],[]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 5
[[],[[[[[]],[[]]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 6
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 6
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[[[]],[],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[[[]],[],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[[[]],[],[],[[]],[],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[[[]],[],[],[[]],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[[[]],[],[],[[],[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[[[]],[],[],[[[]]],[]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[[[]],[],[],[[],[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[[[]],[],[],[[],[[]]]] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 4
[[[]],[],[],[[[]],[]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 4
[[[]],[],[],[[[],[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 4
[[[]],[],[],[[[[]]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[[[]],[],[[]],[],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[[[]],[],[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[[[]],[],[[]],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[[[]],[],[[]],[[],[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4
[[[]],[],[[]],[[[]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 5
[[[]],[],[[],[]],[],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[[[]],[],[[[]]],[],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[[[]],[],[[],[]],[[]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4
[[[]],[],[[[]]],[[]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 5
[[[]],[],[[],[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[[[]],[],[[],[[]]],[]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 4
[[[]],[],[[[]],[]],[]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4
[[[]],[],[[[],[]]],[]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 4
[[[]],[],[[[[]]]],[]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5
[[[]],[],[[],[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[[[]],[],[[],[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 4
[[[]],[],[[],[[]],[]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 4
[[[]],[],[[],[[],[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 4
[[[]],[],[[],[[[]]]]] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[[[]],[],[[[]],[],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[[[]],[],[[[]],[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5
[[[]],[],[[[],[]],[]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 4
[[[]],[],[[[[]]],[]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[[[]],[],[[[],[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 4
[[[]],[],[[[],[[]]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 5
[[[]],[],[[[[]],[]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 5
[[[]],[],[[[[],[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 5
[[[]],[],[[[[[]]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[[[]],[[]],[],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[[[]],[[]],[],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[[[]],[[]],[],[[]],[]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[[[]],[[]],[],[[],[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 4
[[[]],[[]],[],[[[]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5
[[[]],[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[[[]],[[]],[[],[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 4
[[[]],[[]],[[[]]],[]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 5
[[[]],[[]],[[],[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 4
[[[]],[[]],[[],[[]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5
[[[]],[[]],[[[]],[]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[[[]],[[]],[[[],[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 5
[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 6
[[[]],[[],[]],[],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[[[]],[[],[]],[],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[[[]],[[[]]],[],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5
[[[]],[[],[]],[[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 4
[[[]],[[[]]],[[]],[]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5
[[[]],[[],[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 4
[[[]],[[],[]],[[[]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[[[]],[[[]]],[[],[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5
[[[]],[[[]]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 6
[[[]],[[],[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[[[]],[[],[[]]],[],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 4
[[[]],[[[]],[]],[],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 4
[[[]],[[[],[]]],[],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4
[[[]],[[[[]]]],[],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[[[]],[[],[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4
[[[]],[[],[[]]],[[]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5
[[[]],[[[]],[]],[[]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 5
[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 6
[[[]],[[],[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[[[]],[[],[],[[]]],[]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 4
[[[]],[[],[[]],[]],[]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 4
[[[]],[[],[[],[]]],[]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 4
[[[]],[[],[[[]]]],[]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 5
[[[]],[[[]],[],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 4
[[[]],[[[]],[[]]],[]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[[[]],[[[],[]],[]],[]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 4
[[[]],[[[[]]],[]],[]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[[[]],[[[],[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 4
[[[]],[[[],[[]]]],[]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 5
[[[]],[[[[]],[]]],[]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 5
[[[]],[[[[],[]]]],[]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 5
[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
[[[]],[[],[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[[[]],[[],[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 4
[[[]],[[],[],[[]],[]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 4
[[[]],[[],[],[[],[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 4
[[[]],[[],[],[[[]]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 5
[[[]],[[],[[]],[],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[[[]],[[],[[]],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 5
[[[]],[[],[[],[]],[]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 4
[[[]],[[],[[[]]],[]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 5
[[[]],[[],[[],[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4
[[[]],[[],[[],[[]]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 5
[[[]],[[],[[[]],[]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 5
[[[]],[[],[[[],[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 5
[[[]],[[],[[[[]]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 6
[[[]],[[[]],[],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[[[]],[[[]],[],[[]]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[[[]],[[[]],[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5
[[[]],[[[]],[[],[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 5
[[[]],[[[]],[[[]]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 6
[[[]],[[[],[]],[],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[[[]],[[[[]]],[],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[[[]],[[[],[]],[[]]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 5
