edit this statistic or download as text // json
Identifier
Values
[[]] => 2
[[],[]] => 2
[[[]]] => 3
[[],[],[]] => 2
[[],[[]]] => 3
[[[]],[]] => 3
[[[],[]]] => 3
[[[[]]]] => 4
[[],[],[],[]] => 2
[[],[],[[]]] => 3
[[],[[]],[]] => 3
[[],[[],[]]] => 3
[[],[[[]]]] => 4
[[[]],[],[]] => 3
[[[]],[[]]] => 3
[[[],[]],[]] => 3
[[[[]]],[]] => 4
[[[],[],[]]] => 3
[[[],[[]]]] => 4
[[[[]],[]]] => 4
[[[[],[]]]] => 4
[[[[[]]]]] => 5
[[],[],[],[],[]] => 2
[[],[],[],[[]]] => 3
[[],[],[[]],[]] => 3
[[],[],[[],[]]] => 3
[[],[],[[[]]]] => 4
[[],[[]],[],[]] => 3
[[],[[]],[[]]] => 3
[[],[[],[]],[]] => 3
[[],[[[]]],[]] => 4
[[],[[],[],[]]] => 3
[[],[[],[[]]]] => 4
[[],[[[]],[]]] => 4
[[],[[[],[]]]] => 4
[[],[[[[]]]]] => 5
[[[]],[],[],[]] => 3
[[[]],[],[[]]] => 3
[[[]],[[]],[]] => 3
[[[]],[[],[]]] => 4
[[[]],[[[]]]] => 4
[[[],[]],[],[]] => 3
[[[[]]],[],[]] => 4
[[[],[]],[[]]] => 4
[[[[]]],[[]]] => 4
[[[],[],[]],[]] => 3
[[[],[[]]],[]] => 4
[[[[]],[]],[]] => 4
[[[[],[]]],[]] => 4
[[[[[]]]],[]] => 5
[[[],[],[],[]]] => 3
[[[],[],[[]]]] => 4
[[[],[[]],[]]] => 4
[[[],[[],[]]]] => 4
[[[],[[[]]]]] => 5
[[[[]],[],[]]] => 4
[[[[]],[[]]]] => 4
[[[[],[]],[]]] => 4
[[[[[]]],[]]] => 5
[[[[],[],[]]]] => 4
[[[[],[[]]]]] => 5
[[[[[]],[]]]] => 5
[[[[[],[]]]]] => 5
[[[[[[]]]]]] => 6
[[],[],[],[],[],[]] => 2
[[],[],[],[],[[]]] => 3
[[],[],[],[[]],[]] => 3
[[],[],[],[[],[]]] => 3
[[],[],[],[[[]]]] => 4
[[],[],[[]],[],[]] => 3
[[],[],[[]],[[]]] => 3
[[],[],[[],[]],[]] => 3
[[],[],[[[]]],[]] => 4
[[],[],[[],[],[]]] => 3
[[],[],[[],[[]]]] => 4
[[],[],[[[]],[]]] => 4
[[],[],[[[],[]]]] => 4
[[],[],[[[[]]]]] => 5
[[],[[]],[],[],[]] => 3
[[],[[]],[],[[]]] => 3
[[],[[]],[[]],[]] => 3
[[],[[]],[[],[]]] => 4
[[],[[]],[[[]]]] => 4
[[],[[],[]],[],[]] => 3
[[],[[[]]],[],[]] => 4
[[],[[],[]],[[]]] => 4
[[],[[[]]],[[]]] => 4
[[],[[],[],[]],[]] => 3
[[],[[],[[]]],[]] => 4
[[],[[[]],[]],[]] => 4
[[],[[[],[]]],[]] => 4
[[],[[[[]]]],[]] => 5
[[],[[],[],[],[]]] => 3
[[],[[],[],[[]]]] => 4
[[],[[],[[]],[]]] => 4
[[],[[],[[],[]]]] => 4
[[],[[],[[[]]]]] => 5
[[],[[[]],[],[]]] => 4
[[],[[[]],[[]]]] => 4
[[],[[[],[]],[]]] => 4
[[],[[[[]]],[]]] => 5
>>> Load all 1200 entries. <<<
[[],[[[],[],[]]]] => 4
[[],[[[],[[]]]]] => 5
[[],[[[[]],[]]]] => 5
[[],[[[[],[]]]]] => 5
[[],[[[[[]]]]]] => 6
[[[]],[],[],[],[]] => 3
[[[]],[],[],[[]]] => 3
[[[]],[],[[]],[]] => 3
[[[]],[],[[],[]]] => 4
[[[]],[],[[[]]]] => 4
[[[]],[[]],[],[]] => 3
[[[]],[[]],[[]]] => 3
[[[]],[[],[]],[]] => 4
[[[]],[[[]]],[]] => 4
