Identifier
-
Mp00328:
Ordered trees
—DeBruijn-Morselt plane tree automorphism⟶
Ordered trees
St000679: Ordered trees ⟶ ℤ
Values
[[]] => [[]] => 1
[[],[]] => [[[]]] => 1
[[[]]] => [[],[]] => 1
[[],[],[]] => [[[[]]]] => 1
[[],[[]]] => [[[],[]]] => 2
[[[]],[]] => [[],[[]]] => 1
[[[],[]]] => [[[]],[]] => 1
[[[[]]]] => [[],[],[]] => 1
[[],[],[],[]] => [[[[[]]]]] => 1
[[],[],[[]]] => [[[[],[]]]] => 2
[[],[[]],[]] => [[[],[[]]]] => 2
[[],[[],[]]] => [[[[]],[]]] => 2
[[],[[[]]]] => [[[],[],[]]] => 2
[[[]],[],[]] => [[],[[[]]]] => 1
[[[]],[[]]] => [[],[[],[]]] => 2
[[[],[]],[]] => [[[]],[[]]] => 1
[[[[]]],[]] => [[],[],[[]]] => 1
[[[],[],[]]] => [[[[]]],[]] => 1
[[[],[[]]]] => [[[],[]],[]] => 2
[[[[]],[]]] => [[],[[]],[]] => 1
[[[[],[]]]] => [[[]],[],[]] => 1
[[[[[]]]]] => [[],[],[],[]] => 1
[[],[],[],[],[]] => [[[[[[]]]]]] => 1
[[],[],[],[[]]] => [[[[[],[]]]]] => 2
[[],[],[[]],[]] => [[[[],[[]]]]] => 2
[[],[],[[],[]]] => [[[[[]],[]]]] => 2
[[],[],[[[]]]] => [[[[],[],[]]]] => 2
[[],[[]],[],[]] => [[[],[[[]]]]] => 2
[[],[[]],[[]]] => [[[],[[],[]]]] => 2
[[],[[],[]],[]] => [[[[]],[[]]]] => 2
[[],[[[]]],[]] => [[[],[],[[]]]] => 2
[[],[[],[],[]]] => [[[[[]]],[]]] => 2
[[],[[],[[]]]] => [[[[],[]],[]]] => 2
[[],[[[]],[]]] => [[[],[[]],[]]] => 2
[[],[[[],[]]]] => [[[[]],[],[]]] => 2
[[],[[[[]]]]] => [[[],[],[],[]]] => 2
[[[]],[],[],[]] => [[],[[[[]]]]] => 1
[[[]],[],[[]]] => [[],[[[],[]]]] => 2
[[[]],[[]],[]] => [[],[[],[[]]]] => 2
[[[]],[[],[]]] => [[],[[[]],[]]] => 2
[[[]],[[[]]]] => [[],[[],[],[]]] => 2
[[[],[]],[],[]] => [[[]],[[[]]]] => 1
[[[[]]],[],[]] => [[],[],[[[]]]] => 1
[[[],[]],[[]]] => [[[]],[[],[]]] => 2
[[[[]]],[[]]] => [[],[],[[],[]]] => 2
[[[],[],[]],[]] => [[[[]]],[[]]] => 1
[[[],[[]]],[]] => [[[],[]],[[]]] => 2
[[[[]],[]],[]] => [[],[[]],[[]]] => 1
[[[[],[]]],[]] => [[[]],[],[[]]] => 1
[[[[[]]]],[]] => [[],[],[],[[]]] => 1
[[[],[],[],[]]] => [[[[[]]]],[]] => 1
[[[],[],[[]]]] => [[[[],[]]],[]] => 2
[[[],[[]],[]]] => [[[],[[]]],[]] => 2
[[[],[[],[]]]] => [[[[]],[]],[]] => 2
[[[],[[[]]]]] => [[[],[],[]],[]] => 2
[[[[]],[],[]]] => [[],[[[]]],[]] => 1
[[[[]],[[]]]] => [[],[[],[]],[]] => 2
[[[[],[]],[]]] => [[[]],[[]],[]] => 1
[[[[[]]],[]]] => [[],[],[[]],[]] => 1
[[[[],[],[]]]] => [[[[]]],[],[]] => 1
[[[[],[[]]]]] => [[[],[]],[],[]] => 2
[[[[[]],[]]]] => [[],[[]],[],[]] => 1
[[[[[],[]]]]] => [[[]],[],[],[]] => 1
[[[[[[]]]]]] => [[],[],[],[],[]] => 1
[[],[],[],[],[],[]] => [[[[[[[]]]]]]] => 1
[[],[],[],[],[[]]] => [[[[[[],[]]]]]] => 2
[[],[],[],[[]],[]] => [[[[[],[[]]]]]] => 2
[[],[],[],[[],[]]] => [[[[[[]],[]]]]] => 2
[[],[],[],[[[]]]] => [[[[[],[],[]]]]] => 2
[[],[],[[]],[],[]] => [[[[],[[[]]]]]] => 2
[[],[],[[]],[[]]] => [[[[],[[],[]]]]] => 2
[[],[],[[],[]],[]] => [[[[[]],[[]]]]] => 2
[[],[],[[[]]],[]] => [[[[],[],[[]]]]] => 2
[[],[],[[],[],[]]] => [[[[[[]]],[]]]] => 2
[[],[],[[],[[]]]] => [[[[[],[]],[]]]] => 2
[[],[],[[[]],[]]] => [[[[],[[]],[]]]] => 2
[[],[],[[[],[]]]] => [[[[[]],[],[]]]] => 2
[[],[],[[[[]]]]] => [[[[],[],[],[]]]] => 2
[[],[[]],[],[],[]] => [[[],[[[[]]]]]] => 2
[[],[[]],[],[[]]] => [[[],[[[],[]]]]] => 2
[[],[[]],[[]],[]] => [[[],[[],[[]]]]] => 2
[[],[[]],[[],[]]] => [[[],[[[]],[]]]] => 2
[[],[[]],[[[]]]] => [[[],[[],[],[]]]] => 2
[[],[[],[]],[],[]] => [[[[]],[[[]]]]] => 2
[[],[[[]]],[],[]] => [[[],[],[[[]]]]] => 2
[[],[[],[]],[[]]] => [[[[]],[[],[]]]] => 2
[[],[[[]]],[[]]] => [[[],[],[[],[]]]] => 2
[[],[[],[],[]],[]] => [[[[[]]],[[]]]] => 2
[[],[[],[[]]],[]] => [[[[],[]],[[]]]] => 2
[[],[[[]],[]],[]] => [[[],[[]],[[]]]] => 2
[[],[[[],[]]],[]] => [[[[]],[],[[]]]] => 2
[[],[[[[]]]],[]] => [[[],[],[],[[]]]] => 2
[[],[[],[],[],[]]] => [[[[[[]]]],[]]] => 2
[[],[[],[],[[]]]] => [[[[[],[]]],[]]] => 2
[[],[[],[[]],[]]] => [[[[],[[]]],[]]] => 2
[[],[[],[[],[]]]] => [[[[[]],[]],[]]] => 2
[[],[[],[[[]]]]] => [[[[],[],[]],[]]] => 2
[[],[[[]],[],[]]] => [[[],[[[]]],[]]] => 2
[[],[[[]],[[]]]] => [[[],[[],[]],[]]] => 2
[[],[[[],[]],[]]] => [[[[]],[[]],[]]] => 2
[[],[[[[]]],[]]] => [[[],[],[[]],[]]] => 2
>>> Load all 1200 entries. <<<[[],[[[],[],[]]]] => [[[[[]]],[],[]]] => 2
[[],[[[],[[]]]]] => [[[[],[]],[],[]]] => 2
[[],[[[[]],[]]]] => [[[],[[]],[],[]]] => 2
[[],[[[[],[]]]]] => [[[[]],[],[],[]]] => 2
[[],[[[[[]]]]]] => [[[],[],[],[],[]]] => 2
[[[]],[],[],[],[]] => [[],[[[[[]]]]]] => 1
[[[]],[],[],[[]]] => [[],[[[[],[]]]]] => 2
[[[]],[],[[]],[]] => [[],[[[],[[]]]]] => 2
[[[]],[],[[],[]]] => [[],[[[[]],[]]]] => 2
[[[]],[],[[[]]]] => [[],[[[],[],[]]]] => 2
[[[]],[[]],[],[]] => [[],[[],[[[]]]]] => 2
[[[]],[[]],[[]]] => [[],[[],[[],[]]]] => 2
[[[]],[[],[]],[]] => [[],[[[]],[[]]]] => 2
[[[]],[[[]]],[]] => [[],[[],[],[[]]]] => 2
[[[]],[[],[],[]]] => [[],[[[[]]],[]]] => 2
[[[]],[[],[[]]]] => [[],[[[],[]],[]]] => 2
[[[]],[[[]],[]]] => [[],[[],[[]],[]]] => 2
[[[]],[[[],[]]]] => [[],[[[]],[],[]]] => 2
[[[]],[[[[]]]]] => [[],[[],[],[],[]]] => 2
[[[],[]],[],[],[]] => [[[]],[[[[]]]]] => 1
[[[[]]],[],[],[]] => [[],[],[[[[]]]]] => 1
[[[],[]],[],[[]]] => [[[]],[[[],[]]]] => 2
[[[[]]],[],[[]]] => [[],[],[[[],[]]]] => 2
[[[],[]],[[]],[]] => [[[]],[[],[[]]]] => 2
[[[[]]],[[]],[]] => [[],[],[[],[[]]]] => 2
[[[],[]],[[],[]]] => [[[]],[[[]],[]]] => 2
[[[],[]],[[[]]]] => [[[]],[[],[],[]]] => 2
[[[[]]],[[],[]]] => [[],[],[[[]],[]]] => 2
[[[[]]],[[[]]]] => [[],[],[[],[],[]]] => 2
[[[],[],[]],[],[]] => [[[[]]],[[[]]]] => 1
[[[],[[]]],[],[]] => [[[],[]],[[[]]]] => 2
[[[[]],[]],[],[]] => [[],[[]],[[[]]]] => 1
[[[[],[]]],[],[]] => [[[]],[],[[[]]]] => 1
[[[[[]]]],[],[]] => [[],[],[],[[[]]]] => 1
[[[],[],[]],[[]]] => [[[[]]],[[],[]]] => 2
[[[],[[]]],[[]]] => [[[],[]],[[],[]]] => 2
[[[[]],[]],[[]]] => [[],[[]],[[],[]]] => 2
[[[[],[]]],[[]]] => [[[]],[],[[],[]]] => 2
[[[[[]]]],[[]]] => [[],[],[],[[],[]]] => 2
[[[],[],[],[]],[]] => [[[[[]]]],[[]]] => 1
[[[],[],[[]]],[]] => [[[[],[]]],[[]]] => 2
[[[],[[]],[]],[]] => [[[],[[]]],[[]]] => 2
[[[],[[],[]]],[]] => [[[[]],[]],[[]]] => 2
[[[],[[[]]]],[]] => [[[],[],[]],[[]]] => 2
[[[[]],[],[]],[]] => [[],[[[]]],[[]]] => 1
[[[[]],[[]]],[]] => [[],[[],[]],[[]]] => 2
[[[[],[]],[]],[]] => [[[]],[[]],[[]]] => 1
[[[[[]]],[]],[]] => [[],[],[[]],[[]]] => 1
[[[[],[],[]]],[]] => [[[[]]],[],[[]]] => 1
[[[[],[[]]]],[]] => [[[],[]],[],[[]]] => 2
[[[[[]],[]]],[]] => [[],[[]],[],[[]]] => 1
[[[[[],[]]]],[]] => [[[]],[],[],[[]]] => 1
[[[[[[]]]]],[]] => [[],[],[],[],[[]]] => 1
[[[],[],[],[],[]]] => [[[[[[]]]]],[]] => 1
[[[],[],[],[[]]]] => [[[[[],[]]]],[]] => 2
[[[],[],[[]],[]]] => [[[[],[[]]]],[]] => 2
[[[],[],[[],[]]]] => [[[[[]],[]]],[]] => 2
[[[],[],[[[]]]]] => [[[[],[],[]]],[]] => 2
[[[],[[]],[],[]]] => [[[],[[[]]]],[]] => 2
[[[],[[]],[[]]]] => [[[],[[],[]]],[]] => 2
[[[],[[],[]],[]]] => [[[[]],[[]]],[]] => 2
[[[],[[[]]],[]]] => [[[],[],[[]]],[]] => 2
[[[],[[],[],[]]]] => [[[[[]]],[]],[]] => 2
[[[],[[],[[]]]]] => [[[[],[]],[]],[]] => 2
[[[],[[[]],[]]]] => [[[],[[]],[]],[]] => 2
[[[],[[[],[]]]]] => [[[[]],[],[]],[]] => 2
[[[],[[[[]]]]]] => [[[],[],[],[]],[]] => 2
[[[[]],[],[],[]]] => [[],[[[[]]]],[]] => 1
[[[[]],[],[[]]]] => [[],[[[],[]]],[]] => 2
[[[[]],[[]],[]]] => [[],[[],[[]]],[]] => 2
[[[[]],[[],[]]]] => [[],[[[]],[]],[]] => 2
[[[[]],[[[]]]]] => [[],[[],[],[]],[]] => 2
[[[[],[]],[],[]]] => [[[]],[[[]]],[]] => 1
[[[[[]]],[],[]]] => [[],[],[[[]]],[]] => 1
[[[[],[]],[[]]]] => [[[]],[[],[]],[]] => 2
[[[[[]]],[[]]]] => [[],[],[[],[]],[]] => 2
[[[[],[],[]],[]]] => [[[[]]],[[]],[]] => 1
[[[[],[[]]],[]]] => [[[],[]],[[]],[]] => 2
[[[[[]],[]],[]]] => [[],[[]],[[]],[]] => 1
[[[[[],[]]],[]]] => [[[]],[],[[]],[]] => 1
[[[[[[]]]],[]]] => [[],[],[],[[]],[]] => 1
[[[[],[],[],[]]]] => [[[[[]]]],[],[]] => 1
[[[[],[],[[]]]]] => [[[[],[]]],[],[]] => 2
[[[[],[[]],[]]]] => [[[],[[]]],[],[]] => 2