[[[]],[[[[]]],[[]]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 6
[[[]],[[[],[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 4
[[[]],[[[],[[]]],[]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 5
[[[]],[[[[]],[]],[]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 5
[[[]],[[[[],[]]],[]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 5
[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 6
[[[]],[[[],[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 4
[[[]],[[[],[],[[]]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 5
[[[]],[[[],[[]],[]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 5
[[[]],[[[],[[],[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 5
[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6
[[[]],[[[[]],[],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[[[]],[[[[]],[[]]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6
[[[]],[[[[],[]],[]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 5
[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 5
[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 6
[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 6
[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 6
[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[[[[]]],[],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[[[[]]],[],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[[[[]]],[],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[[[[]]],[],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[[[[]]],[],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5
[[[[]]],[],[[]],[],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[[[[]]],[],[[]],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 5
[[[[]]],[],[[],[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[[[[]]],[],[[[]]],[]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5
[[[[]]],[],[[],[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[[[[]]],[],[[],[[]]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[[[[]]],[],[[[]],[]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[[[[]]],[],[[[],[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 5
[[[[]]],[],[[[[]]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6
[[[[]]],[[]],[],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[[[[]]],[[]],[],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 5
[[[[]]],[[]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[[[[]]],[[]],[[],[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5
[[[[]]],[[]],[[[]]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 6
[[[[]]],[[],[]],[],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4
[[[[]]],[[[]]],[],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5
[[[[]]],[[],[]],[[]]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[[[[]]],[[[]]],[[]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 6
[[[[]]],[[],[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[[[[]]],[[],[[]]],[]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5
[[[[]]],[[[]],[]],[]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5
[[[[]]],[[[],[]]],[]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 5
[[[[]]],[[[[]]]],[]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 6
[[[[]]],[[],[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[[[[]]],[[],[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 5
[[[[]]],[[],[[]],[]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 5
[[[[]]],[[],[[],[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 5
[[[[]]],[[],[[[]]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 6
[[[[]]],[[[]],[],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 5
[[[[]]],[[[]],[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[[[[]]],[[[],[]],[]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 5
[[[[]]],[[[[]]],[]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 6
[[[[]]],[[[],[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 5
[[[[]]],[[[],[[]]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[[[[]]],[[[[]],[]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6
[[[[]]],[[[[],[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 6
[[[[]]],[[[[[]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[[[[]],[]],[],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[[[[[]]]],[],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[[[]],[]],[],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[[[[[]]]],[],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5
[[[[]],[]],[],[[]],[]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 4
[[[[[]]]],[],[[]],[]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5
[[[[]],[]],[],[[],[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 4
[[[[]],[]],[],[[[]]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[[[[[]]]],[],[[],[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[[[[[]]]],[],[[[]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6
[[[[]],[]],[[]],[],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[[[[[]]]],[[]],[],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 5
[[[[]],[]],[[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[[[[[]]]],[[]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 6
[[[[]],[]],[[],[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 4
[[[[]],[]],[[[]]],[]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5
[[[[[]]]],[[],[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[[[[[]]]],[[[]]],[]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 6
[[[[]],[]],[[],[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 4
[[[[]],[]],[[],[[]]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 5
[[[[]],[]],[[[]],[]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 5
[[[[]],[]],[[[],[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 5
[[[[]],[]],[[[[]]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 6
[[[[[]]]],[[],[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 5
[[[[[]]]],[[],[[]]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 6
[[[[[]]]],[[[]],[]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 6
[[[[[]]]],[[[],[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[[[[[]]]],[[[[]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[[[[]],[],[]],[],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[[[[]],[[]]],[],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 4
[[[[[]]],[]],[],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[[[[]],[]]],[],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[[[[[[]]]]],[],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[[[[]],[],[]],[],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4
[[[[]],[[]]],[],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 5
[[[[[]]],[]],[],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[[[[[]],[]]],[],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5
[[[[[[]]]]],[],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6
[[[[]],[],[]],[[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 4
[[[[]],[[]]],[[]],[]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[[[[[]]],[]],[[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5
[[[[[]],[]]],[[]],[]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 5
[[[[[[]]]]],[[]],[]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
[[[[]],[],[]],[[],[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 4
[[[[]],[],[]],[[[]]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[[[[]],[[]]],[[],[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 5
[[[[]],[[]]],[[[]]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 6