[[[]],[[],[],[]]] => 4
[[[]],[[],[[]]]] => 4
[[[]],[[[]],[]]] => 4
[[[]],[[[],[]]]] => 5
[[[]],[[[[]]]]] => 5
[[[],[]],[],[],[]] => 3
[[[[]]],[],[],[]] => 4
[[[],[]],[],[[]]] => 4
[[[[]]],[],[[]]] => 4
[[[],[]],[[]],[]] => 4
[[[[]]],[[]],[]] => 4
[[[],[]],[[],[]]] => 3
[[[],[]],[[[]]]] => 5
[[[[]]],[[],[]]] => 5
[[[[]]],[[[]]]] => 4
[[[],[],[]],[],[]] => 3
[[[],[[]]],[],[]] => 4
[[[[]],[]],[],[]] => 4
[[[[],[]]],[],[]] => 4
[[[[[]]]],[],[]] => 5
[[[],[],[]],[[]]] => 4
[[[],[[]]],[[]]] => 4
[[[[]],[]],[[]]] => 4
[[[[],[]]],[[]]] => 5
[[[[[]]]],[[]]] => 5
[[[],[],[],[]],[]] => 3
[[[],[],[[]]],[]] => 4
[[[],[[]],[]],[]] => 4
[[[],[[],[]]],[]] => 4
[[[],[[[]]]],[]] => 5
[[[[]],[],[]],[]] => 4
[[[[]],[[]]],[]] => 4
[[[[],[]],[]],[]] => 4
[[[[[]]],[]],[]] => 5
[[[[],[],[]]],[]] => 4
[[[[],[[]]]],[]] => 5
[[[[[]],[]]],[]] => 5
[[[[[],[]]]],[]] => 5
[[[[[[]]]]],[]] => 6
[[[],[],[],[],[]]] => 3
[[[],[],[],[[]]]] => 4
[[[],[],[[]],[]]] => 4
[[[],[],[[],[]]]] => 4
[[[],[],[[[]]]]] => 5
[[[],[[]],[],[]]] => 4
[[[],[[]],[[]]]] => 4
[[[],[[],[]],[]]] => 4
[[[],[[[]]],[]]] => 5
[[[],[[],[],[]]]] => 4
[[[],[[],[[]]]]] => 5
[[[],[[[]],[]]]] => 5
[[[],[[[],[]]]]] => 5
[[[],[[[[]]]]]] => 6
[[[[]],[],[],[]]] => 4
[[[[]],[],[[]]]] => 4
[[[[]],[[]],[]]] => 4
[[[[]],[[],[]]]] => 5
[[[[]],[[[]]]]] => 5
[[[[],[]],[],[]]] => 4
[[[[[]]],[],[]]] => 5
[[[[],[]],[[]]]] => 5
[[[[[]]],[[]]]] => 5
[[[[],[],[]],[]]] => 4
[[[[],[[]]],[]]] => 5
[[[[[]],[]],[]]] => 5
[[[[[],[]]],[]]] => 5
[[[[[[]]]],[]]] => 6
[[[[],[],[],[]]]] => 4
[[[[],[],[[]]]]] => 5
[[[[],[[]],[]]]] => 5
[[[[],[[],[]]]]] => 5
[[[[],[[[]]]]]] => 6
[[[[[]],[],[]]]] => 5
[[[[[]],[[]]]]] => 5
[[[[[],[]],[]]]] => 5
[[[[[[]]],[]]]] => 6
[[[[[],[],[]]]]] => 5
[[[[[],[[]]]]]] => 6
[[[[[[]],[]]]]] => 6
[[[[[[],[]]]]]] => 6
[[[[[[[]]]]]]] => 7
[[],[],[],[],[],[],[]] => 2
[[],[],[],[],[],[[]]] => 3
[[],[],[],[],[[]],[]] => 3
[[],[],[],[],[[],[]]] => 3
[[],[],[],[],[[[]]]] => 4
[[],[],[],[[]],[],[]] => 3
[[],[],[],[[]],[[]]] => 3
[[],[],[],[[],[]],[]] => 3
[[],[],[],[[[]]],[]] => 4
[[],[],[],[[],[],[]]] => 3
[[],[],[],[[],[[]]]] => 4
[[],[],[],[[[]],[]]] => 4
[[],[],[],[[[],[]]]] => 4
[[],[],[],[[[[]]]]] => 5
[[],[],[[]],[],[],[]] => 3
[[],[],[[]],[],[[]]] => 3
[[],[],[[]],[[]],[]] => 3
[[],[],[[]],[[],[]]] => 4
[[],[],[[]],[[[]]]] => 4
[[],[],[[],[]],[],[]] => 3
[[],[],[[[]]],[],[]] => 4
[[],[],[[],[]],[[]]] => 4
[[],[],[[[]]],[[]]] => 4
[[],[],[[],[],[]],[]] => 3
[[],[],[[],[[]]],[]] => 4
[[],[],[[[]],[]],[]] => 4