[[[[],[[],[]]]]] => [[[[]],[]],[],[]] => 2
[[[[],[[[]]]]]] => [[[],[],[]],[],[]] => 2
[[[[[]],[],[]]]] => [[],[[[]]],[],[]] => 1
[[[[[]],[[]]]]] => [[],[[],[]],[],[]] => 2
[[[[[],[]],[]]]] => [[[]],[[]],[],[]] => 1
[[[[[[]]],[]]]] => [[],[],[[]],[],[]] => 1
[[[[[],[],[]]]]] => [[[[]]],[],[],[]] => 1
[[[[[],[[]]]]]] => [[[],[]],[],[],[]] => 2
[[[[[[]],[]]]]] => [[],[[]],[],[],[]] => 1
[[[[[[],[]]]]]] => [[[]],[],[],[],[]] => 1
[[[[[[[]]]]]]] => [[],[],[],[],[],[]] => 1
[[],[],[],[],[],[],[]] => [[[[[[[[]]]]]]]] => 1
[[],[],[],[],[],[[]]] => [[[[[[[],[]]]]]]] => 2
[[],[],[],[],[[]],[]] => [[[[[[],[[]]]]]]] => 2
[[],[],[],[],[[],[]]] => [[[[[[[]],[]]]]]] => 2
[[],[],[],[],[[[]]]] => [[[[[[],[],[]]]]]] => 2
[[],[],[],[[]],[],[]] => [[[[[],[[[]]]]]]] => 2
[[],[],[],[[]],[[]]] => [[[[[],[[],[]]]]]] => 2
[[],[],[],[[],[]],[]] => [[[[[[]],[[]]]]]] => 2
[[],[],[],[[[]]],[]] => [[[[[],[],[[]]]]]] => 2
[[],[],[],[[],[],[]]] => [[[[[[[]]],[]]]]] => 2
[[],[],[],[[],[[]]]] => [[[[[[],[]],[]]]]] => 2
[[],[],[],[[[]],[]]] => [[[[[],[[]],[]]]]] => 2
[[],[],[],[[[],[]]]] => [[[[[[]],[],[]]]]] => 2
[[],[],[],[[[[]]]]] => [[[[[],[],[],[]]]]] => 2
[[],[],[[]],[],[],[]] => [[[[],[[[[]]]]]]] => 2
[[],[],[[]],[],[[]]] => [[[[],[[[],[]]]]]] => 2
[[],[],[[]],[[]],[]] => [[[[],[[],[[]]]]]] => 2
[[],[],[[]],[[],[]]] => [[[[],[[[]],[]]]]] => 2
[[],[],[[]],[[[]]]] => [[[[],[[],[],[]]]]] => 2
[[],[],[[],[]],[],[]] => [[[[[]],[[[]]]]]] => 2
[[],[],[[[]]],[],[]] => [[[[],[],[[[]]]]]] => 2
[[],[],[[],[]],[[]]] => [[[[[]],[[],[]]]]] => 2
[[],[],[[[]]],[[]]] => [[[[],[],[[],[]]]]] => 2
[[],[],[[],[],[]],[]] => [[[[[[]]],[[]]]]] => 2
[[],[],[[],[[]]],[]] => [[[[[],[]],[[]]]]] => 2
[[],[],[[[]],[]],[]] => [[[[],[[]],[[]]]]] => 2
[[],[],[[[],[]]],[]] => [[[[[]],[],[[]]]]] => 2
[[],[],[[[[]]]],[]] => [[[[],[],[],[[]]]]] => 2
[[],[],[[],[],[],[]]] => [[[[[[[]]]],[]]]] => 2
[[],[],[[],[],[[]]]] => [[[[[[],[]]],[]]]] => 2
[[],[],[[],[[]],[]]] => [[[[[],[[]]],[]]]] => 2
[[],[],[[],[[],[]]]] => [[[[[[]],[]],[]]]] => 2
[[],[],[[],[[[]]]]] => [[[[[],[],[]],[]]]] => 2
[[],[],[[[]],[],[]]] => [[[[],[[[]]],[]]]] => 2
[[],[],[[[]],[[]]]] => [[[[],[[],[]],[]]]] => 2
[[],[],[[[],[]],[]]] => [[[[[]],[[]],[]]]] => 2
[[],[],[[[[]]],[]]] => [[[[],[],[[]],[]]]] => 2
[[],[],[[[],[],[]]]] => [[[[[[]]],[],[]]]] => 2
[[],[],[[[],[[]]]]] => [[[[[],[]],[],[]]]] => 2
[[],[],[[[[]],[]]]] => [[[[],[[]],[],[]]]] => 2
[[],[],[[[[],[]]]]] => [[[[[]],[],[],[]]]] => 2
[[],[],[[[[[]]]]]] => [[[[],[],[],[],[]]]] => 2
[[],[[]],[],[],[],[]] => [[[],[[[[[]]]]]]] => 2
[[],[[]],[],[],[[]]] => [[[],[[[[],[]]]]]] => 2
[[],[[]],[],[[]],[]] => [[[],[[[],[[]]]]]] => 2
[[],[[]],[],[[],[]]] => [[[],[[[[]],[]]]]] => 2
[[],[[]],[],[[[]]]] => [[[],[[[],[],[]]]]] => 2
[[],[[]],[[]],[],[]] => [[[],[[],[[[]]]]]] => 2
[[],[[]],[[]],[[]]] => [[[],[[],[[],[]]]]] => 2
[[],[[]],[[],[]],[]] => [[[],[[[]],[[]]]]] => 2
[[],[[]],[[[]]],[]] => [[[],[[],[],[[]]]]] => 2
[[],[[]],[[],[],[]]] => [[[],[[[[]]],[]]]] => 2
[[],[[]],[[],[[]]]] => [[[],[[[],[]],[]]]] => 2
[[],[[]],[[[]],[]]] => [[[],[[],[[]],[]]]] => 2
[[],[[]],[[[],[]]]] => [[[],[[[]],[],[]]]] => 2
[[],[[]],[[[[]]]]] => [[[],[[],[],[],[]]]] => 2
[[],[[],[]],[],[],[]] => [[[[]],[[[[]]]]]] => 2
[[],[[[]]],[],[],[]] => [[[],[],[[[[]]]]]] => 2
[[],[[],[]],[],[[]]] => [[[[]],[[[],[]]]]] => 2
[[],[[[]]],[],[[]]] => [[[],[],[[[],[]]]]] => 2
[[],[[],[]],[[]],[]] => [[[[]],[[],[[]]]]] => 2
[[],[[[]]],[[]],[]] => [[[],[],[[],[[]]]]] => 2
[[],[[],[]],[[],[]]] => [[[[]],[[[]],[]]]] => 2
[[],[[],[]],[[[]]]] => [[[[]],[[],[],[]]]] => 2
[[],[[[]]],[[],[]]] => [[[],[],[[[]],[]]]] => 2
[[],[[[]]],[[[]]]] => [[[],[],[[],[],[]]]] => 2
[[],[[],[],[]],[],[]] => [[[[[]]],[[[]]]]] => 2
[[],[[],[[]]],[],[]] => [[[[],[]],[[[]]]]] => 2
[[],[[[]],[]],[],[]] => [[[],[[]],[[[]]]]] => 2
[[],[[[],[]]],[],[]] => [[[[]],[],[[[]]]]] => 2
[[],[[[[]]]],[],[]] => [[[],[],[],[[[]]]]] => 2
[[],[[],[],[]],[[]]] => [[[[[]]],[[],[]]]] => 2
[[],[[],[[]]],[[]]] => [[[[],[]],[[],[]]]] => 3
[[],[[[]],[]],[[]]] => [[[],[[]],[[],[]]]] => 2
[[],[[[],[]]],[[]]] => [[[[]],[],[[],[]]]] => 2
[[],[[[[]]]],[[]]] => [[[],[],[],[[],[]]]] => 2
[[],[[],[],[],[]],[]] => [[[[[[]]]],[[]]]] => 2
[[],[[],[],[[]]],[]] => [[[[[],[]]],[[]]]] => 2
[[],[[],[[]],[]],[]] => [[[[],[[]]],[[]]]] => 2
[[],[[],[[],[]]],[]] => [[[[[]],[]],[[]]]] => 2
[[],[[],[[[]]]],[]] => [[[[],[],[]],[[]]]] => 2
[[],[[[]],[],[]],[]] => [[[],[[[]]],[[]]]] => 2
[[],[[[]],[[]]],[]] => [[[],[[],[]],[[]]]] => 2
[[],[[[],[]],[]],[]] => [[[[]],[[]],[[]]]] => 2
[[],[[[[]]],[]],[]] => [[[],[],[[]],[[]]]] => 2
[[],[[[],[],[]]],[]] => [[[[[]]],[],[[]]]] => 2
[[],[[[],[[]]]],[]] => [[[[],[]],[],[[]]]] => 2
[[],[[[[]],[]]],[]] => [[[],[[]],[],[[]]]] => 2
[[],[[[[],[]]]],[]] => [[[[]],[],[],[[]]]] => 2
[[],[[[[[]]]]],[]] => [[[],[],[],[],[[]]]] => 2
[[],[[],[],[],[],[]]] => [[[[[[[]]]]],[]]] => 2
[[],[[],[],[],[[]]]] => [[[[[[],[]]]],[]]] => 2
[[],[[],[],[[]],[]]] => [[[[[],[[]]]],[]]] => 2
[[],[[],[],[[],[]]]] => [[[[[[]],[]]],[]]] => 2
[[],[[],[],[[[]]]]] => [[[[[],[],[]]],[]]] => 2
[[],[[],[[]],[],[]]] => [[[[],[[[]]]],[]]] => 2
[[],[[],[[]],[[]]]] => [[[[],[[],[]]],[]]] => 2
[[],[[],[[],[]],[]]] => [[[[[]],[[]]],[]]] => 2
[[],[[],[[[]]],[]]] => [[[[],[],[[]]],[]]] => 2
[[],[[],[[],[],[]]]] => [[[[[[]]],[]],[]]] => 2
[[],[[],[[],[[]]]]] => [[[[[],[]],[]],[]]] => 2
[[],[[],[[[]],[]]]] => [[[[],[[]],[]],[]]] => 2
[[],[[],[[[],[]]]]] => [[[[[]],[],[]],[]]] => 2
[[],[[],[[[[]]]]]] => [[[[],[],[],[]],[]]] => 2
[[],[[[]],[],[],[]]] => [[[],[[[[]]]],[]]] => 2
[[],[[[]],[],[[]]]] => [[[],[[[],[]]],[]]] => 2
[[],[[[]],[[]],[]]] => [[[],[[],[[]]],[]]] => 2
[[],[[[]],[[],[]]]] => [[[],[[[]],[]],[]]] => 2
[[],[[[]],[[[]]]]] => [[[],[[],[],[]],[]]] => 2
[[],[[[],[]],[],[]]] => [[[[]],[[[]]],[]]] => 2
[[],[[[[]]],[],[]]] => [[[],[],[[[]]],[]]] => 2
[[],[[[],[]],[[]]]] => [[[[]],[[],[]],[]]] => 2
[[],[[[[]]],[[]]]] => [[[],[],[[],[]],[]]] => 2
[[],[[[],[],[]],[]]] => [[[[[]]],[[]],[]]] => 2
[[],[[[],[[]]],[]]] => [[[[],[]],[[]],[]]] => 2
[[],[[[[]],[]],[]]] => [[[],[[]],[[]],[]]] => 2
[[],[[[[],[]]],[]]] => [[[[]],[],[[]],[]]] => 2
[[],[[[[[]]]],[]]] => [[[],[],[],[[]],[]]] => 2
[[],[[[],[],[],[]]]] => [[[[[[]]]],[],[]]] => 2
[[],[[[],[],[[]]]]] => [[[[[],[]]],[],[]]] => 2
[[],[[[],[[]],[]]]] => [[[[],[[]]],[],[]]] => 2
[[],[[[],[[],[]]]]] => [[[[[]],[]],[],[]]] => 2
[[],[[[],[[[]]]]]] => [[[[],[],[]],[],[]]] => 2
[[],[[[[]],[],[]]]] => [[[],[[[]]],[],[]]] => 2
[[],[[[[]],[[]]]]] => [[[],[[],[]],[],[]]] => 2
[[],[[[[],[]],[]]]] => [[[[]],[[]],[],[]]] => 2
[[],[[[[[]]],[]]]] => [[[],[],[[]],[],[]]] => 2
[[],[[[[],[],[]]]]] => [[[[[]]],[],[],[]]] => 2
[[],[[[[],[[]]]]]] => [[[[],[]],[],[],[]]] => 2
[[],[[[[[]],[]]]]] => [[[],[[]],[],[],[]]] => 2
[[],[[[[[],[]]]]]] => [[[[]],[],[],[],[]]] => 2
[[],[[[[[[]]]]]]] => [[[],[],[],[],[],[]]] => 2
[[[]],[],[],[],[],[]] => [[],[[[[[[]]]]]]] => 1
[[[]],[],[],[],[[]]] => [[],[[[[[],[]]]]]] => 2
[[[]],[],[],[[]],[]] => [[],[[[[],[[]]]]]] => 2
[[[]],[],[],[[],[]]] => [[],[[[[[]],[]]]]] => 2
[[[]],[],[],[[[]]]] => [[],[[[[],[],[]]]]] => 2
[[[]],[],[[]],[],[]] => [[],[[[],[[[]]]]]] => 2
[[[]],[],[[]],[[]]] => [[],[[[],[[],[]]]]] => 2
[[[]],[],[[],[]],[]] => [[],[[[[]],[[]]]]] => 2
[[[]],[],[[[]]],[]] => [[],[[[],[],[[]]]]] => 2
[[[]],[],[[],[],[]]] => [[],[[[[[]]],[]]]] => 2
[[[]],[],[[],[[]]]] => [[],[[[[],[]],[]]]] => 2
[[[]],[],[[[]],[]]] => [[],[[[],[[]],[]]]] => 2
[[[]],[],[[[],[]]]] => [[],[[[[]],[],[]]]] => 2
[[[]],[],[[[[]]]]] => [[],[[[],[],[],[]]]] => 2
[[[]],[[]],[],[],[]] => [[],[[],[[[[]]]]]] => 2
[[[]],[[]],[],[[]]] => [[],[[],[[[],[]]]]] => 2
[[[]],[[]],[[]],[]] => [[],[[],[[],[[]]]]] => 2
