Identifier
Values
[] => [] => [1,0] => [1] => 1
[[]] => [1,0] => [1,1,0,0] => [1,2] => 1
[[],[]] => [1,0,1,0] => [1,1,0,1,0,0] => [1,3,2] => 2
[[[]]] => [1,1,0,0] => [1,1,1,0,0,0] => [1,2,3] => 1
[[],[],[]] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => 2
[[],[[]]] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [1,3,4,2] => 2
[[[]],[]] => [1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => 2
[[[],[]]] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => 2
[[[[]]]] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 1
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => 2
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => 2
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => 2
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => 2
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => 2
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => 2
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => 2
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => 2
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => 2
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => 2
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => 2
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => 2
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => 2
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 1
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => 2
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => 2
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => 2
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => 2
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => 2
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => 2
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => 2
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => 2
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => 2
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => 2
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => 2
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => 2
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => 2
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => 2
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => 2
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => 2
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => 2
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => 2
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => 2
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => 2
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => 2
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => 2
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => 2
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => 2
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => 2
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => 2
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => 2
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => 2
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => 2
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => 2
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => 2
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => 2
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => 2
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => 2
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => 2
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => 2
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => 2
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => 2
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => 2
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => 2
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => 2
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => 1
[[],[],[],[],[],[]] => [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] => [1,3,2,5,4,7,6] => 2
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => 2
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => 2
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => 2
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => 2
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => 2
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => 2
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => 2
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => 2
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => 2
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => 2
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => 2
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => 2
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => 2
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => 2
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => 2
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => 2
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => 2
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => 2
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => 2
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => 2
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => 2
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => 2
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => 2
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => 2
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => 2
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => 2
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => 2
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => 2
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => 2
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => 2
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => 2
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => 2
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => 2
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => 2
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => 2
>>> Load all 267 entries. <<<
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => 2
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => 2
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => 2
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => 2
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => 2
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => 2
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => 2
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => 2
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => 2
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => 2
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => 2
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => 2
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => 2
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => 2
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => 2
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => 2
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => 2
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => 2
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => 2
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => 2
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => 2
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => 2
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => 2
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => 2
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => 2
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => 2
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => 2
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => 2
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => 2
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => 2
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => 2
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => 2
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => 2
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => 2
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => 2
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => 2
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => 2
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => 2
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => 2
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => 2
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => 2
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => 2
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => 2
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => 2
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => 2
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => 2
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => 2
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => 2
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => 2
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => 2
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => 2
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => 2
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => 2
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => 2
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => 2
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => 2
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => 2
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => 2
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => 2
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => 2
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => 2
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => 2
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => 2
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => 2
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => 2
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => 2
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => 2
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => 2
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => 2
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => 2
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => 2
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => 2
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => 2
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => 2
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => 2
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => 2
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => 2
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => 2
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => 2
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => 2
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => 2
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => 2
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => 2
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => 2
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => 2
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => 1
[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,8] => 2
[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,8,6,7] => 2
[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => 2
[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7,8] => 2
[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,8] => 2
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5,8] => 2
[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,8,5,7] => 2
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,3,2,7,4,8,5,6] => 2
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7,8] => 2
[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6,8] => 2
[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,2,8,4,5,6,7] => 2
[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6,8] => 2
[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => 2
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8] => 2
[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5,8] => 2
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,8] => 2
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,8,6,7] => 2
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7,8] => 2
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => 2
[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,8] => 2
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4,8] => 2
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,6,7,8,3,5] => 2
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,7] => 2
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,2,7,3,8,5,6] => 2
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,8,4,7] => 2
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,7,3,8,4,6] => 2
[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,5] => 2
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => 2
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7,8] => 2
[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6,8] => 2
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,4,2,8,3,5,6,7] => 2
[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7,8] => 2
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6,8] => 2
[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,5,2,8,3,4,6,7] => 2
[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5,8] => 2
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,6,2,8,3,4,5,7] => 2
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,7,2,8,3,4,5,6] => 2
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,5,8,2,3,4,6,7] => 2
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5,8] => 2
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,6,8,2,3,4,5,7] => 2
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,8,2,3,4,5,6] => 2
[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6,8] => 2
[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6,8] => 2
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => 2
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8] => 2
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,7,2,3,8,4,5,6] => 2
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6,8] => 2
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => 2
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7,8] => 2
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5,8] => 2
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => 2
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => 2
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7,8] => 2
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => 2
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8] => 2
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7] => 2
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7,8] => 2
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => 2
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,2,7,3,4,5,8,6] => 2
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,8] => 2
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,8,6,7] => 2
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => 2
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => 2
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,8] => 2
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,8,5,7] => 2
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,6] => 2
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => 2
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => 2
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => 2
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8] => 2
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7] => 2
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7] => 2
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => 1
[[[[[[[]]]]]],[],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,8,2,9,3,4,5,6,7] => 2
[[[[[[],[]]]]],[[]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,7,9,2,3,4,5,6,8] => 2
[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,8,9,2,3,4,5,6,7] => 2
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => 2
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8] => 2
[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8] => 2
[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => 1
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Description
The number of parts of the shifted shape of a permutation.
The diagram of a strict partition $\lambda_1 < \lambda_2 < \dots < \lambda_\ell$ of $n$ is a tableau with $\ell$ rows, the $i$-th row being indented by $i$ cells. A shifted standard Young tableau is a filling of such a diagram, where entries in rows and columns are strictly increasing.
The shifted Robinson-Schensted algorithm [1] associates to a permutation a pair $(P, Q)$ of standard shifted Young tableaux of the same shape, where off-diagonal entries in $Q$ may be circled.
This statistic records the number of parts of the shifted shape.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
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.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.