[[[[[]]],[]],[[],[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 5
[[[[[]]],[]],[[[]]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 6
[[[[[]],[]]],[[],[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 5
[[[[[]],[]]],[[[]]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[[[[[[]]]]],[[],[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 6
[[[[[[]]]]],[[[]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[[[[]],[],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[[[[]],[],[[]]],[],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 4
[[[[]],[[]],[]],[],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 4
[[[[]],[[],[]]],[],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4
[[[[]],[[[]]]],[],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5
[[[[[]]],[],[]],[],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[[[[]]],[[]]],[],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[[[[[]],[]],[]],[],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[[[[[[]]]],[]],[],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[[[[[]],[],[]]],[],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[[[[[]],[[]]]],[],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 5
[[[[[[]]],[]]],[],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[[[[[[]],[]]]],[],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5
[[[[[[[]]]]]],[],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[[[[]],[],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[[[[]],[],[[]]],[[]]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 5
[[[[]],[[]],[]],[[]]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 5
[[[[]],[[],[]]],[[]]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 5
[[[[]],[[[]]]],[[]]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 6
[[[[[]]],[],[]],[[]]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 5
[[[[[]]],[[]]],[[]]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[[[[[]],[]],[]],[[]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 5
[[[[[[]]]],[]],[[]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 6
[[[[[]],[],[]]],[[]]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 5
[[[[[]],[[]]]],[[]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6
[[[[[[]]],[]]],[[]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6
[[[[[[]],[]]]],[[]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 6
[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[[[[]],[],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[[[[]],[],[],[[]]],[]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 4
[[[[]],[],[[]],[]],[]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 4
[[[[]],[],[[],[]]],[]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[[[[]],[],[[[]]]],[]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
[[[[]],[[]],[],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 4
[[[[]],[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5
[[[[]],[[],[]],[]],[]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 4
[[[[]],[[[]]],[]],[]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[[[[]],[[],[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 4
[[[[]],[[],[[]]]],[]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 5
[[[[]],[[[]],[]]],[]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 5
[[[[]],[[[],[]]]],[]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 5
[[[[]],[[[[]]]]],[]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 6
[[[[[]]],[],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[[[[]]],[],[[]]],[]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
[[[[[]]],[[]],[]],[]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 5
[[[[[]]],[[],[]]],[]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 5
[[[[[]]],[[[]]]],[]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 6
[[[[[]],[]],[],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[[[[[[]]]],[],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[[[[[]],[]],[[]]],[]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 5
[[[[[[]]]],[[]]],[]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 6
[[[[[]],[],[]],[]],[]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 4
[[[[[]],[[]]],[]],[]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 5
[[[[[[]]],[]],[]],[]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 5
[[[[[[]],[]]],[]],[]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[[[[[[[]]]]],[]],[]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[[[[[]],[],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 4
[[[[[]],[],[[]]]],[]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[[[[]],[[]],[]]],[]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 5
[[[[[]],[[],[]]]],[]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 5
[[[[[]],[[[]]]]],[]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[[[[[[]]],[],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[[[[[[]]],[[]]]],[]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6
[[[[[[]],[]],[]]],[]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 5
[[[[[[[]]]],[]]],[]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[[[[[[]],[],[]]]],[]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 5
[[[[[[]],[[]]]]],[]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 6
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 6
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 6
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[[[[]],[],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[[[[]],[],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4
[[[[]],[],[],[[]],[]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 4
[[[[]],[],[],[[],[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4
[[[[]],[],[],[[[]]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5
[[[[]],[],[[]],[],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 4
[[[[]],[],[[]],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[[[[]],[],[[],[]],[]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 4
[[[[]],[],[[[]]],[]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[[[[]],[],[[],[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 4
[[[[]],[],[[],[[]]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[[[[]],[],[[[]],[]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 5
[[[[]],[],[[[],[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 5
[[[[]],[],[[[[]]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[[[[]],[[]],[],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 4
[[[[]],[[]],[],[[]]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 5
[[[[]],[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 5
[[[[]],[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 5
[[[[]],[[]],[[[]]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[[[[]],[[],[]],[],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 4
[[[[]],[[[]]],[],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[[[[]],[[],[]],[[]]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 5
[[[[]],[[[]]],[[]]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[[[[]],[[],[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 4
[[[[]],[[],[[]]],[]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 5
[[[[]],[[[]],[]],[]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 5
[[[[]],[[[],[]]],[]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 5
[[[[]],[[[[]]]],[]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[[[[]],[[],[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 4
[[[[]],[[],[],[[]]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 5
[[[[]],[[],[[]],[]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 5
[[[[]],[[],[[],[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 5