[[[]],[[]],[[],[]]] => [[],[[],[[[]],[]]]] => 2
[[[]],[[]],[[[]]]] => [[],[[],[[],[],[]]]] => 2
[[[]],[[],[]],[],[]] => [[],[[[]],[[[]]]]] => 2
[[[]],[[[]]],[],[]] => [[],[[],[],[[[]]]]] => 2
[[[]],[[],[]],[[]]] => [[],[[[]],[[],[]]]] => 2
[[[]],[[[]]],[[]]] => [[],[[],[],[[],[]]]] => 2
[[[]],[[],[],[]],[]] => [[],[[[[]]],[[]]]] => 2
[[[]],[[],[[]]],[]] => [[],[[[],[]],[[]]]] => 2
[[[]],[[[]],[]],[]] => [[],[[],[[]],[[]]]] => 2
[[[]],[[[],[]]],[]] => [[],[[[]],[],[[]]]] => 2
[[[]],[[[[]]]],[]] => [[],[[],[],[],[[]]]] => 2
[[[]],[[],[],[],[]]] => [[],[[[[[]]]],[]]] => 2
[[[]],[[],[],[[]]]] => [[],[[[[],[]]],[]]] => 2
[[[]],[[],[[]],[]]] => [[],[[[],[[]]],[]]] => 2
[[[]],[[],[[],[]]]] => [[],[[[[]],[]],[]]] => 2
[[[]],[[],[[[]]]]] => [[],[[[],[],[]],[]]] => 2
[[[]],[[[]],[],[]]] => [[],[[],[[[]]],[]]] => 2
[[[]],[[[]],[[]]]] => [[],[[],[[],[]],[]]] => 2
[[[]],[[[],[]],[]]] => [[],[[[]],[[]],[]]] => 2
[[[]],[[[[]]],[]]] => [[],[[],[],[[]],[]]] => 2
[[[]],[[[],[],[]]]] => [[],[[[[]]],[],[]]] => 2
[[[]],[[[],[[]]]]] => [[],[[[],[]],[],[]]] => 2
[[[]],[[[[]],[]]]] => [[],[[],[[]],[],[]]] => 2
[[[]],[[[[],[]]]]] => [[],[[[]],[],[],[]]] => 2
[[[]],[[[[[]]]]]] => [[],[[],[],[],[],[]]] => 2
[[[],[]],[],[],[],[]] => [[[]],[[[[[]]]]]] => 1
[[[[]]],[],[],[],[]] => [[],[],[[[[[]]]]]] => 1
[[[],[]],[],[],[[]]] => [[[]],[[[[],[]]]]] => 2
[[[[]]],[],[],[[]]] => [[],[],[[[[],[]]]]] => 2
[[[],[]],[],[[]],[]] => [[[]],[[[],[[]]]]] => 2
[[[[]]],[],[[]],[]] => [[],[],[[[],[[]]]]] => 2
[[[],[]],[],[[],[]]] => [[[]],[[[[]],[]]]] => 2
[[[],[]],[],[[[]]]] => [[[]],[[[],[],[]]]] => 2
[[[[]]],[],[[],[]]] => [[],[],[[[[]],[]]]] => 2
[[[[]]],[],[[[]]]] => [[],[],[[[],[],[]]]] => 2
[[[],[]],[[]],[],[]] => [[[]],[[],[[[]]]]] => 2
[[[[]]],[[]],[],[]] => [[],[],[[],[[[]]]]] => 2
[[[],[]],[[]],[[]]] => [[[]],[[],[[],[]]]] => 2
[[[[]]],[[]],[[]]] => [[],[],[[],[[],[]]]] => 2
[[[],[]],[[],[]],[]] => [[[]],[[[]],[[]]]] => 2
[[[],[]],[[[]]],[]] => [[[]],[[],[],[[]]]] => 2
[[[[]]],[[],[]],[]] => [[],[],[[[]],[[]]]] => 2
[[[[]]],[[[]]],[]] => [[],[],[[],[],[[]]]] => 2
[[[],[]],[[],[],[]]] => [[[]],[[[[]]],[]]] => 2
[[[],[]],[[],[[]]]] => [[[]],[[[],[]],[]]] => 2
[[[],[]],[[[]],[]]] => [[[]],[[],[[]],[]]] => 2
[[[],[]],[[[],[]]]] => [[[]],[[[]],[],[]]] => 2
[[[],[]],[[[[]]]]] => [[[]],[[],[],[],[]]] => 2
[[[[]]],[[],[],[]]] => [[],[],[[[[]]],[]]] => 2
[[[[]]],[[],[[]]]] => [[],[],[[[],[]],[]]] => 2
[[[[]]],[[[]],[]]] => [[],[],[[],[[]],[]]] => 2
[[[[]]],[[[],[]]]] => [[],[],[[[]],[],[]]] => 2
[[[[]]],[[[[]]]]] => [[],[],[[],[],[],[]]] => 2
[[[],[],[]],[],[],[]] => [[[[]]],[[[[]]]]] => 1
[[[],[[]]],[],[],[]] => [[[],[]],[[[[]]]]] => 2
[[[[]],[]],[],[],[]] => [[],[[]],[[[[]]]]] => 1
[[[[],[]]],[],[],[]] => [[[]],[],[[[[]]]]] => 1
[[[[[]]]],[],[],[]] => [[],[],[],[[[[]]]]] => 1
[[[],[],[]],[],[[]]] => [[[[]]],[[[],[]]]] => 2
[[[],[[]]],[],[[]]] => [[[],[]],[[[],[]]]] => 2
[[[[]],[]],[],[[]]] => [[],[[]],[[[],[]]]] => 2
[[[[],[]]],[],[[]]] => [[[]],[],[[[],[]]]] => 2
[[[[[]]]],[],[[]]] => [[],[],[],[[[],[]]]] => 2
[[[],[],[]],[[]],[]] => [[[[]]],[[],[[]]]] => 2
[[[],[[]]],[[]],[]] => [[[],[]],[[],[[]]]] => 2
[[[[]],[]],[[]],[]] => [[],[[]],[[],[[]]]] => 2
[[[[],[]]],[[]],[]] => [[[]],[],[[],[[]]]] => 2
[[[[[]]]],[[]],[]] => [[],[],[],[[],[[]]]] => 2
[[[],[],[]],[[],[]]] => [[[[]]],[[[]],[]]] => 2
[[[],[],[]],[[[]]]] => [[[[]]],[[],[],[]]] => 2
[[[],[[]]],[[],[]]] => [[[],[]],[[[]],[]]] => 2
[[[],[[]]],[[[]]]] => [[[],[]],[[],[],[]]] => 2
[[[[]],[]],[[],[]]] => [[],[[]],[[[]],[]]] => 2
[[[[]],[]],[[[]]]] => [[],[[]],[[],[],[]]] => 2
[[[[],[]]],[[],[]]] => [[[]],[],[[[]],[]]] => 2
[[[[],[]]],[[[]]]] => [[[]],[],[[],[],[]]] => 2
[[[[[]]]],[[],[]]] => [[],[],[],[[[]],[]]] => 2
[[[[[]]]],[[[]]]] => [[],[],[],[[],[],[]]] => 2
[[[],[],[],[]],[],[]] => [[[[[]]]],[[[]]]] => 1
[[[],[],[[]]],[],[]] => [[[[],[]]],[[[]]]] => 2
[[[],[[]],[]],[],[]] => [[[],[[]]],[[[]]]] => 2
[[[],[[],[]]],[],[]] => [[[[]],[]],[[[]]]] => 2
[[[],[[[]]]],[],[]] => [[[],[],[]],[[[]]]] => 2
[[[[]],[],[]],[],[]] => [[],[[[]]],[[[]]]] => 1
[[[[]],[[]]],[],[]] => [[],[[],[]],[[[]]]] => 2
[[[[],[]],[]],[],[]] => [[[]],[[]],[[[]]]] => 1
[[[[[]]],[]],[],[]] => [[],[],[[]],[[[]]]] => 1
[[[[],[],[]]],[],[]] => [[[[]]],[],[[[]]]] => 1
[[[[],[[]]]],[],[]] => [[[],[]],[],[[[]]]] => 2
[[[[[]],[]]],[],[]] => [[],[[]],[],[[[]]]] => 1
[[[[[],[]]]],[],[]] => [[[]],[],[],[[[]]]] => 1
[[[[[[]]]]],[],[]] => [[],[],[],[],[[[]]]] => 1
[[[],[],[],[]],[[]]] => [[[[[]]]],[[],[]]] => 2
[[[],[],[[]]],[[]]] => [[[[],[]]],[[],[]]] => 2
[[[],[[]],[]],[[]]] => [[[],[[]]],[[],[]]] => 2
[[[],[[],[]]],[[]]] => [[[[]],[]],[[],[]]] => 2
[[[],[[[]]]],[[]]] => [[[],[],[]],[[],[]]] => 2
[[[[]],[],[]],[[]]] => [[],[[[]]],[[],[]]] => 2
[[[[]],[[]]],[[]]] => [[],[[],[]],[[],[]]] => 2
[[[[],[]],[]],[[]]] => [[[]],[[]],[[],[]]] => 2
[[[[[]]],[]],[[]]] => [[],[],[[]],[[],[]]] => 2
[[[[],[],[]]],[[]]] => [[[[]]],[],[[],[]]] => 2
[[[[],[[]]]],[[]]] => [[[],[]],[],[[],[]]] => 2
[[[[[]],[]]],[[]]] => [[],[[]],[],[[],[]]] => 2
[[[[[],[]]]],[[]]] => [[[]],[],[],[[],[]]] => 2
[[[[[[]]]]],[[]]] => [[],[],[],[],[[],[]]] => 2
[[[],[],[],[],[]],[]] => [[[[[[]]]]],[[]]] => 1
[[[],[],[],[[]]],[]] => [[[[[],[]]]],[[]]] => 2
[[[],[],[[]],[]],[]] => [[[[],[[]]]],[[]]] => 2
[[[],[],[[],[]]],[]] => [[[[[]],[]]],[[]]] => 2
[[[],[],[[[]]]],[]] => [[[[],[],[]]],[[]]] => 2
[[[],[[]],[],[]],[]] => [[[],[[[]]]],[[]]] => 2
[[[],[[]],[[]]],[]] => [[[],[[],[]]],[[]]] => 2
[[[],[[],[]],[]],[]] => [[[[]],[[]]],[[]]] => 2
[[[],[[[]]],[]],[]] => [[[],[],[[]]],[[]]] => 2
[[[],[[],[],[]]],[]] => [[[[[]]],[]],[[]]] => 2
[[[],[[],[[]]]],[]] => [[[[],[]],[]],[[]]] => 2
[[[],[[[]],[]]],[]] => [[[],[[]],[]],[[]]] => 2
[[[],[[[],[]]]],[]] => [[[[]],[],[]],[[]]] => 2
[[[],[[[[]]]]],[]] => [[[],[],[],[]],[[]]] => 2
[[[[]],[],[],[]],[]] => [[],[[[[]]]],[[]]] => 1
[[[[]],[],[[]]],[]] => [[],[[[],[]]],[[]]] => 2
[[[[]],[[]],[]],[]] => [[],[[],[[]]],[[]]] => 2
[[[[]],[[],[]]],[]] => [[],[[[]],[]],[[]]] => 2
[[[[]],[[[]]]],[]] => [[],[[],[],[]],[[]]] => 2
[[[[],[]],[],[]],[]] => [[[]],[[[]]],[[]]] => 1
[[[[[]]],[],[]],[]] => [[],[],[[[]]],[[]]] => 1
[[[[],[]],[[]]],[]] => [[[]],[[],[]],[[]]] => 2
[[[[[]]],[[]]],[]] => [[],[],[[],[]],[[]]] => 2
[[[[],[],[]],[]],[]] => [[[[]]],[[]],[[]]] => 1
[[[[],[[]]],[]],[]] => [[[],[]],[[]],[[]]] => 2
[[[[[]],[]],[]],[]] => [[],[[]],[[]],[[]]] => 1
[[[[[],[]]],[]],[]] => [[[]],[],[[]],[[]]] => 1
[[[[[[]]]],[]],[]] => [[],[],[],[[]],[[]]] => 1
[[[[],[],[],[]]],[]] => [[[[[]]]],[],[[]]] => 1
[[[[],[],[[]]]],[]] => [[[[],[]]],[],[[]]] => 2
[[[[],[[]],[]]],[]] => [[[],[[]]],[],[[]]] => 2
[[[[],[[],[]]]],[]] => [[[[]],[]],[],[[]]] => 2
[[[[],[[[]]]]],[]] => [[[],[],[]],[],[[]]] => 2
[[[[[]],[],[]]],[]] => [[],[[[]]],[],[[]]] => 1
[[[[[]],[[]]]],[]] => [[],[[],[]],[],[[]]] => 2
[[[[[],[]],[]]],[]] => [[[]],[[]],[],[[]]] => 1
[[[[[[]]],[]]],[]] => [[],[],[[]],[],[[]]] => 1
[[[[[],[],[]]]],[]] => [[[[]]],[],[],[[]]] => 1
[[[[[],[[]]]]],[]] => [[[],[]],[],[],[[]]] => 2
[[[[[[]],[]]]],[]] => [[],[[]],[],[],[[]]] => 1
[[[[[[],[]]]]],[]] => [[[]],[],[],[],[[]]] => 1
[[[[[[[]]]]]],[]] => [[],[],[],[],[],[[]]] => 1
[[[],[],[],[],[],[]]] => [[[[[[[]]]]]],[]] => 1
[[[],[],[],[],[[]]]] => [[[[[[],[]]]]],[]] => 2
[[[],[],[],[[]],[]]] => [[[[[],[[]]]]],[]] => 2
[[[],[],[],[[],[]]]] => [[[[[[]],[]]]],[]] => 2
[[[],[],[],[[[]]]]] => [[[[[],[],[]]]],[]] => 2
[[[],[],[[]],[],[]]] => [[[[],[[[]]]]],[]] => 2
[[[],[],[[]],[[]]]] => [[[[],[[],[]]]],[]] => 2
[[[],[],[[],[]],[]]] => [[[[[]],[[]]]],[]] => 2
[[[],[],[[[]]],[]]] => [[[[],[],[[]]]],[]] => 2
[[[],[],[[],[],[]]]] => [[[[[[]]],[]]],[]] => 2
[[[],[],[[],[[]]]]] => [[[[[],[]],[]]],[]] => 2