[[],[],[[[],[]]],[]] => 4
[[],[],[[[[]]]],[]] => 5
[[],[],[[],[],[],[]]] => 3
[[],[],[[],[],[[]]]] => 4
[[],[],[[],[[]],[]]] => 4
[[],[],[[],[[],[]]]] => 4
[[],[],[[],[[[]]]]] => 5
[[],[],[[[]],[],[]]] => 4
[[],[],[[[]],[[]]]] => 4
[[],[],[[[],[]],[]]] => 4
[[],[],[[[[]]],[]]] => 5
[[],[],[[[],[],[]]]] => 4
[[],[],[[[],[[]]]]] => 5
[[],[],[[[[]],[]]]] => 5
[[],[],[[[[],[]]]]] => 5
[[],[],[[[[[]]]]]] => 6
[[],[[]],[],[],[],[]] => 3
[[],[[]],[],[],[[]]] => 3
[[],[[]],[],[[]],[]] => 3
[[],[[]],[],[[],[]]] => 4
[[],[[]],[],[[[]]]] => 4
[[],[[]],[[]],[],[]] => 3
[[],[[]],[[]],[[]]] => 3
[[],[[]],[[],[]],[]] => 4
[[],[[]],[[[]]],[]] => 4
[[],[[]],[[],[],[]]] => 4
[[],[[]],[[],[[]]]] => 4
[[],[[]],[[[]],[]]] => 4
[[],[[]],[[[],[]]]] => 5
[[],[[]],[[[[]]]]] => 5
[[],[[],[]],[],[],[]] => 3
[[],[[[]]],[],[],[]] => 4
[[],[[],[]],[],[[]]] => 4
[[],[[[]]],[],[[]]] => 4
[[],[[],[]],[[]],[]] => 4
[[],[[[]]],[[]],[]] => 4
[[],[[],[]],[[],[]]] => 3
[[],[[],[]],[[[]]]] => 5
[[],[[[]]],[[],[]]] => 5
[[],[[[]]],[[[]]]] => 4
[[],[[],[],[]],[],[]] => 3
[[],[[],[[]]],[],[]] => 4
[[],[[[]],[]],[],[]] => 4
[[],[[[],[]]],[],[]] => 4
[[],[[[[]]]],[],[]] => 5
[[],[[],[],[]],[[]]] => 4
[[],[[],[[]]],[[]]] => 4
[[],[[[]],[]],[[]]] => 4
[[],[[[],[]]],[[]]] => 5
[[],[[[[]]]],[[]]] => 5
[[],[[],[],[],[]],[]] => 3
[[],[[],[],[[]]],[]] => 4
[[],[[],[[]],[]],[]] => 4
[[],[[],[[],[]]],[]] => 4
[[],[[],[[[]]]],[]] => 5
[[],[[[]],[],[]],[]] => 4
[[],[[[]],[[]]],[]] => 4
[[],[[[],[]],[]],[]] => 4
[[],[[[[]]],[]],[]] => 5
[[],[[[],[],[]]],[]] => 4
[[],[[[],[[]]]],[]] => 5
[[],[[[[]],[]]],[]] => 5
[[],[[[[],[]]]],[]] => 5
[[],[[[[[]]]]],[]] => 6
[[],[[],[],[],[],[]]] => 3
[[],[[],[],[],[[]]]] => 4
[[],[[],[],[[]],[]]] => 4
[[],[[],[],[[],[]]]] => 4
[[],[[],[],[[[]]]]] => 5
[[],[[],[[]],[],[]]] => 4
[[],[[],[[]],[[]]]] => 4
[[],[[],[[],[]],[]]] => 4
[[],[[],[[[]]],[]]] => 5
[[],[[],[[],[],[]]]] => 4
[[],[[],[[],[[]]]]] => 5
[[],[[],[[[]],[]]]] => 5
[[],[[],[[[],[]]]]] => 5
[[],[[],[[[[]]]]]] => 6
[[],[[[]],[],[],[]]] => 4
[[],[[[]],[],[[]]]] => 4
[[],[[[]],[[]],[]]] => 4
[[],[[[]],[[],[]]]] => 5
[[],[[[]],[[[]]]]] => 5
[[],[[[],[]],[],[]]] => 4
[[],[[[[]]],[],[]]] => 5
[[],[[[],[]],[[]]]] => 5
[[],[[[[]]],[[]]]] => 5
[[],[[[],[],[]],[]]] => 4
[[],[[[],[[]]],[]]] => 5
[[],[[[[]],[]],[]]] => 5
[[],[[[[],[]]],[]]] => 5
[[],[[[[[]]]],[]]] => 6
[[],[[[],[],[],[]]]] => 4
[[],[[[],[],[[]]]]] => 5
[[],[[[],[[]],[]]]] => 5
[[],[[[],[[],[]]]]] => 5
[[],[[[],[[[]]]]]] => 6