[[[[]],[[],[[[]]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 6
[[[[]],[[[]],[],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 5
[[[[]],[[[]],[[]]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[[[[]],[[[],[]],[]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 5
[[[[]],[[[[]]],[]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 6
[[[[]],[[[],[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 5
[[[[]],[[[],[[]]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 6
[[[[]],[[[[]],[]]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 6
[[[[]],[[[[],[]]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 6
[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[[[[[]]],[],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[[[[[]]],[],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 5
[[[[[]]],[],[[]],[]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 5
[[[[[]]],[],[[],[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 5
[[[[[]]],[],[[[]]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[[[[]]],[[]],[],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 5
[[[[[]]],[[]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 6
[[[[[]]],[[],[]],[]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 5
[[[[[]]],[[[]]],[]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[[[[[]]],[[],[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 5
[[[[[]]],[[],[[]]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 6
[[[[[]]],[[[]],[]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 6
[[[[[]]],[[[],[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 6
[[[[[]]],[[[[]]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[[[[[]],[]],[],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 4
[[[[[[]]]],[],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 5
[[[[[]],[]],[],[[]]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 5
[[[[[[]]]],[],[[]]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[[[[[]],[]],[[]],[]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 5
[[[[[[]]]],[[]],[]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 6
[[[[[]],[]],[[],[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 5
[[[[[]],[]],[[[]]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6
[[[[[[]]]],[[],[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6
[[[[[[]]]],[[[]]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7
[[[[[]],[],[]],[],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 4
[[[[[]],[[]]],[],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 5
[[[[[[]]],[]],[],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[[[[[[]],[]]],[],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 5
[[[[[[[]]]]],[],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[[[[[]],[],[]],[[]]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 5
[[[[[]],[[]]],[[]]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6
[[[[[[]]],[]],[[]]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 6
[[[[[[]],[]]],[[]]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 6
[[[[[[[]]]]],[[]]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 7
[[[[[]],[],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[[[[[]],[],[[]]],[]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5
[[[[[]],[[]],[]],[]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 5
[[[[[]],[[],[]]],[]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 5
[[[[[]],[[[]]]],[]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 6
[[[[[[]]],[],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 5
[[[[[[]]],[[]]],[]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 6
[[[[[[]],[]],[]],[]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 5
[[[[[[[]]]],[]],[]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 6
[[[[[[]],[],[]]],[]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 6
[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 6
[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 6
[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 4
[[[[[]],[],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
[[[[[]],[],[[]],[]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 5
[[[[[]],[],[[],[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 5
[[[[[]],[],[[[]]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[[[[[]],[[]],[],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 5
[[[[[]],[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 6
[[[[[]],[[],[]],[]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 5
[[[[[]],[[[]]],[]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 6
[[[[[]],[[],[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
[[[[[]],[[],[[]]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[[[[[]],[[[]],[]]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 6
[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[[[[[]],[[[[]]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 7
[[[[[[]]],[],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
[[[[[[]]],[],[[]]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 6
[[[[[[]]],[[],[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 6
[[[[[[]]],[[[]]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 7
[[[[[[]],[]],[],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 5
[[[[[[[]]]],[],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[[[[[[]],[]],[[]]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 6
[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 7
[[[[[[]],[],[]],[]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 5
[[[[[[]],[[]]],[]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 6
[[[[[[[]]],[]],[]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 6
[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 6
[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7
[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[[[[[[]],[],[[]]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[[[[[[]],[[]],[]]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 6
[[[[[[]],[[],[]]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[[[[[[]],[[[]]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7
[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 6
[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 7
[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 7
[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 7
[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,6,6,1 1,10,20,10,1 1,15,50,50,15,1 1,21,105,175,105,21,1
$F_{1} = 1$
$F_{2} = q$
$F_{3} = q + q^{2}$
$F_{4} = q + 3\ q^{2} + q^{3}$
$F_{5} = q + 6\ q^{2} + 6\ q^{3} + q^{4}$
$F_{6} = q + 10\ q^{2} + 20\ q^{3} + 10\ q^{4} + q^{5}$
$F_{7} = q + 15\ q^{2} + 50\ q^{3} + 50\ q^{4} + 15\ q^{5} + q^{6}$
$F_{8} = q + 21\ q^{2} + 105\ q^{3} + 175\ q^{4} + 105\ q^{5} + 21\ q^{6} + q^{7}$
Description
The number of odd rises of a Dyck path.
This is the number of ones at an odd position, with the initial position equal to 1.
The number of Dyck paths of semilength $n$ with $k$ up steps in odd positions and $k$ returns to the main diagonal are counted by the binomial coefficient $\binom{n-1}{k-1}$ [3,4].
This is the number of ones at an odd position, with the initial position equal to 1.
The number of Dyck paths of semilength $n$ with $k$ up steps in odd positions and $k$ returns to the main diagonal are counted by the binomial coefficient $\binom{n-1}{k-1}$ [3,4].
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.
Map
Delest-Viennot
Description
Return the Dyck path corresponding to the parallelogram polyomino obtained by applying Delest-Viennot's bijection.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
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