[[[],[],[[[]],[]]]] => [[[[],[[]],[]]],[]] => 2
[[[],[],[[[],[]]]]] => [[[[[]],[],[]]],[]] => 2
[[[],[],[[[[]]]]]] => [[[[],[],[],[]]],[]] => 2
[[[],[[]],[],[],[]]] => [[[],[[[[]]]]],[]] => 2
[[[],[[]],[],[[]]]] => [[[],[[[],[]]]],[]] => 2
[[[],[[]],[[]],[]]] => [[[],[[],[[]]]],[]] => 2
[[[],[[]],[[],[]]]] => [[[],[[[]],[]]],[]] => 2
[[[],[[]],[[[]]]]] => [[[],[[],[],[]]],[]] => 2
[[[],[[],[]],[],[]]] => [[[[]],[[[]]]],[]] => 2
[[[],[[[]]],[],[]]] => [[[],[],[[[]]]],[]] => 2
[[[],[[],[]],[[]]]] => [[[[]],[[],[]]],[]] => 2
[[[],[[[]]],[[]]]] => [[[],[],[[],[]]],[]] => 2
[[[],[[],[],[]],[]]] => [[[[[]]],[[]]],[]] => 2
[[[],[[],[[]]],[]]] => [[[[],[]],[[]]],[]] => 2
[[[],[[[]],[]],[]]] => [[[],[[]],[[]]],[]] => 2
[[[],[[[],[]]],[]]] => [[[[]],[],[[]]],[]] => 2
[[[],[[[[]]]],[]]] => [[[],[],[],[[]]],[]] => 2
[[[],[[],[],[],[]]]] => [[[[[[]]]],[]],[]] => 2
[[[],[[],[],[[]]]]] => [[[[[],[]]],[]],[]] => 2
[[[],[[],[[]],[]]]] => [[[[],[[]]],[]],[]] => 2
[[[],[[],[[],[]]]]] => [[[[[]],[]],[]],[]] => 2
[[[],[[],[[[]]]]]] => [[[[],[],[]],[]],[]] => 2
[[[],[[[]],[],[]]]] => [[[],[[[]]],[]],[]] => 2
[[[],[[[]],[[]]]]] => [[[],[[],[]],[]],[]] => 2
[[[],[[[],[]],[]]]] => [[[[]],[[]],[]],[]] => 2
[[[],[[[[]]],[]]]] => [[[],[],[[]],[]],[]] => 2
[[[],[[[],[],[]]]]] => [[[[[]]],[],[]],[]] => 2
[[[],[[[],[[]]]]]] => [[[[],[]],[],[]],[]] => 2
[[[],[[[[]],[]]]]] => [[[],[[]],[],[]],[]] => 2
[[[],[[[[],[]]]]]] => [[[[]],[],[],[]],[]] => 2
[[[],[[[[[]]]]]]] => [[[],[],[],[],[]],[]] => 2
[[[[]],[],[],[],[]]] => [[],[[[[[]]]]],[]] => 1
[[[[]],[],[],[[]]]] => [[],[[[[],[]]]],[]] => 2
[[[[]],[],[[]],[]]] => [[],[[[],[[]]]],[]] => 2
[[[[]],[],[[],[]]]] => [[],[[[[]],[]]],[]] => 2
[[[[]],[],[[[]]]]] => [[],[[[],[],[]]],[]] => 2
[[[[]],[[]],[],[]]] => [[],[[],[[[]]]],[]] => 2
[[[[]],[[]],[[]]]] => [[],[[],[[],[]]],[]] => 2
[[[[]],[[],[]],[]]] => [[],[[[]],[[]]],[]] => 2
[[[[]],[[[]]],[]]] => [[],[[],[],[[]]],[]] => 2
[[[[]],[[],[],[]]]] => [[],[[[[]]],[]],[]] => 2
[[[[]],[[],[[]]]]] => [[],[[[],[]],[]],[]] => 2
[[[[]],[[[]],[]]]] => [[],[[],[[]],[]],[]] => 2
[[[[]],[[[],[]]]]] => [[],[[[]],[],[]],[]] => 2
[[[[]],[[[[]]]]]] => [[],[[],[],[],[]],[]] => 2
[[[[],[]],[],[],[]]] => [[[]],[[[[]]]],[]] => 1
[[[[[]]],[],[],[]]] => [[],[],[[[[]]]],[]] => 1
[[[[],[]],[],[[]]]] => [[[]],[[[],[]]],[]] => 2
[[[[[]]],[],[[]]]] => [[],[],[[[],[]]],[]] => 2
[[[[],[]],[[]],[]]] => [[[]],[[],[[]]],[]] => 2
[[[[[]]],[[]],[]]] => [[],[],[[],[[]]],[]] => 2
[[[[],[]],[[],[]]]] => [[[]],[[[]],[]],[]] => 2
[[[[],[]],[[[]]]]] => [[[]],[[],[],[]],[]] => 2
[[[[[]]],[[],[]]]] => [[],[],[[[]],[]],[]] => 2
[[[[[]]],[[[]]]]] => [[],[],[[],[],[]],[]] => 2
[[[[],[],[]],[],[]]] => [[[[]]],[[[]]],[]] => 1
[[[[],[[]]],[],[]]] => [[[],[]],[[[]]],[]] => 2
[[[[[]],[]],[],[]]] => [[],[[]],[[[]]],[]] => 1
[[[[[],[]]],[],[]]] => [[[]],[],[[[]]],[]] => 1
[[[[[[]]]],[],[]]] => [[],[],[],[[[]]],[]] => 1
[[[[],[],[]],[[]]]] => [[[[]]],[[],[]],[]] => 2
[[[[],[[]]],[[]]]] => [[[],[]],[[],[]],[]] => 2
[[[[[]],[]],[[]]]] => [[],[[]],[[],[]],[]] => 2
[[[[[],[]]],[[]]]] => [[[]],[],[[],[]],[]] => 2
[[[[[[]]]],[[]]]] => [[],[],[],[[],[]],[]] => 2
[[[[],[],[],[]],[]]] => [[[[[]]]],[[]],[]] => 1
[[[[],[],[[]]],[]]] => [[[[],[]]],[[]],[]] => 2
[[[[],[[]],[]],[]]] => [[[],[[]]],[[]],[]] => 2
[[[[],[[],[]]],[]]] => [[[[]],[]],[[]],[]] => 2
[[[[],[[[]]]],[]]] => [[[],[],[]],[[]],[]] => 2
[[[[[]],[],[]],[]]] => [[],[[[]]],[[]],[]] => 1
[[[[[]],[[]]],[]]] => [[],[[],[]],[[]],[]] => 2
[[[[[],[]],[]],[]]] => [[[]],[[]],[[]],[]] => 1
[[[[[[]]],[]],[]]] => [[],[],[[]],[[]],[]] => 1
[[[[[],[],[]]],[]]] => [[[[]]],[],[[]],[]] => 1
[[[[[],[[]]]],[]]] => [[[],[]],[],[[]],[]] => 2
[[[[[[]],[]]],[]]] => [[],[[]],[],[[]],[]] => 1
[[[[[[],[]]]],[]]] => [[[]],[],[],[[]],[]] => 1
[[[[[[[]]]]],[]]] => [[],[],[],[],[[]],[]] => 1
[[[[],[],[],[],[]]]] => [[[[[[]]]]],[],[]] => 1
[[[[],[],[],[[]]]]] => [[[[[],[]]]],[],[]] => 2
[[[[],[],[[]],[]]]] => [[[[],[[]]]],[],[]] => 2
[[[[],[],[[],[]]]]] => [[[[[]],[]]],[],[]] => 2
[[[[],[],[[[]]]]]] => [[[[],[],[]]],[],[]] => 2
[[[[],[[]],[],[]]]] => [[[],[[[]]]],[],[]] => 2
[[[[],[[]],[[]]]]] => [[[],[[],[]]],[],[]] => 2
[[[[],[[],[]],[]]]] => [[[[]],[[]]],[],[]] => 2
[[[[],[[[]]],[]]]] => [[[],[],[[]]],[],[]] => 2
[[[[],[[],[],[]]]]] => [[[[[]]],[]],[],[]] => 2
[[[[],[[],[[]]]]]] => [[[[],[]],[]],[],[]] => 2
[[[[],[[[]],[]]]]] => [[[],[[]],[]],[],[]] => 2
[[[[],[[[],[]]]]]] => [[[[]],[],[]],[],[]] => 2
[[[[],[[[[]]]]]]] => [[[],[],[],[]],[],[]] => 2
[[[[[]],[],[],[]]]] => [[],[[[[]]]],[],[]] => 1
[[[[[]],[],[[]]]]] => [[],[[[],[]]],[],[]] => 2
[[[[[]],[[]],[]]]] => [[],[[],[[]]],[],[]] => 2
[[[[[]],[[],[]]]]] => [[],[[[]],[]],[],[]] => 2
[[[[[]],[[[]]]]]] => [[],[[],[],[]],[],[]] => 2
[[[[[],[]],[],[]]]] => [[[]],[[[]]],[],[]] => 1
[[[[[[]]],[],[]]]] => [[],[],[[[]]],[],[]] => 1
[[[[[],[]],[[]]]]] => [[[]],[[],[]],[],[]] => 2
[[[[[[]]],[[]]]]] => [[],[],[[],[]],[],[]] => 2
[[[[[],[],[]],[]]]] => [[[[]]],[[]],[],[]] => 1
[[[[[],[[]]],[]]]] => [[[],[]],[[]],[],[]] => 2
[[[[[[]],[]],[]]]] => [[],[[]],[[]],[],[]] => 1
[[[[[[],[]]],[]]]] => [[[]],[],[[]],[],[]] => 1
[[[[[[[]]]],[]]]] => [[],[],[],[[]],[],[]] => 1
[[[[[],[],[],[]]]]] => [[[[[]]]],[],[],[]] => 1
[[[[[],[],[[]]]]]] => [[[[],[]]],[],[],[]] => 2
[[[[[],[[]],[]]]]] => [[[],[[]]],[],[],[]] => 2
[[[[[],[[],[]]]]]] => [[[[]],[]],[],[],[]] => 2
[[[[[],[[[]]]]]]] => [[[],[],[]],[],[],[]] => 2
[[[[[[]],[],[]]]]] => [[],[[[]]],[],[],[]] => 1
[[[[[[]],[[]]]]]] => [[],[[],[]],[],[],[]] => 2
[[[[[[],[]],[]]]]] => [[[]],[[]],[],[],[]] => 1
[[[[[[[]]],[]]]]] => [[],[],[[]],[],[],[]] => 1
[[[[[[],[],[]]]]]] => [[[[]]],[],[],[],[]] => 1
[[[[[[],[[]]]]]]] => [[[],[]],[],[],[],[]] => 2
[[[[[[[]],[]]]]]] => [[],[[]],[],[],[],[]] => 1
[[[[[[[],[]]]]]]] => [[[]],[],[],[],[],[]] => 1
[[[[[[[[]]]]]]]] => [[],[],[],[],[],[],[]] => 1
[[[]],[],[],[],[],[],[]] => [[],[[[[[[[]]]]]]]] => 1
[[[]],[],[],[],[],[[]]] => [[],[[[[[[],[]]]]]]] => 2
[[[]],[],[],[],[[]],[]] => [[],[[[[[],[[]]]]]]] => 2
[[[]],[],[],[],[[],[]]] => [[],[[[[[[]],[]]]]]] => 2
[[[]],[],[],[],[[[]]]] => [[],[[[[[],[],[]]]]]] => 2
[[[]],[],[],[[]],[],[]] => [[],[[[[],[[[]]]]]]] => 2
[[[]],[],[],[[]],[[]]] => [[],[[[[],[[],[]]]]]] => 2
[[[]],[],[],[[],[]],[]] => [[],[[[[[]],[[]]]]]] => 2
[[[]],[],[],[[[]]],[]] => [[],[[[[],[],[[]]]]]] => 2
[[[]],[],[],[[],[],[]]] => [[],[[[[[[]]],[]]]]] => 2
[[[]],[],[],[[],[[]]]] => [[],[[[[[],[]],[]]]]] => 2
[[[]],[],[],[[[]],[]]] => [[],[[[[],[[]],[]]]]] => 2
[[[]],[],[],[[[],[]]]] => [[],[[[[[]],[],[]]]]] => 2
[[[]],[],[],[[[[]]]]] => [[],[[[[],[],[],[]]]]] => 2
[[[]],[],[[]],[],[],[]] => [[],[[[],[[[[]]]]]]] => 2
[[[]],[],[[]],[],[[]]] => [[],[[[],[[[],[]]]]]] => 2
[[[]],[],[[]],[[]],[]] => [[],[[[],[[],[[]]]]]] => 2
[[[]],[],[[]],[[],[]]] => [[],[[[],[[[]],[]]]]] => 2
[[[]],[],[[]],[[[]]]] => [[],[[[],[[],[],[]]]]] => 2
[[[]],[],[[],[]],[],[]] => [[],[[[[]],[[[]]]]]] => 2
[[[]],[],[[[]]],[],[]] => [[],[[[],[],[[[]]]]]] => 2
[[[]],[],[[],[]],[[]]] => [[],[[[[]],[[],[]]]]] => 2
[[[]],[],[[[]]],[[]]] => [[],[[[],[],[[],[]]]]] => 2
[[[]],[],[[],[],[]],[]] => [[],[[[[[]]],[[]]]]] => 2
[[[]],[],[[],[[]]],[]] => [[],[[[[],[]],[[]]]]] => 2
[[[]],[],[[[]],[]],[]] => [[],[[[],[[]],[[]]]]] => 2
[[[]],[],[[[],[]]],[]] => [[],[[[[]],[],[[]]]]] => 2
[[[]],[],[[[[]]]],[]] => [[],[[[],[],[],[[]]]]] => 2
[[[]],[],[[],[],[],[]]] => [[],[[[[[[]]]],[]]]] => 2
[[[]],[],[[],[],[[]]]] => [[],[[[[[],[]]],[]]]] => 2
[[[]],[],[[],[[]],[]]] => [[],[[[[],[[]]],[]]]] => 2
[[[]],[],[[],[[],[]]]] => [[],[[[[[]],[]],[]]]] => 2
[[[]],[],[[],[[[]]]]] => [[],[[[[],[],[]],[]]]] => 2
[[[]],[],[[[]],[],[]]] => [[],[[[],[[[]]],[]]]] => 2
[[[]],[],[[[]],[[]]]] => [[],[[[],[[],[]],[]]]] => 2