[[],[[[[]],[],[]]]] => 5
[[],[[[[]],[[]]]]] => 5
[[],[[[[],[]],[]]]] => 5
[[],[[[[[]]],[]]]] => 6
[[],[[[[],[],[]]]]] => 5
[[],[[[[],[[]]]]]] => 6
[[],[[[[[]],[]]]]] => 6
[[],[[[[[],[]]]]]] => 6
[[],[[[[[[]]]]]]] => 7
[[[]],[],[],[],[],[]] => 3
[[[]],[],[],[],[[]]] => 3
[[[]],[],[],[[]],[]] => 3
[[[]],[],[],[[],[]]] => 4
[[[]],[],[],[[[]]]] => 4
[[[]],[],[[]],[],[]] => 3
[[[]],[],[[]],[[]]] => 3
[[[]],[],[[],[]],[]] => 4
[[[]],[],[[[]]],[]] => 4
[[[]],[],[[],[],[]]] => 4
[[[]],[],[[],[[]]]] => 4
[[[]],[],[[[]],[]]] => 4
[[[]],[],[[[],[]]]] => 5
[[[]],[],[[[[]]]]] => 5
[[[]],[[]],[],[],[]] => 3
[[[]],[[]],[],[[]]] => 3
[[[]],[[]],[[]],[]] => 3
[[[]],[[]],[[],[]]] => 4
[[[]],[[]],[[[]]]] => 4
[[[]],[[],[]],[],[]] => 4
[[[]],[[[]]],[],[]] => 4
[[[]],[[],[]],[[]]] => 4
[[[]],[[[]]],[[]]] => 4
[[[]],[[],[],[]],[]] => 4
[[[]],[[],[[]]],[]] => 4
[[[]],[[[]],[]],[]] => 4
[[[]],[[[],[]]],[]] => 5
[[[]],[[[[]]]],[]] => 5
[[[]],[[],[],[],[]]] => 4
[[[]],[[],[],[[]]]] => 4
[[[]],[[],[[]],[]]] => 4
[[[]],[[],[[],[]]]] => 5
[[[]],[[],[[[]]]]] => 5
[[[]],[[[]],[],[]]] => 4
[[[]],[[[]],[[]]]] => 4
[[[]],[[[],[]],[]]] => 5
[[[]],[[[[]]],[]]] => 5
[[[]],[[[],[],[]]]] => 5
[[[]],[[[],[[]]]]] => 5
[[[]],[[[[]],[]]]] => 5
[[[]],[[[[],[]]]]] => 6
[[[]],[[[[[]]]]]] => 6
[[[],[]],[],[],[],[]] => 3
[[[[]]],[],[],[],[]] => 4
[[[],[]],[],[],[[]]] => 4
[[[[]]],[],[],[[]]] => 4
[[[],[]],[],[[]],[]] => 4
[[[[]]],[],[[]],[]] => 4
[[[],[]],[],[[],[]]] => 3
[[[],[]],[],[[[]]]] => 5
[[[[]]],[],[[],[]]] => 5
[[[[]]],[],[[[]]]] => 4
[[[],[]],[[]],[],[]] => 4
[[[[]]],[[]],[],[]] => 4
[[[],[]],[[]],[[]]] => 4
[[[[]]],[[]],[[]]] => 4
[[[],[]],[[],[]],[]] => 3
[[[],[]],[[[]]],[]] => 5
[[[[]]],[[],[]],[]] => 5
[[[[]]],[[[]]],[]] => 4
[[[],[]],[[],[],[]]] => 4
[[[],[]],[[],[[]]]] => 5
[[[],[]],[[[]],[]]] => 5
[[[],[]],[[[],[]]]] => 4
[[[],[]],[[[[]]]]] => 6
[[[[]]],[[],[],[]]] => 5
[[[[]]],[[],[[]]]] => 5
[[[[]]],[[[]],[]]] => 5
[[[[]]],[[[],[]]]] => 6
[[[[]]],[[[[]]]]] => 5
[[[],[],[]],[],[],[]] => 3
[[[],[[]]],[],[],[]] => 4
[[[[]],[]],[],[],[]] => 4
[[[[],[]]],[],[],[]] => 4
[[[[[]]]],[],[],[]] => 5
[[[],[],[]],[],[[]]] => 4
[[[],[[]]],[],[[]]] => 4
[[[[]],[]],[],[[]]] => 4
[[[[],[]]],[],[[]]] => 5
[[[[[]]]],[],[[]]] => 5
[[[],[],[]],[[]],[]] => 4
[[[],[[]]],[[]],[]] => 4
[[[[]],[]],[[]],[]] => 4
[[[[],[]]],[[]],[]] => 5
[[[[[]]]],[[]],[]] => 5
[[[],[],[]],[[],[]]] => 4
[[[],[],[]],[[[]]]] => 5
[[[],[[]]],[[],[]]] => 5
[[[],[[]]],[[[]]]] => 5
[[[[]],[]],[[],[]]] => 5