[[[]],[],[[[],[]],[]]] => [[],[[[[]],[[]],[]]]] => 2
[[[]],[],[[[[]]],[]]] => [[],[[[],[],[[]],[]]]] => 2
[[[]],[],[[[],[],[]]]] => [[],[[[[[]]],[],[]]]] => 2
[[[]],[],[[[],[[]]]]] => [[],[[[[],[]],[],[]]]] => 2
[[[]],[],[[[[]],[]]]] => [[],[[[],[[]],[],[]]]] => 2
[[[]],[],[[[[],[]]]]] => [[],[[[[]],[],[],[]]]] => 2
[[[]],[],[[[[[]]]]]] => [[],[[[],[],[],[],[]]]] => 2
[[[]],[[]],[],[],[],[]] => [[],[[],[[[[[]]]]]]] => 2
[[[]],[[]],[],[],[[]]] => [[],[[],[[[[],[]]]]]] => 2
[[[]],[[]],[],[[]],[]] => [[],[[],[[[],[[]]]]]] => 2
[[[]],[[]],[],[[],[]]] => [[],[[],[[[[]],[]]]]] => 2
[[[]],[[]],[],[[[]]]] => [[],[[],[[[],[],[]]]]] => 2
[[[]],[[]],[[]],[],[]] => [[],[[],[[],[[[]]]]]] => 2
[[[]],[[]],[[]],[[]]] => [[],[[],[[],[[],[]]]]] => 2
[[[]],[[]],[[],[]],[]] => [[],[[],[[[]],[[]]]]] => 2
[[[]],[[]],[[[]]],[]] => [[],[[],[[],[],[[]]]]] => 2
[[[]],[[]],[[],[],[]]] => [[],[[],[[[[]]],[]]]] => 2
[[[]],[[]],[[],[[]]]] => [[],[[],[[[],[]],[]]]] => 2
[[[]],[[]],[[[]],[]]] => [[],[[],[[],[[]],[]]]] => 2
[[[]],[[]],[[[],[]]]] => [[],[[],[[[]],[],[]]]] => 2
[[[]],[[]],[[[[]]]]] => [[],[[],[[],[],[],[]]]] => 2
[[[]],[[],[]],[],[],[]] => [[],[[[]],[[[[]]]]]] => 2
[[[]],[[[]]],[],[],[]] => [[],[[],[],[[[[]]]]]] => 2
[[[]],[[],[]],[],[[]]] => [[],[[[]],[[[],[]]]]] => 2
[[[]],[[[]]],[],[[]]] => [[],[[],[],[[[],[]]]]] => 2
[[[]],[[],[]],[[]],[]] => [[],[[[]],[[],[[]]]]] => 2
[[[]],[[[]]],[[]],[]] => [[],[[],[],[[],[[]]]]] => 2
[[[]],[[],[]],[[],[]]] => [[],[[[]],[[[]],[]]]] => 2
[[[]],[[],[]],[[[]]]] => [[],[[[]],[[],[],[]]]] => 2
[[[]],[[[]]],[[],[]]] => [[],[[],[],[[[]],[]]]] => 2
[[[]],[[[]]],[[[]]]] => [[],[[],[],[[],[],[]]]] => 2
[[[]],[[],[],[]],[],[]] => [[],[[[[]]],[[[]]]]] => 2
[[[]],[[],[[]]],[],[]] => [[],[[[],[]],[[[]]]]] => 2
[[[]],[[[]],[]],[],[]] => [[],[[],[[]],[[[]]]]] => 2
[[[]],[[[],[]]],[],[]] => [[],[[[]],[],[[[]]]]] => 2
[[[]],[[[[]]]],[],[]] => [[],[[],[],[],[[[]]]]] => 2
[[[]],[[],[],[]],[[]]] => [[],[[[[]]],[[],[]]]] => 2
[[[]],[[],[[]]],[[]]] => [[],[[[],[]],[[],[]]]] => 3
[[[]],[[[]],[]],[[]]] => [[],[[],[[]],[[],[]]]] => 2
[[[]],[[[],[]]],[[]]] => [[],[[[]],[],[[],[]]]] => 2
[[[]],[[[[]]]],[[]]] => [[],[[],[],[],[[],[]]]] => 2
[[[]],[[],[],[],[]],[]] => [[],[[[[[]]]],[[]]]] => 2
[[[]],[[],[],[[]]],[]] => [[],[[[[],[]]],[[]]]] => 2
[[[]],[[],[[]],[]],[]] => [[],[[[],[[]]],[[]]]] => 2
[[[]],[[],[[],[]]],[]] => [[],[[[[]],[]],[[]]]] => 2
[[[]],[[],[[[]]]],[]] => [[],[[[],[],[]],[[]]]] => 2
[[[]],[[[]],[],[]],[]] => [[],[[],[[[]]],[[]]]] => 2
[[[]],[[[]],[[]]],[]] => [[],[[],[[],[]],[[]]]] => 2
[[[]],[[[],[]],[]],[]] => [[],[[[]],[[]],[[]]]] => 2
[[[]],[[[[]]],[]],[]] => [[],[[],[],[[]],[[]]]] => 2
[[[]],[[[],[],[]]],[]] => [[],[[[[]]],[],[[]]]] => 2
[[[]],[[[],[[]]]],[]] => [[],[[[],[]],[],[[]]]] => 2
[[[]],[[[[]],[]]],[]] => [[],[[],[[]],[],[[]]]] => 2
[[[]],[[[[],[]]]],[]] => [[],[[[]],[],[],[[]]]] => 2
[[[]],[[[[[]]]]],[]] => [[],[[],[],[],[],[[]]]] => 2
[[[]],[[],[],[],[],[]]] => [[],[[[[[[]]]]],[]]] => 2
[[[]],[[],[],[],[[]]]] => [[],[[[[[],[]]]],[]]] => 2
[[[]],[[],[],[[]],[]]] => [[],[[[[],[[]]]],[]]] => 2
[[[]],[[],[],[[],[]]]] => [[],[[[[[]],[]]],[]]] => 2
[[[]],[[],[],[[[]]]]] => [[],[[[[],[],[]]],[]]] => 2
[[[]],[[],[[]],[],[]]] => [[],[[[],[[[]]]],[]]] => 2
[[[]],[[],[[]],[[]]]] => [[],[[[],[[],[]]],[]]] => 2
[[[]],[[],[[],[]],[]]] => [[],[[[[]],[[]]],[]]] => 2
[[[]],[[],[[[]]],[]]] => [[],[[[],[],[[]]],[]]] => 2
[[[]],[[],[[],[],[]]]] => [[],[[[[[]]],[]],[]]] => 2
[[[]],[[],[[],[[]]]]] => [[],[[[[],[]],[]],[]]] => 2
[[[]],[[],[[[]],[]]]] => [[],[[[],[[]],[]],[]]] => 2
[[[]],[[],[[[],[]]]]] => [[],[[[[]],[],[]],[]]] => 2
[[[]],[[],[[[[]]]]]] => [[],[[[],[],[],[]],[]]] => 2
[[[]],[[[]],[],[],[]]] => [[],[[],[[[[]]]],[]]] => 2
[[[]],[[[]],[],[[]]]] => [[],[[],[[[],[]]],[]]] => 2
[[[]],[[[]],[[]],[]]] => [[],[[],[[],[[]]],[]]] => 2
[[[]],[[[]],[[],[]]]] => [[],[[],[[[]],[]],[]]] => 2
[[[]],[[[]],[[[]]]]] => [[],[[],[[],[],[]],[]]] => 2
[[[]],[[[],[]],[],[]]] => [[],[[[]],[[[]]],[]]] => 2
[[[]],[[[[]]],[],[]]] => [[],[[],[],[[[]]],[]]] => 2
[[[]],[[[],[]],[[]]]] => [[],[[[]],[[],[]],[]]] => 2
[[[]],[[[[]]],[[]]]] => [[],[[],[],[[],[]],[]]] => 2
[[[]],[[[],[],[]],[]]] => [[],[[[[]]],[[]],[]]] => 2
[[[]],[[[],[[]]],[]]] => [[],[[[],[]],[[]],[]]] => 2
[[[]],[[[[]],[]],[]]] => [[],[[],[[]],[[]],[]]] => 2
[[[]],[[[[],[]]],[]]] => [[],[[[]],[],[[]],[]]] => 2
[[[]],[[[[[]]]],[]]] => [[],[[],[],[],[[]],[]]] => 2
[[[]],[[[],[],[],[]]]] => [[],[[[[[]]]],[],[]]] => 2
[[[]],[[[],[],[[]]]]] => [[],[[[[],[]]],[],[]]] => 2
[[[]],[[[],[[]],[]]]] => [[],[[[],[[]]],[],[]]] => 2
[[[]],[[[],[[],[]]]]] => [[],[[[[]],[]],[],[]]] => 2
[[[]],[[[],[[[]]]]]] => [[],[[[],[],[]],[],[]]] => 2
[[[]],[[[[]],[],[]]]] => [[],[[],[[[]]],[],[]]] => 2
[[[]],[[[[]],[[]]]]] => [[],[[],[[],[]],[],[]]] => 2
[[[]],[[[[],[]],[]]]] => [[],[[[]],[[]],[],[]]] => 2
[[[]],[[[[[]]],[]]]] => [[],[[],[],[[]],[],[]]] => 2
[[[]],[[[[],[],[]]]]] => [[],[[[[]]],[],[],[]]] => 2
[[[]],[[[[],[[]]]]]] => [[],[[[],[]],[],[],[]]] => 2
[[[]],[[[[[]],[]]]]] => [[],[[],[[]],[],[],[]]] => 2
[[[]],[[[[[],[]]]]]] => [[],[[[]],[],[],[],[]]] => 2
[[[]],[[[[[[]]]]]]] => [[],[[],[],[],[],[],[]]] => 2
[[[],[]],[],[],[],[],[]] => [[[]],[[[[[[]]]]]]] => 1
[[[[]]],[],[],[],[],[]] => [[],[],[[[[[[]]]]]]] => 1
[[[],[]],[],[],[],[[]]] => [[[]],[[[[[],[]]]]]] => 2
[[[[]]],[],[],[],[[]]] => [[],[],[[[[[],[]]]]]] => 2
[[[],[]],[],[],[[]],[]] => [[[]],[[[[],[[]]]]]] => 2
[[[[]]],[],[],[[]],[]] => [[],[],[[[[],[[]]]]]] => 2
[[[],[]],[],[],[[],[]]] => [[[]],[[[[[]],[]]]]] => 2
[[[],[]],[],[],[[[]]]] => [[[]],[[[[],[],[]]]]] => 2
[[[[]]],[],[],[[],[]]] => [[],[],[[[[[]],[]]]]] => 2
[[[[]]],[],[],[[[]]]] => [[],[],[[[[],[],[]]]]] => 2
[[[],[]],[],[[]],[],[]] => [[[]],[[[],[[[]]]]]] => 2
[[[[]]],[],[[]],[],[]] => [[],[],[[[],[[[]]]]]] => 2
[[[],[]],[],[[]],[[]]] => [[[]],[[[],[[],[]]]]] => 2
[[[[]]],[],[[]],[[]]] => [[],[],[[[],[[],[]]]]] => 2
[[[],[]],[],[[],[]],[]] => [[[]],[[[[]],[[]]]]] => 2
[[[],[]],[],[[[]]],[]] => [[[]],[[[],[],[[]]]]] => 2
[[[[]]],[],[[],[]],[]] => [[],[],[[[[]],[[]]]]] => 2
[[[[]]],[],[[[]]],[]] => [[],[],[[[],[],[[]]]]] => 2
[[[],[]],[],[[],[],[]]] => [[[]],[[[[[]]],[]]]] => 2
[[[],[]],[],[[],[[]]]] => [[[]],[[[[],[]],[]]]] => 2
[[[],[]],[],[[[]],[]]] => [[[]],[[[],[[]],[]]]] => 2
[[[],[]],[],[[[],[]]]] => [[[]],[[[[]],[],[]]]] => 2
[[[],[]],[],[[[[]]]]] => [[[]],[[[],[],[],[]]]] => 2
[[[[]]],[],[[],[],[]]] => [[],[],[[[[[]]],[]]]] => 2
[[[[]]],[],[[],[[]]]] => [[],[],[[[[],[]],[]]]] => 2
[[[[]]],[],[[[]],[]]] => [[],[],[[[],[[]],[]]]] => 2
[[[[]]],[],[[[],[]]]] => [[],[],[[[[]],[],[]]]] => 2
[[[[]]],[],[[[[]]]]] => [[],[],[[[],[],[],[]]]] => 2
[[[],[]],[[]],[],[],[]] => [[[]],[[],[[[[]]]]]] => 2
[[[[]]],[[]],[],[],[]] => [[],[],[[],[[[[]]]]]] => 2
[[[],[]],[[]],[],[[]]] => [[[]],[[],[[[],[]]]]] => 2
[[[[]]],[[]],[],[[]]] => [[],[],[[],[[[],[]]]]] => 2
[[[],[]],[[]],[[]],[]] => [[[]],[[],[[],[[]]]]] => 2
[[[[]]],[[]],[[]],[]] => [[],[],[[],[[],[[]]]]] => 2
[[[],[]],[[]],[[],[]]] => [[[]],[[],[[[]],[]]]] => 2
[[[],[]],[[]],[[[]]]] => [[[]],[[],[[],[],[]]]] => 2
[[[[]]],[[]],[[],[]]] => [[],[],[[],[[[]],[]]]] => 2
[[[[]]],[[]],[[[]]]] => [[],[],[[],[[],[],[]]]] => 2
[[[],[]],[[],[]],[],[]] => [[[]],[[[]],[[[]]]]] => 2
[[[],[]],[[[]]],[],[]] => [[[]],[[],[],[[[]]]]] => 2
[[[[]]],[[],[]],[],[]] => [[],[],[[[]],[[[]]]]] => 2
[[[[]]],[[[]]],[],[]] => [[],[],[[],[],[[[]]]]] => 2
[[[],[]],[[],[]],[[]]] => [[[]],[[[]],[[],[]]]] => 2
[[[],[]],[[[]]],[[]]] => [[[]],[[],[],[[],[]]]] => 2
[[[[]]],[[],[]],[[]]] => [[],[],[[[]],[[],[]]]] => 2
[[[[]]],[[[]]],[[]]] => [[],[],[[],[],[[],[]]]] => 2
[[[],[]],[[],[],[]],[]] => [[[]],[[[[]]],[[]]]] => 2
[[[],[]],[[],[[]]],[]] => [[[]],[[[],[]],[[]]]] => 2
[[[],[]],[[[]],[]],[]] => [[[]],[[],[[]],[[]]]] => 2
[[[],[]],[[[],[]]],[]] => [[[]],[[[]],[],[[]]]] => 2
[[[],[]],[[[[]]]],[]] => [[[]],[[],[],[],[[]]]] => 2
[[[[]]],[[],[],[]],[]] => [[],[],[[[[]]],[[]]]] => 2
[[[[]]],[[],[[]]],[]] => [[],[],[[[],[]],[[]]]] => 2
[[[[]]],[[[]],[]],[]] => [[],[],[[],[[]],[[]]]] => 2
[[[[]]],[[[],[]]],[]] => [[],[],[[[]],[],[[]]]] => 2
[[[[]]],[[[[]]]],[]] => [[],[],[[],[],[],[[]]]] => 2
[[[],[]],[[],[],[],[]]] => [[[]],[[[[[]]]],[]]] => 2
[[[],[]],[[],[],[[]]]] => [[[]],[[[[],[]]],[]]] => 2
[[[],[]],[[],[[]],[]]] => [[[]],[[[],[[]]],[]]] => 2
[[[],[]],[[],[[],[]]]] => [[[]],[[[[]],[]],[]]] => 2
[[[],[]],[[],[[[]]]]] => [[[]],[[[],[],[]],[]]] => 2
[[[],[]],[[[]],[],[]]] => [[[]],[[],[[[]]],[]]] => 2
[[[],[]],[[[]],[[]]]] => [[[]],[[],[[],[]],[]]] => 2
[[[],[]],[[[],[]],[]]] => [[[]],[[[]],[[]],[]]] => 2
[[[],[]],[[[[]]],[]]] => [[[]],[[],[],[[]],[]]] => 2
[[[],[]],[[[],[],[]]]] => [[[]],[[[[]]],[],[]]] => 2
[[[],[]],[[[],[[]]]]] => [[[]],[[[],[]],[],[]]] => 2
[[[],[]],[[[[]],[]]]] => [[[]],[[],[[]],[],[]]] => 2
[[[],[]],[[[[],[]]]]] => [[[]],[[[]],[],[],[]]] => 2
[[[],[]],[[[[[]]]]]] => [[[]],[[],[],[],[],[]]] => 2
[[[[]]],[[],[],[],[]]] => [[],[],[[[[[]]]],[]]] => 2
[[[[]]],[[],[],[[]]]] => [[],[],[[[[],[]]],[]]] => 2
[[[[]]],[[],[[]],[]]] => [[],[],[[[],[[]]],[]]] => 2
[[[[]]],[[],[[],[]]]] => [[],[],[[[[]],[]],[]]] => 2
[[[[]]],[[],[[[]]]]] => [[],[],[[[],[],[]],[]]] => 2
[[[[]]],[[[]],[],[]]] => [[],[],[[],[[[]]],[]]] => 2
[[[[]]],[[[]],[[]]]] => [[],[],[[],[[],[]],[]]] => 2
[[[[]]],[[[],[]],[]]] => [[],[],[[[]],[[]],[]]] => 2
[[[[]]],[[[[]]],[]]] => [[],[],[[],[],[[]],[]]] => 2
[[[[]]],[[[],[],[]]]] => [[],[],[[[[]]],[],[]]] => 2
[[[[]]],[[[],[[]]]]] => [[],[],[[[],[]],[],[]]] => 2
[[[[]]],[[[[]],[]]]] => [[],[],[[],[[]],[],[]]] => 2
[[[[]]],[[[[],[]]]]] => [[],[],[[[]],[],[],[]]] => 2
[[[[]]],[[[[[]]]]]] => [[],[],[[],[],[],[],[]]] => 2
[[[[]],[]],[],[],[],[]] => [[],[[]],[[[[[]]]]]] => 1
[[[[],[]]],[],[],[],[]] => [[[]],[],[[[[[]]]]]] => 1
[[[[[]]]],[],[],[],[]] => [[],[],[],[[[[[]]]]]] => 1
[[[[]],[]],[],[],[[]]] => [[],[[]],[[[[],[]]]]] => 2
[[[[],[]]],[],[],[[]]] => [[[]],[],[[[[],[]]]]] => 2
[[[[[]]]],[],[],[[]]] => [[],[],[],[[[[],[]]]]] => 2
[[[[]],[]],[],[[]],[]] => [[],[[]],[[[],[[]]]]] => 2
[[[[],[]]],[],[[]],[]] => [[[]],[],[[[],[[]]]]] => 2
[[[[[]]]],[],[[]],[]] => [[],[],[],[[[],[[]]]]] => 2
[[[[]],[]],[],[[],[]]] => [[],[[]],[[[[]],[]]]] => 2
[[[[]],[]],[],[[[]]]] => [[],[[]],[[[],[],[]]]] => 2
[[[[],[]]],[],[[],[]]] => [[[]],[],[[[[]],[]]]] => 2
[[[[],[]]],[],[[[]]]] => [[[]],[],[[[],[],[]]]] => 2
[[[[[]]]],[],[[],[]]] => [[],[],[],[[[[]],[]]]] => 2
[[[[[]]]],[],[[[]]]] => [[],[],[],[[[],[],[]]]] => 2
[[[[]],[]],[[]],[],[]] => [[],[[]],[[],[[[]]]]] => 2
[[[[],[]]],[[]],[],[]] => [[[]],[],[[],[[[]]]]] => 2
[[[[[]]]],[[]],[],[]] => [[],[],[],[[],[[[]]]]] => 2
[[[[]],[]],[[]],[[]]] => [[],[[]],[[],[[],[]]]] => 2
[[[[],[]]],[[]],[[]]] => [[[]],[],[[],[[],[]]]] => 2
[[[[[]]]],[[]],[[]]] => [[],[],[],[[],[[],[]]]] => 2
[[[[]],[]],[[],[]],[]] => [[],[[]],[[[]],[[]]]] => 2
[[[[]],[]],[[[]]],[]] => [[],[[]],[[],[],[[]]]] => 2
[[[[],[]]],[[],[]],[]] => [[[]],[],[[[]],[[]]]] => 2
[[[[],[]]],[[[]]],[]] => [[[]],[],[[],[],[[]]]] => 2
[[[[[]]]],[[],[]],[]] => [[],[],[],[[[]],[[]]]] => 2
[[[[[]]]],[[[]]],[]] => [[],[],[],[[],[],[[]]]] => 2
[[[[]],[]],[[],[],[]]] => [[],[[]],[[[[]]],[]]] => 2
[[[[]],[]],[[],[[]]]] => [[],[[]],[[[],[]],[]]] => 2
[[[[]],[]],[[[]],[]]] => [[],[[]],[[],[[]],[]]] => 2
[[[[]],[]],[[[],[]]]] => [[],[[]],[[[]],[],[]]] => 2
[[[[]],[]],[[[[]]]]] => [[],[[]],[[],[],[],[]]] => 2
[[[[],[]]],[[],[],[]]] => [[[]],[],[[[[]]],[]]] => 2
[[[[],[]]],[[],[[]]]] => [[[]],[],[[[],[]],[]]] => 2
[[[[],[]]],[[[]],[]]] => [[[]],[],[[],[[]],[]]] => 2
[[[[],[]]],[[[],[]]]] => [[[]],[],[[[]],[],[]]] => 2
[[[[],[]]],[[[[]]]]] => [[[]],[],[[],[],[],[]]] => 2
[[[[[]]]],[[],[],[]]] => [[],[],[],[[[[]]],[]]] => 2
[[[[[]]]],[[],[[]]]] => [[],[],[],[[[],[]],[]]] => 2
[[[[[]]]],[[[]],[]]] => [[],[],[],[[],[[]],[]]] => 2
[[[[[]]]],[[[],[]]]] => [[],[],[],[[[]],[],[]]] => 2
[[[[[]]]],[[[[]]]]] => [[],[],[],[[],[],[],[]]] => 2
[[[[]],[],[]],[],[],[]] => [[],[[[]]],[[[[]]]]] => 1
[[[[]],[[]]],[],[],[]] => [[],[[],[]],[[[[]]]]] => 2
[[[[],[]],[]],[],[],[]] => [[[]],[[]],[[[[]]]]] => 1
[[[[[]]],[]],[],[],[]] => [[],[],[[]],[[[[]]]]] => 1
[[[[[]],[]]],[],[],[]] => [[],[[]],[],[[[[]]]]] => 1
[[[[[],[]]]],[],[],[]] => [[[]],[],[],[[[[]]]]] => 1
[[[[[[]]]]],[],[],[]] => [[],[],[],[],[[[[]]]]] => 1
[[[[]],[],[]],[],[[]]] => [[],[[[]]],[[[],[]]]] => 2
[[[[]],[[]]],[],[[]]] => [[],[[],[]],[[[],[]]]] => 2
[[[[],[]],[]],[],[[]]] => [[[]],[[]],[[[],[]]]] => 2
[[[[[]]],[]],[],[[]]] => [[],[],[[]],[[[],[]]]] => 2
[[[[[]],[]]],[],[[]]] => [[],[[]],[],[[[],[]]]] => 2
[[[[[],[]]]],[],[[]]] => [[[]],[],[],[[[],[]]]] => 2
[[[[[[]]]]],[],[[]]] => [[],[],[],[],[[[],[]]]] => 2
[[[[]],[],[]],[[]],[]] => [[],[[[]]],[[],[[]]]] => 2
[[[[]],[[]]],[[]],[]] => [[],[[],[]],[[],[[]]]] => 2
[[[[],[]],[]],[[]],[]] => [[[]],[[]],[[],[[]]]] => 2
[[[[[]]],[]],[[]],[]] => [[],[],[[]],[[],[[]]]] => 2
[[[[[]],[]]],[[]],[]] => [[],[[]],[],[[],[[]]]] => 2
[[[[[],[]]]],[[]],[]] => [[[]],[],[],[[],[[]]]] => 2
[[[[[[]]]]],[[]],[]] => [[],[],[],[],[[],[[]]]] => 2
[[[[]],[],[]],[[],[]]] => [[],[[[]]],[[[]],[]]] => 2
[[[[]],[],[]],[[[]]]] => [[],[[[]]],[[],[],[]]] => 2
[[[[]],[[]]],[[],[]]] => [[],[[],[]],[[[]],[]]] => 2
[[[[]],[[]]],[[[]]]] => [[],[[],[]],[[],[],[]]] => 2
[[[[],[]],[]],[[],[]]] => [[[]],[[]],[[[]],[]]] => 2
[[[[],[]],[]],[[[]]]] => [[[]],[[]],[[],[],[]]] => 2
[[[[[]]],[]],[[],[]]] => [[],[],[[]],[[[]],[]]] => 2
[[[[[]]],[]],[[[]]]] => [[],[],[[]],[[],[],[]]] => 2
[[[[[]],[]]],[[],[]]] => [[],[[]],[],[[[]],[]]] => 2
[[[[[]],[]]],[[[]]]] => [[],[[]],[],[[],[],[]]] => 2
[[[[[],[]]]],[[],[]]] => [[[]],[],[],[[[]],[]]] => 2
[[[[[],[]]]],[[[]]]] => [[[]],[],[],[[],[],[]]] => 2
[[[[[[]]]]],[[],[]]] => [[],[],[],[],[[[]],[]]] => 2
[[[[[[]]]]],[[[]]]] => [[],[],[],[],[[],[],[]]] => 2
[[[[]],[],[],[]],[],[]] => [[],[[[[]]]],[[[]]]] => 1
[[[[]],[],[[]]],[],[]] => [[],[[[],[]]],[[[]]]] => 2
[[[[]],[[]],[]],[],[]] => [[],[[],[[]]],[[[]]]] => 2
[[[[]],[[],[]]],[],[]] => [[],[[[]],[]],[[[]]]] => 2
[[[[]],[[[]]]],[],[]] => [[],[[],[],[]],[[[]]]] => 2
[[[[],[]],[],[]],[],[]] => [[[]],[[[]]],[[[]]]] => 1
[[[[[]]],[],[]],[],[]] => [[],[],[[[]]],[[[]]]] => 1
[[[[],[]],[[]]],[],[]] => [[[]],[[],[]],[[[]]]] => 2
[[[[[]]],[[]]],[],[]] => [[],[],[[],[]],[[[]]]] => 2
[[[[[]],[]],[]],[],[]] => [[],[[]],[[]],[[[]]]] => 1
[[[[[],[]]],[]],[],[]] => [[[]],[],[[]],[[[]]]] => 1
[[[[[[]]]],[]],[],[]] => [[],[],[],[[]],[[[]]]] => 1
[[[[[]],[],[]]],[],[]] => [[],[[[]]],[],[[[]]]] => 1
[[[[[]],[[]]]],[],[]] => [[],[[],[]],[],[[[]]]] => 2
[[[[[],[]],[]]],[],[]] => [[[]],[[]],[],[[[]]]] => 1
[[[[[[]]],[]]],[],[]] => [[],[],[[]],[],[[[]]]] => 1
[[[[[],[],[]]]],[],[]] => [[[[]]],[],[],[[[]]]] => 1
[[[[[],[[]]]]],[],[]] => [[[],[]],[],[],[[[]]]] => 2
[[[[[[]],[]]]],[],[]] => [[],[[]],[],[],[[[]]]] => 1
[[[[[[],[]]]]],[],[]] => [[[]],[],[],[],[[[]]]] => 1
[[[[[[[]]]]]],[],[]] => [[],[],[],[],[],[[[]]]] => 1
[[[[]],[],[],[]],[[]]] => [[],[[[[]]]],[[],[]]] => 2
[[[[]],[],[[]]],[[]]] => [[],[[[],[]]],[[],[]]] => 2
[[[[]],[[]],[]],[[]]] => [[],[[],[[]]],[[],[]]] => 2
[[[[]],[[],[]]],[[]]] => [[],[[[]],[]],[[],[]]] => 2
[[[[]],[[[]]]],[[]]] => [[],[[],[],[]],[[],[]]] => 2
[[[[],[]],[],[]],[[]]] => [[[]],[[[]]],[[],[]]] => 2
[[[[[]]],[],[]],[[]]] => [[],[],[[[]]],[[],[]]] => 2
[[[[],[]],[[]]],[[]]] => [[[]],[[],[]],[[],[]]] => 2
[[[[[]]],[[]]],[[]]] => [[],[],[[],[]],[[],[]]] => 2