[[[[]],[]],[[[]]]] => 5
[[[[],[]]],[[],[]]] => 4
[[[[],[]]],[[[]]]] => 6
[[[[[]]]],[[],[]]] => 6
[[[[[]]]],[[[]]]] => 5
[[[],[],[],[]],[],[]] => 3
[[[],[],[[]]],[],[]] => 4
[[[],[[]],[]],[],[]] => 4
[[[],[[],[]]],[],[]] => 4
[[[],[[[]]]],[],[]] => 5
[[[[]],[],[]],[],[]] => 4
[[[[]],[[]]],[],[]] => 4
[[[[],[]],[]],[],[]] => 4
[[[[[]]],[]],[],[]] => 5
[[[[],[],[]]],[],[]] => 4
[[[[],[[]]]],[],[]] => 5
[[[[[]],[]]],[],[]] => 5
[[[[[],[]]]],[],[]] => 5
[[[[[[]]]]],[],[]] => 6
[[[],[],[],[]],[[]]] => 4
[[[],[],[[]]],[[]]] => 4
[[[],[[]],[]],[[]]] => 4
[[[],[[],[]]],[[]]] => 5
[[[],[[[]]]],[[]]] => 5
[[[[]],[],[]],[[]]] => 4
[[[[]],[[]]],[[]]] => 4
[[[[],[]],[]],[[]]] => 5
[[[[[]]],[]],[[]]] => 5
[[[[],[],[]]],[[]]] => 5
[[[[],[[]]]],[[]]] => 5
[[[[[]],[]]],[[]]] => 5
[[[[[],[]]]],[[]]] => 6
[[[[[[]]]]],[[]]] => 6
[[[],[],[],[],[]],[]] => 3
[[[],[],[],[[]]],[]] => 4
[[[],[],[[]],[]],[]] => 4
[[[],[],[[],[]]],[]] => 4
[[[],[],[[[]]]],[]] => 5
[[[],[[]],[],[]],[]] => 4
[[[],[[]],[[]]],[]] => 4
[[[],[[],[]],[]],[]] => 4
[[[],[[[]]],[]],[]] => 5
[[[],[[],[],[]]],[]] => 4
[[[],[[],[[]]]],[]] => 5
[[[],[[[]],[]]],[]] => 5
[[[],[[[],[]]]],[]] => 5
[[[],[[[[]]]]],[]] => 6
[[[[]],[],[],[]],[]] => 4
[[[[]],[],[[]]],[]] => 4
[[[[]],[[]],[]],[]] => 4
[[[[]],[[],[]]],[]] => 5
[[[[]],[[[]]]],[]] => 5
[[[[],[]],[],[]],[]] => 4
[[[[[]]],[],[]],[]] => 5
[[[[],[]],[[]]],[]] => 5
[[[[[]]],[[]]],[]] => 5
[[[[],[],[]],[]],[]] => 4
[[[[],[[]]],[]],[]] => 5
[[[[[]],[]],[]],[]] => 5
[[[[[],[]]],[]],[]] => 5
[[[[[[]]]],[]],[]] => 6
[[[[],[],[],[]]],[]] => 4
[[[[],[],[[]]]],[]] => 5
[[[[],[[]],[]]],[]] => 5
[[[[],[[],[]]]],[]] => 5
[[[[],[[[]]]]],[]] => 6
[[[[[]],[],[]]],[]] => 5
[[[[[]],[[]]]],[]] => 5
[[[[[],[]],[]]],[]] => 5
[[[[[[]]],[]]],[]] => 6
[[[[[],[],[]]]],[]] => 5
[[[[[],[[]]]]],[]] => 6
[[[[[[]],[]]]],[]] => 6
[[[[[[],[]]]]],[]] => 6
[[[[[[[]]]]]],[]] => 7
[[[],[],[],[],[],[]]] => 3
[[[],[],[],[],[[]]]] => 4
[[[],[],[],[[]],[]]] => 4
[[[],[],[],[[],[]]]] => 4
[[[],[],[],[[[]]]]] => 5
[[[],[],[[]],[],[]]] => 4
[[[],[],[[]],[[]]]] => 4
[[[],[],[[],[]],[]]] => 4
[[[],[],[[[]]],[]]] => 5
[[[],[],[[],[],[]]]] => 4
[[[],[],[[],[[]]]]] => 5
[[[],[],[[[]],[]]]] => 5
[[[],[],[[[],[]]]]] => 5
[[[],[],[[[[]]]]]] => 6
[[[],[[]],[],[],[]]] => 4
[[[],[[]],[],[[]]]] => 4
[[[],[[]],[[]],[]]] => 4
[[[],[[]],[[],[]]]] => 5
[[[],[[]],[[[]]]]] => 5
[[[],[[],[]],[],[]]] => 4
[[[],[[[]]],[],[]]] => 5
[[[],[[],[]],[[]]]] => 5
[[[],[[[]]],[[]]]] => 5
[[[],[[],[],[]],[]]] => 4