[[[[[]],[]],[]],[[]]] => [[],[[]],[[]],[[],[]]] => 2
[[[[[],[]]],[]],[[]]] => [[[]],[],[[]],[[],[]]] => 2
[[[[[[]]]],[]],[[]]] => [[],[],[],[[]],[[],[]]] => 2
[[[[[]],[],[]]],[[]]] => [[],[[[]]],[],[[],[]]] => 2
[[[[[]],[[]]]],[[]]] => [[],[[],[]],[],[[],[]]] => 2
[[[[[],[]],[]]],[[]]] => [[[]],[[]],[],[[],[]]] => 2
[[[[[[]]],[]]],[[]]] => [[],[],[[]],[],[[],[]]] => 2
[[[[[],[],[]]]],[[]]] => [[[[]]],[],[],[[],[]]] => 2
[[[[[],[[]]]]],[[]]] => [[[],[]],[],[],[[],[]]] => 2
[[[[[[]],[]]]],[[]]] => [[],[[]],[],[],[[],[]]] => 2
[[[[[[],[]]]]],[[]]] => [[[]],[],[],[],[[],[]]] => 2
[[[[[[[]]]]]],[[]]] => [[],[],[],[],[],[[],[]]] => 2
[[[[]],[],[],[],[]],[]] => [[],[[[[[]]]]],[[]]] => 1
[[[[]],[],[],[[]]],[]] => [[],[[[[],[]]]],[[]]] => 2
[[[[]],[],[[]],[]],[]] => [[],[[[],[[]]]],[[]]] => 2
[[[[]],[],[[],[]]],[]] => [[],[[[[]],[]]],[[]]] => 2
[[[[]],[],[[[]]]],[]] => [[],[[[],[],[]]],[[]]] => 2
[[[[]],[[]],[],[]],[]] => [[],[[],[[[]]]],[[]]] => 2
[[[[]],[[]],[[]]],[]] => [[],[[],[[],[]]],[[]]] => 2
[[[[]],[[],[]],[]],[]] => [[],[[[]],[[]]],[[]]] => 2
[[[[]],[[[]]],[]],[]] => [[],[[],[],[[]]],[[]]] => 2
[[[[]],[[],[],[]]],[]] => [[],[[[[]]],[]],[[]]] => 2
[[[[]],[[],[[]]]],[]] => [[],[[[],[]],[]],[[]]] => 2
[[[[]],[[[]],[]]],[]] => [[],[[],[[]],[]],[[]]] => 2
[[[[]],[[[],[]]]],[]] => [[],[[[]],[],[]],[[]]] => 2
[[[[]],[[[[]]]]],[]] => [[],[[],[],[],[]],[[]]] => 2
[[[[],[]],[],[],[]],[]] => [[[]],[[[[]]]],[[]]] => 1
[[[[[]]],[],[],[]],[]] => [[],[],[[[[]]]],[[]]] => 1
[[[[],[]],[],[[]]],[]] => [[[]],[[[],[]]],[[]]] => 2
[[[[[]]],[],[[]]],[]] => [[],[],[[[],[]]],[[]]] => 2
[[[[],[]],[[]],[]],[]] => [[[]],[[],[[]]],[[]]] => 2
[[[[[]]],[[]],[]],[]] => [[],[],[[],[[]]],[[]]] => 2
[[[[],[]],[[],[]]],[]] => [[[]],[[[]],[]],[[]]] => 2
[[[[],[]],[[[]]]],[]] => [[[]],[[],[],[]],[[]]] => 2
[[[[[]]],[[],[]]],[]] => [[],[],[[[]],[]],[[]]] => 2
[[[[[]]],[[[]]]],[]] => [[],[],[[],[],[]],[[]]] => 2
[[[[[]],[]],[],[]],[]] => [[],[[]],[[[]]],[[]]] => 1
[[[[[],[]]],[],[]],[]] => [[[]],[],[[[]]],[[]]] => 1
[[[[[[]]]],[],[]],[]] => [[],[],[],[[[]]],[[]]] => 1
[[[[[]],[]],[[]]],[]] => [[],[[]],[[],[]],[[]]] => 2
[[[[[],[]]],[[]]],[]] => [[[]],[],[[],[]],[[]]] => 2
[[[[[[]]]],[[]]],[]] => [[],[],[],[[],[]],[[]]] => 2
[[[[[]],[],[]],[]],[]] => [[],[[[]]],[[]],[[]]] => 1
[[[[[]],[[]]],[]],[]] => [[],[[],[]],[[]],[[]]] => 2
[[[[[],[]],[]],[]],[]] => [[[]],[[]],[[]],[[]]] => 1
[[[[[[]]],[]],[]],[]] => [[],[],[[]],[[]],[[]]] => 1
[[[[[],[],[]]],[]],[]] => [[[[]]],[],[[]],[[]]] => 1
[[[[[],[[]]]],[]],[]] => [[[],[]],[],[[]],[[]]] => 2
[[[[[[]],[]]],[]],[]] => [[],[[]],[],[[]],[[]]] => 1
[[[[[[],[]]]],[]],[]] => [[[]],[],[],[[]],[[]]] => 1
[[[[[[[]]]]],[]],[]] => [[],[],[],[],[[]],[[]]] => 1
[[[[[]],[],[],[]]],[]] => [[],[[[[]]]],[],[[]]] => 1
[[[[[]],[],[[]]]],[]] => [[],[[[],[]]],[],[[]]] => 2
[[[[[]],[[]],[]]],[]] => [[],[[],[[]]],[],[[]]] => 2
[[[[[]],[[],[]]]],[]] => [[],[[[]],[]],[],[[]]] => 2
[[[[[]],[[[]]]]],[]] => [[],[[],[],[]],[],[[]]] => 2
[[[[[],[]],[],[]]],[]] => [[[]],[[[]]],[],[[]]] => 1
[[[[[[]]],[],[]]],[]] => [[],[],[[[]]],[],[[]]] => 1
[[[[[],[]],[[]]]],[]] => [[[]],[[],[]],[],[[]]] => 2
[[[[[[]]],[[]]]],[]] => [[],[],[[],[]],[],[[]]] => 2
[[[[[[]],[]],[]]],[]] => [[],[[]],[[]],[],[[]]] => 1
[[[[[[],[]]],[]]],[]] => [[[]],[],[[]],[],[[]]] => 1
[[[[[[[]]]],[]]],[]] => [[],[],[],[[]],[],[[]]] => 1
[[[[[[]],[],[]]]],[]] => [[],[[[]]],[],[],[[]]] => 1
[[[[[[]],[[]]]]],[]] => [[],[[],[]],[],[],[[]]] => 2
[[[[[[],[]],[]]]],[]] => [[[]],[[]],[],[],[[]]] => 1
[[[[[[[]]],[]]]],[]] => [[],[],[[]],[],[],[[]]] => 1
[[[[[[],[],[]]]]],[]] => [[[[]]],[],[],[],[[]]] => 1
[[[[[[],[[]]]]]],[]] => [[[],[]],[],[],[],[[]]] => 2
[[[[[[[]],[]]]]],[]] => [[],[[]],[],[],[],[[]]] => 1
[[[[[[[],[]]]]]],[]] => [[[]],[],[],[],[],[[]]] => 1
[[[[[[[[]]]]]]],[]] => [[],[],[],[],[],[],[[]]] => 1
[[[[]],[],[],[],[],[]]] => [[],[[[[[[]]]]]],[]] => 1
[[[[]],[],[],[],[[]]]] => [[],[[[[[],[]]]]],[]] => 2
[[[[]],[],[],[[]],[]]] => [[],[[[[],[[]]]]],[]] => 2
[[[[]],[],[],[[],[]]]] => [[],[[[[[]],[]]]],[]] => 2
[[[[]],[],[],[[[]]]]] => [[],[[[[],[],[]]]],[]] => 2
[[[[]],[],[[]],[],[]]] => [[],[[[],[[[]]]]],[]] => 2
[[[[]],[],[[]],[[]]]] => [[],[[[],[[],[]]]],[]] => 2
[[[[]],[],[[],[]],[]]] => [[],[[[[]],[[]]]],[]] => 2
[[[[]],[],[[[]]],[]]] => [[],[[[],[],[[]]]],[]] => 2
[[[[]],[],[[],[],[]]]] => [[],[[[[[]]],[]]],[]] => 2
[[[[]],[],[[],[[]]]]] => [[],[[[[],[]],[]]],[]] => 2
[[[[]],[],[[[]],[]]]] => [[],[[[],[[]],[]]],[]] => 2
[[[[]],[],[[[],[]]]]] => [[],[[[[]],[],[]]],[]] => 2
[[[[]],[],[[[[]]]]]] => [[],[[[],[],[],[]]],[]] => 2
[[[[]],[[]],[],[],[]]] => [[],[[],[[[[]]]]],[]] => 2
[[[[]],[[]],[],[[]]]] => [[],[[],[[[],[]]]],[]] => 2
[[[[]],[[]],[[]],[]]] => [[],[[],[[],[[]]]],[]] => 2
[[[[]],[[]],[[],[]]]] => [[],[[],[[[]],[]]],[]] => 2
[[[[]],[[]],[[[]]]]] => [[],[[],[[],[],[]]],[]] => 2
[[[[]],[[],[]],[],[]]] => [[],[[[]],[[[]]]],[]] => 2
[[[[]],[[[]]],[],[]]] => [[],[[],[],[[[]]]],[]] => 2
[[[[]],[[],[]],[[]]]] => [[],[[[]],[[],[]]],[]] => 2
[[[[]],[[[]]],[[]]]] => [[],[[],[],[[],[]]],[]] => 2
[[[[]],[[],[],[]],[]]] => [[],[[[[]]],[[]]],[]] => 2
[[[[]],[[],[[]]],[]]] => [[],[[[],[]],[[]]],[]] => 2
[[[[]],[[[]],[]],[]]] => [[],[[],[[]],[[]]],[]] => 2
[[[[]],[[[],[]]],[]]] => [[],[[[]],[],[[]]],[]] => 2
[[[[]],[[[[]]]],[]]] => [[],[[],[],[],[[]]],[]] => 2
[[[[]],[[],[],[],[]]]] => [[],[[[[[]]]],[]],[]] => 2
[[[[]],[[],[],[[]]]]] => [[],[[[[],[]]],[]],[]] => 2
[[[[]],[[],[[]],[]]]] => [[],[[[],[[]]],[]],[]] => 2
[[[[]],[[],[[],[]]]]] => [[],[[[[]],[]],[]],[]] => 2
[[[[]],[[],[[[]]]]]] => [[],[[[],[],[]],[]],[]] => 2
[[[[]],[[[]],[],[]]]] => [[],[[],[[[]]],[]],[]] => 2
[[[[]],[[[]],[[]]]]] => [[],[[],[[],[]],[]],[]] => 2
[[[[]],[[[],[]],[]]]] => [[],[[[]],[[]],[]],[]] => 2
[[[[]],[[[[]]],[]]]] => [[],[[],[],[[]],[]],[]] => 2
[[[[]],[[[],[],[]]]]] => [[],[[[[]]],[],[]],[]] => 2
[[[[]],[[[],[[]]]]]] => [[],[[[],[]],[],[]],[]] => 2
[[[[]],[[[[]],[]]]]] => [[],[[],[[]],[],[]],[]] => 2
[[[[]],[[[[],[]]]]]] => [[],[[[]],[],[],[]],[]] => 2
[[[[]],[[[[[]]]]]]] => [[],[[],[],[],[],[]],[]] => 2
[[[[],[]],[],[],[],[]]] => [[[]],[[[[[]]]]],[]] => 1
[[[[[]]],[],[],[],[]]] => [[],[],[[[[[]]]]],[]] => 1
[[[[],[]],[],[],[[]]]] => [[[]],[[[[],[]]]],[]] => 2
[[[[[]]],[],[],[[]]]] => [[],[],[[[[],[]]]],[]] => 2
[[[[],[]],[],[[]],[]]] => [[[]],[[[],[[]]]],[]] => 2
[[[[[]]],[],[[]],[]]] => [[],[],[[[],[[]]]],[]] => 2
[[[[],[]],[],[[],[]]]] => [[[]],[[[[]],[]]],[]] => 2
[[[[],[]],[],[[[]]]]] => [[[]],[[[],[],[]]],[]] => 2
[[[[[]]],[],[[],[]]]] => [[],[],[[[[]],[]]],[]] => 2
[[[[[]]],[],[[[]]]]] => [[],[],[[[],[],[]]],[]] => 2
[[[[],[]],[[]],[],[]]] => [[[]],[[],[[[]]]],[]] => 2
[[[[[]]],[[]],[],[]]] => [[],[],[[],[[[]]]],[]] => 2
[[[[],[]],[[]],[[]]]] => [[[]],[[],[[],[]]],[]] => 2
[[[[[]]],[[]],[[]]]] => [[],[],[[],[[],[]]],[]] => 2
[[[[],[]],[[],[]],[]]] => [[[]],[[[]],[[]]],[]] => 2
[[[[],[]],[[[]]],[]]] => [[[]],[[],[],[[]]],[]] => 2
[[[[[]]],[[],[]],[]]] => [[],[],[[[]],[[]]],[]] => 2
[[[[[]]],[[[]]],[]]] => [[],[],[[],[],[[]]],[]] => 2
[[[[],[]],[[],[],[]]]] => [[[]],[[[[]]],[]],[]] => 2
[[[[],[]],[[],[[]]]]] => [[[]],[[[],[]],[]],[]] => 2
[[[[],[]],[[[]],[]]]] => [[[]],[[],[[]],[]],[]] => 2
[[[[],[]],[[[],[]]]]] => [[[]],[[[]],[],[]],[]] => 2
[[[[],[]],[[[[]]]]]] => [[[]],[[],[],[],[]],[]] => 2
[[[[[]]],[[],[],[]]]] => [[],[],[[[[]]],[]],[]] => 2
[[[[[]]],[[],[[]]]]] => [[],[],[[[],[]],[]],[]] => 2
[[[[[]]],[[[]],[]]]] => [[],[],[[],[[]],[]],[]] => 2
[[[[[]]],[[[],[]]]]] => [[],[],[[[]],[],[]],[]] => 2
[[[[[]]],[[[[]]]]]] => [[],[],[[],[],[],[]],[]] => 2
[[[[[]],[]],[],[],[]]] => [[],[[]],[[[[]]]],[]] => 1
[[[[[],[]]],[],[],[]]] => [[[]],[],[[[[]]]],[]] => 1