[[[],[[],[[]]],[]]] => 5
[[[],[[[]],[]],[]]] => 5
[[[],[[[],[]]],[]]] => 5
[[[],[[[[]]]],[]]] => 6
[[[],[[],[],[],[]]]] => 4
[[[],[[],[],[[]]]]] => 5
[[[],[[],[[]],[]]]] => 5
[[[],[[],[[],[]]]]] => 5
[[[],[[],[[[]]]]]] => 6
[[[],[[[]],[],[]]]] => 5
[[[],[[[]],[[]]]]] => 5
[[[],[[[],[]],[]]]] => 5
[[[],[[[[]]],[]]]] => 6
[[[],[[[],[],[]]]]] => 5
[[[],[[[],[[]]]]]] => 6
[[[],[[[[]],[]]]]] => 6
[[[],[[[[],[]]]]]] => 6
[[[],[[[[[]]]]]]] => 7
[[[[]],[],[],[],[]]] => 4
[[[[]],[],[],[[]]]] => 4
[[[[]],[],[[]],[]]] => 4
[[[[]],[],[[],[]]]] => 5
[[[[]],[],[[[]]]]] => 5
[[[[]],[[]],[],[]]] => 4
[[[[]],[[]],[[]]]] => 4
[[[[]],[[],[]],[]]] => 5
[[[[]],[[[]]],[]]] => 5
[[[[]],[[],[],[]]]] => 5
[[[[]],[[],[[]]]]] => 5
[[[[]],[[[]],[]]]] => 5
[[[[]],[[[],[]]]]] => 6
[[[[]],[[[[]]]]]] => 6
[[[[],[]],[],[],[]]] => 4
[[[[[]]],[],[],[]]] => 5
[[[[],[]],[],[[]]]] => 5
[[[[[]]],[],[[]]]] => 5
[[[[],[]],[[]],[]]] => 5
[[[[[]]],[[]],[]]] => 5
[[[[],[]],[[],[]]]] => 4
[[[[],[]],[[[]]]]] => 6
[[[[[]]],[[],[]]]] => 6
[[[[[]]],[[[]]]]] => 5
[[[[],[],[]],[],[]]] => 4
[[[[],[[]]],[],[]]] => 5
[[[[[]],[]],[],[]]] => 5
[[[[[],[]]],[],[]]] => 5
[[[[[[]]]],[],[]]] => 6
[[[[],[],[]],[[]]]] => 5
[[[[],[[]]],[[]]]] => 5
[[[[[]],[]],[[]]]] => 5
[[[[[],[]]],[[]]]] => 6
[[[[[[]]]],[[]]]] => 6
[[[[],[],[],[]],[]]] => 4
[[[[],[],[[]]],[]]] => 5
[[[[],[[]],[]],[]]] => 5
[[[[],[[],[]]],[]]] => 5
[[[[],[[[]]]],[]]] => 6
[[[[[]],[],[]],[]]] => 5
[[[[[]],[[]]],[]]] => 5
[[[[[],[]],[]],[]]] => 5
[[[[[[]]],[]],[]]] => 6
[[[[[],[],[]]],[]]] => 5
[[[[[],[[]]]],[]]] => 6
[[[[[[]],[]]],[]]] => 6
[[[[[[],[]]]],[]]] => 6
[[[[[[[]]]]],[]]] => 7
[[[[],[],[],[],[]]]] => 4
[[[[],[],[],[[]]]]] => 5
[[[[],[],[[]],[]]]] => 5
[[[[],[],[[],[]]]]] => 5
[[[[],[],[[[]]]]]] => 6
[[[[],[[]],[],[]]]] => 5
[[[[],[[]],[[]]]]] => 5
[[[[],[[],[]],[]]]] => 5
[[[[],[[[]]],[]]]] => 6
[[[[],[[],[],[]]]]] => 5
[[[[],[[],[[]]]]]] => 6
[[[[],[[[]],[]]]]] => 6
[[[[],[[[],[]]]]]] => 6
[[[[],[[[[]]]]]]] => 7
[[[[[]],[],[],[]]]] => 5
[[[[[]],[],[[]]]]] => 5
[[[[[]],[[]],[]]]] => 5
[[[[[]],[[],[]]]]] => 6
[[[[[]],[[[]]]]]] => 6
[[[[[],[]],[],[]]]] => 5
[[[[[[]]],[],[]]]] => 6
[[[[[],[]],[[]]]]] => 6
[[[[[[]]],[[]]]]] => 6
[[[[[],[],[]],[]]]] => 5
[[[[[],[[]]],[]]]] => 6
[[[[[[]],[]],[]]]] => 6
[[[[[[],[]]],[]]]] => 6
[[[[[[[]]]],[]]]] => 7
[[[[[],[],[],[]]]]] => 5
[[[[[],[],[[]]]]]] => 6
[[[[[],[[]],[]]]]] => 6
[[[[[],[[],[]]]]]] => 6
[[[[[],[[[]]]]]]] => 7
[[[[[[]],[],[]]]]] => 6
[[[[[[]],[[]]]]]] => 6
[[[[[[],[]],[]]]]] => 6