[[[[[[]]]],[],[],[]]] => [[],[],[],[[[[]]]],[]] => 1
[[[[[]],[]],[],[[]]]] => [[],[[]],[[[],[]]],[]] => 2
[[[[[],[]]],[],[[]]]] => [[[]],[],[[[],[]]],[]] => 2
[[[[[[]]]],[],[[]]]] => [[],[],[],[[[],[]]],[]] => 2
[[[[[]],[]],[[]],[]]] => [[],[[]],[[],[[]]],[]] => 2
[[[[[],[]]],[[]],[]]] => [[[]],[],[[],[[]]],[]] => 2
[[[[[[]]]],[[]],[]]] => [[],[],[],[[],[[]]],[]] => 2
[[[[[]],[]],[[],[]]]] => [[],[[]],[[[]],[]],[]] => 2
[[[[[]],[]],[[[]]]]] => [[],[[]],[[],[],[]],[]] => 2
[[[[[],[]]],[[],[]]]] => [[[]],[],[[[]],[]],[]] => 2
[[[[[],[]]],[[[]]]]] => [[[]],[],[[],[],[]],[]] => 2
[[[[[[]]]],[[],[]]]] => [[],[],[],[[[]],[]],[]] => 2
[[[[[[]]]],[[[]]]]] => [[],[],[],[[],[],[]],[]] => 2
[[[[[]],[],[]],[],[]]] => [[],[[[]]],[[[]]],[]] => 1
[[[[[]],[[]]],[],[]]] => [[],[[],[]],[[[]]],[]] => 2
[[[[[],[]],[]],[],[]]] => [[[]],[[]],[[[]]],[]] => 1
[[[[[[]]],[]],[],[]]] => [[],[],[[]],[[[]]],[]] => 1
[[[[[[]],[]]],[],[]]] => [[],[[]],[],[[[]]],[]] => 1
[[[[[[],[]]]],[],[]]] => [[[]],[],[],[[[]]],[]] => 1
[[[[[[[]]]]],[],[]]] => [[],[],[],[],[[[]]],[]] => 1
[[[[[]],[],[]],[[]]]] => [[],[[[]]],[[],[]],[]] => 2
[[[[[]],[[]]],[[]]]] => [[],[[],[]],[[],[]],[]] => 2
[[[[[],[]],[]],[[]]]] => [[[]],[[]],[[],[]],[]] => 2
[[[[[[]]],[]],[[]]]] => [[],[],[[]],[[],[]],[]] => 2
[[[[[[]],[]]],[[]]]] => [[],[[]],[],[[],[]],[]] => 2
[[[[[[],[]]]],[[]]]] => [[[]],[],[],[[],[]],[]] => 2
[[[[[[[]]]]],[[]]]] => [[],[],[],[],[[],[]],[]] => 2
[[[[[]],[],[],[]],[]]] => [[],[[[[]]]],[[]],[]] => 1
[[[[[]],[],[[]]],[]]] => [[],[[[],[]]],[[]],[]] => 2
[[[[[]],[[]],[]],[]]] => [[],[[],[[]]],[[]],[]] => 2
[[[[[]],[[],[]]],[]]] => [[],[[[]],[]],[[]],[]] => 2
[[[[[]],[[[]]]],[]]] => [[],[[],[],[]],[[]],[]] => 2
[[[[[],[]],[],[]],[]]] => [[[]],[[[]]],[[]],[]] => 1
[[[[[[]]],[],[]],[]]] => [[],[],[[[]]],[[]],[]] => 1
[[[[[],[]],[[]]],[]]] => [[[]],[[],[]],[[]],[]] => 2
[[[[[[]]],[[]]],[]]] => [[],[],[[],[]],[[]],[]] => 2
[[[[[[]],[]],[]],[]]] => [[],[[]],[[]],[[]],[]] => 1
[[[[[[],[]]],[]],[]]] => [[[]],[],[[]],[[]],[]] => 1
[[[[[[[]]]],[]],[]]] => [[],[],[],[[]],[[]],[]] => 1
[[[[[[]],[],[]]],[]]] => [[],[[[]]],[],[[]],[]] => 1
[[[[[[]],[[]]]],[]]] => [[],[[],[]],[],[[]],[]] => 2
[[[[[[],[]],[]]],[]]] => [[[]],[[]],[],[[]],[]] => 1
[[[[[[[]]],[]]],[]]] => [[],[],[[]],[],[[]],[]] => 1
[[[[[[],[],[]]]],[]]] => [[[[]]],[],[],[[]],[]] => 1
[[[[[[],[[]]]]],[]]] => [[[],[]],[],[],[[]],[]] => 2
[[[[[[[]],[]]]],[]]] => [[],[[]],[],[],[[]],[]] => 1
[[[[[[[],[]]]]],[]]] => [[[]],[],[],[],[[]],[]] => 1
[[[[[[[[]]]]]],[]]] => [[],[],[],[],[],[[]],[]] => 1
[[[[[]],[],[],[],[]]]] => [[],[[[[[]]]]],[],[]] => 1
[[[[[]],[],[],[[]]]]] => [[],[[[[],[]]]],[],[]] => 2
[[[[[]],[],[[]],[]]]] => [[],[[[],[[]]]],[],[]] => 2
[[[[[]],[],[[],[]]]]] => [[],[[[[]],[]]],[],[]] => 2
[[[[[]],[],[[[]]]]]] => [[],[[[],[],[]]],[],[]] => 2
[[[[[]],[[]],[],[]]]] => [[],[[],[[[]]]],[],[]] => 2
[[[[[]],[[]],[[]]]]] => [[],[[],[[],[]]],[],[]] => 2
[[[[[]],[[],[]],[]]]] => [[],[[[]],[[]]],[],[]] => 2
[[[[[]],[[[]]],[]]]] => [[],[[],[],[[]]],[],[]] => 2
[[[[[]],[[],[],[]]]]] => [[],[[[[]]],[]],[],[]] => 2
[[[[[]],[[],[[]]]]]] => [[],[[[],[]],[]],[],[]] => 2
[[[[[]],[[[]],[]]]]] => [[],[[],[[]],[]],[],[]] => 2
[[[[[]],[[[],[]]]]]] => [[],[[[]],[],[]],[],[]] => 2
[[[[[]],[[[[]]]]]]] => [[],[[],[],[],[]],[],[]] => 2
[[[[[],[]],[],[],[]]]] => [[[]],[[[[]]]],[],[]] => 1
[[[[[[]]],[],[],[]]]] => [[],[],[[[[]]]],[],[]] => 1
[[[[[],[]],[],[[]]]]] => [[[]],[[[],[]]],[],[]] => 2
[[[[[[]]],[],[[]]]]] => [[],[],[[[],[]]],[],[]] => 2
[[[[[],[]],[[]],[]]]] => [[[]],[[],[[]]],[],[]] => 2
[[[[[[]]],[[]],[]]]] => [[],[],[[],[[]]],[],[]] => 2
[[[[[],[]],[[],[]]]]] => [[[]],[[[]],[]],[],[]] => 2
[[[[[],[]],[[[]]]]]] => [[[]],[[],[],[]],[],[]] => 2
[[[[[[]]],[[],[]]]]] => [[],[],[[[]],[]],[],[]] => 2
[[[[[[]]],[[[]]]]]] => [[],[],[[],[],[]],[],[]] => 2
[[[[[[]],[]],[],[]]]] => [[],[[]],[[[]]],[],[]] => 1
[[[[[[],[]]],[],[]]]] => [[[]],[],[[[]]],[],[]] => 1
[[[[[[[]]]],[],[]]]] => [[],[],[],[[[]]],[],[]] => 1
[[[[[[]],[]],[[]]]]] => [[],[[]],[[],[]],[],[]] => 2
[[[[[[],[]]],[[]]]]] => [[[]],[],[[],[]],[],[]] => 2
[[[[[[[]]]],[[]]]]] => [[],[],[],[[],[]],[],[]] => 2
[[[[[[]],[],[]],[]]]] => [[],[[[]]],[[]],[],[]] => 1
[[[[[[]],[[]]],[]]]] => [[],[[],[]],[[]],[],[]] => 2
[[[[[[],[]],[]],[]]]] => [[[]],[[]],[[]],[],[]] => 1
[[[[[[[]]],[]],[]]]] => [[],[],[[]],[[]],[],[]] => 1
[[[[[[],[],[]]],[]]]] => [[[[]]],[],[[]],[],[]] => 1
[[[[[[],[[]]]],[]]]] => [[[],[]],[],[[]],[],[]] => 2
[[[[[[[]],[]]],[]]]] => [[],[[]],[],[[]],[],[]] => 1
[[[[[[[],[]]]],[]]]] => [[[]],[],[],[[]],[],[]] => 1
[[[[[[[[]]]]],[]]]] => [[],[],[],[],[[]],[],[]] => 1
[[[[[[]],[],[],[]]]]] => [[],[[[[]]]],[],[],[]] => 1
[[[[[[]],[],[[]]]]]] => [[],[[[],[]]],[],[],[]] => 2
[[[[[[]],[[]],[]]]]] => [[],[[],[[]]],[],[],[]] => 2
[[[[[[]],[[],[]]]]]] => [[],[[[]],[]],[],[],[]] => 2
[[[[[[]],[[[]]]]]]] => [[],[[],[],[]],[],[],[]] => 2
[[[[[[],[]],[],[]]]]] => [[[]],[[[]]],[],[],[]] => 1
[[[[[[[]]],[],[]]]]] => [[],[],[[[]]],[],[],[]] => 1
[[[[[[],[]],[[]]]]]] => [[[]],[[],[]],[],[],[]] => 2
[[[[[[[]]],[[]]]]]] => [[],[],[[],[]],[],[],[]] => 2
[[[[[[[]],[]],[]]]]] => [[],[[]],[[]],[],[],[]] => 1
[[[[[[[],[]]],[]]]]] => [[[]],[],[[]],[],[],[]] => 1
[[[[[[[[]]]],[]]]]] => [[],[],[],[[]],[],[],[]] => 1
[[[[[[[]],[],[]]]]]] => [[],[[[]]],[],[],[],[]] => 1
[[[[[[[]],[[]]]]]]] => [[],[[],[]],[],[],[],[]] => 2
[[[[[[[],[]],[]]]]]] => [[[]],[[]],[],[],[],[]] => 1
[[[[[[[[]]],[]]]]]] => [[],[],[[]],[],[],[],[]] => 1
[[[[[[[],[],[]]]]]]] => [[[[]]],[],[],[],[],[]] => 1
[[[[[[[],[[]]]]]]]] => [[[],[]],[],[],[],[],[]] => 2
[[[[[[[[]],[]]]]]]] => [[],[[]],[],[],[],[],[]] => 1
[[[[[[[[],[]]]]]]]] => [[[]],[],[],[],[],[],[]] => 1
[[[[[[[[[]]]]]]]]] => [[],[],[],[],[],[],[],[]] => 1
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Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,26 32,100 64,364,1
$F_{2} = q$
$F_{3} = 2\ q$
$F_{4} = 4\ q + q^{2}$
$F_{5} = 8\ q + 6\ q^{2}$
$F_{6} = 16\ q + 26\ q^{2}$
$F_{7} = 32\ q + 100\ q^{2}$
$F_{8} = 64\ q + 364\ q^{2} + q^{3}$
Description
The pruning number of an ordered tree.
A hanging branch of an ordered tree is a proper factor of the form $[^r]^r$ for some $r\geq 1$. A hanging branch is a maximal hanging branch if it is not a proper factor of another hanging branch.
A pruning of an ordered tree is the act of deleting all its maximal hanging branches. The pruning order of an ordered tree is the number of prunings required to reduce it to $[]$.
A hanging branch of an ordered tree is a proper factor of the form $[^r]^r$ for some $r\geq 1$. A hanging branch is a maximal hanging branch if it is not a proper factor of another hanging branch.
A pruning of an ordered tree is the act of deleting all its maximal hanging branches. The pruning order of an ordered tree is the number of prunings required to reduce it to $[]$.
Map
DeBruijn-Morselt plane tree automorphism
Description
This automorphism on the set of plane trees with a given number of vertices is the combination of the two "canonical" bijections between plane trees and binary trees, using either the left or right branches. In [3] Shapiro essentially attributes this automorphism to DeBruijn and Morselt [1], hence the name I chose. Shapiro shows in that paper that for a large subset of plane trees (those corresponding to compositions), the sixth power of the automorphism acts as the identity on this subset. However, its behavior in general is quite chaotic. In [2] Donaghey studies this automorphism further and shows that its behavior on all trees can be reduced to its behavior on certain "primitive" trees.
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