[[[[[[[]]],[]]]]] => 7
[[[[[[],[],[]]]]]] => 6
[[[[[[],[[]]]]]]] => 7
[[[[[[[]],[]]]]]] => 7
[[[[[[[],[]]]]]]] => 7
[[[[[[[[]]]]]]]] => 8
[[],[],[],[],[],[],[],[]] => 2
[[],[],[],[],[],[],[[]]] => 3
[[],[],[],[],[],[[]],[]] => 3
[[],[],[],[],[],[[],[]]] => 3
[[],[],[],[],[],[[[]]]] => 4
[[],[],[],[],[[]],[],[]] => 3
[[],[],[],[],[[]],[[]]] => 3
[[],[],[],[],[[],[]],[]] => 3
[[],[],[],[],[[[]]],[]] => 4
[[],[],[],[],[[],[],[]]] => 3
[[],[],[],[],[[],[[]]]] => 4
[[],[],[],[],[[[]],[]]] => 4
[[],[],[],[],[[[],[]]]] => 4
[[],[],[],[],[[[[]]]]] => 5
[[],[],[],[[]],[],[],[]] => 3
[[],[],[],[[]],[],[[]]] => 3
[[],[],[],[[]],[[]],[]] => 3
[[],[],[],[[]],[[],[]]] => 4
[[],[],[],[[]],[[[]]]] => 4
[[],[],[],[[],[]],[],[]] => 3
[[],[],[],[[[]]],[],[]] => 4
[[],[],[],[[],[]],[[]]] => 4
[[],[],[],[[[]]],[[]]] => 4
[[],[],[],[[],[],[]],[]] => 3
[[],[],[],[[],[[]]],[]] => 4
[[],[],[],[[[]],[]],[]] => 4
[[],[],[],[[[],[]]],[]] => 4
[[],[],[],[[[[]]]],[]] => 5
[[],[],[],[[],[],[],[]]] => 3
[[],[],[],[[],[],[[]]]] => 4
[[],[],[],[[],[[]],[]]] => 4
[[],[],[],[[],[[],[]]]] => 4
[[],[],[],[[],[[[]]]]] => 5
[[],[],[],[[[]],[],[]]] => 4
[[],[],[],[[[]],[[]]]] => 4
[[],[],[],[[[],[]],[]]] => 4
[[],[],[],[[[[]]],[]]] => 5
[[],[],[],[[[],[],[]]]] => 4
[[],[],[],[[[],[[]]]]] => 5
[[],[],[],[[[[]],[]]]] => 5
[[],[],[],[[[[],[]]]]] => 5
[[],[],[],[[[[[]]]]]] => 6
[[],[],[[]],[],[],[],[]] => 3
[[],[],[[]],[],[],[[]]] => 3
[[],[],[[]],[],[[]],[]] => 3
[[],[],[[]],[],[[],[]]] => 4
[[],[],[[]],[],[[[]]]] => 4
[[],[],[[]],[[]],[],[]] => 3
[[],[],[[]],[[]],[[]]] => 3
[[],[],[[]],[[],[]],[]] => 4
[[],[],[[]],[[[]]],[]] => 4
[[],[],[[]],[[],[],[]]] => 4
[[],[],[[]],[[],[[]]]] => 4
[[],[],[[]],[[[]],[]]] => 4
[[],[],[[]],[[[],[]]]] => 5
[[],[],[[]],[[[[]]]]] => 5
[[],[],[[],[]],[],[],[]] => 3
[[],[],[[[]]],[],[],[]] => 4
[[],[],[[],[]],[],[[]]] => 4
[[],[],[[[]]],[],[[]]] => 4
[[],[],[[],[]],[[]],[]] => 4
[[],[],[[[]]],[[]],[]] => 4
[[],[],[[],[]],[[],[]]] => 3
[[],[],[[],[]],[[[]]]] => 5
[[],[],[[[]]],[[],[]]] => 5
[[],[],[[[]]],[[[]]]] => 4
[[],[],[[],[],[]],[],[]] => 3
[[],[],[[],[[]]],[],[]] => 4
[[],[],[[[]],[]],[],[]] => 4
[[],[],[[[],[]]],[],[]] => 4
[[],[],[[[[]]]],[],[]] => 5
[[],[],[[],[],[]],[[]]] => 4
[[],[],[[],[[]]],[[]]] => 4
[[],[],[[[]],[]],[[]]] => 4
[[],[],[[[],[]]],[[]]] => 5
[[],[],[[[[]]]],[[]]] => 5
[[],[],[[],[],[],[]],[]] => 3
[[],[],[[],[],[[]]],[]] => 4
[[],[],[[],[[]],[]],[]] => 4
[[],[],[[],[[],[]]],[]] => 4
[[],[],[[],[[[]]]],[]] => 5
[[],[],[[[]],[],[]],[]] => 4
[[],[],[[[]],[[]]],[]] => 4
[[],[],[[[],[]],[]],[]] => 4
[[],[],[[[[]]],[]],[]] => 5
[[],[],[[[],[],[]]],[]] => 4
[[],[],[[[],[[]]]],[]] => 5
[[],[],[[[[]],[]]],[]] => 5
[[],[],[[[[],[]]]],[]] => 5
[[],[],[[[[[]]]]],[]] => 6
[[],[],[[],[],[],[],[]]] => 3
[[],[],[[],[],[],[[]]]] => 4
[[],[],[[],[],[[]],[]]] => 4
[[],[],[[],[],[[],[]]]] => 4
[[],[],[[],[],[[[]]]]] => 5
[[],[],[[],[[]],[],[]]] => 4
[[],[],[[],[[]],[[]]]] => 4
[[],[],[[],[[],[]],[]]] => 4
[[],[],[[],[[[]]],[]]] => 5
[[],[],[[],[[],[],[]]]] => 4
[[],[],[[],[[],[[]]]]] => 5
[[],[],[[],[[[]],[]]]] => 5
[[],[],[[],[[[],[]]]]] => 5
[[],[],[[],[[[[]]]]]] => 6
[[],[],[[[]],[],[],[]]] => 4
[[],[],[[[]],[],[[]]]] => 4
[[],[],[[[]],[[]],[]]] => 4
[[],[],[[[]],[[],[]]]] => 5
[[],[],[[[]],[[[]]]]] => 5
[[],[],[[[],[]],[],[]]] => 4
[[],[],[[[[]]],[],[]]] => 5
[[],[],[[[],[]],[[]]]] => 5
[[],[],[[[[]]],[[]]]] => 5
[[],[],[[[],[],[]],[]]] => 4
[[],[],[[[],[[]]],[]]] => 5
[[],[],[[[[]],[]],[]]] => 5
[[],[],[[[[],[]]],[]]] => 5
[[],[],[[[[[]]]],[]]] => 6
[[],[],[[[],[],[],[]]]] => 4
[[],[],[[[],[],[[]]]]] => 5
[[],[],[[[],[[]],[]]]] => 5
[[],[],[[[],[[],[]]]]] => 5
[[],[],[[[],[[[]]]]]] => 6
[[],[],[[[[]],[],[]]]] => 5
[[],[],[[[[]],[[]]]]] => 5
[[],[],[[[[],[]],[]]]] => 5
[[],[],[[[[[]]],[]]]] => 6
[[],[],[[[[],[],[]]]]] => 5
[[],[],[[[[],[[]]]]]] => 6
[[],[],[[[[[]],[]]]]] => 6
[[],[],[[[[[],[]]]]]] => 6
[[],[],[[[[[[]]]]]]] => 7
[[],[[]],[],[],[],[],[]] => 3
[[],[[]],[],[],[],[[]]] => 3
[[],[[]],[],[],[[]],[]] => 3
[[],[[]],[],[],[[],[]]] => 4
[[],[[]],[],[],[[[]]]] => 4
[[],[[]],[],[[]],[],[]] => 3
[[],[[]],[],[[]],[[]]] => 3
[[],[[]],[],[[],[]],[]] => 4
[[],[[]],[],[[[]]],[]] => 4
[[],[[]],[],[[],[],[]]] => 4
[[],[[]],[],[[],[[]]]] => 4
[[],[[]],[],[[[]],[]]] => 4
[[],[[]],[],[[[],[]]]] => 5
[[],[[]],[],[[[[]]]]] => 5
[[],[[]],[[]],[],[],[]] => 3
[[],[[]],[[]],[],[[]]] => 3
[[],[[]],[[]],[[]],[]] => 3
[[],[[]],[[]],[[],[]]] => 4
[[],[[]],[[]],[[[]]]] => 4
[[],[[]],[[],[]],[],[]] => 4
[[],[[]],[[[]]],[],[]] => 4
[[],[[]],[[],[]],[[]]] => 4
[[],[[]],[[[]]],[[]]] => 4
[[],[[]],[[],[],[]],[]] => 4
[[],[[]],[[],[[]]],[]] => 4
[[],[[]],[[[]],[]],[]] => 4
[[],[[]],[[[],[]]],[]] => 5
[[],[[]],[[[[]]]],[]] => 5
[[],[[]],[[],[],[],[]]] => 4
[[],[[]],[[],[],[[]]]] => 4
[[],[[]],[[],[[]],[]]] => 4
[[],[[]],[[],[[],[]]]] => 5
[[],[[]],[[],[[[]]]]] => 5
[[],[[]],[[[]],[],[]]] => 4
[[],[[]],[[[]],[[]]]] => 4
[[],[[]],[[[],[]],[]]] => 5
[[],[[]],[[[[]]],[]]] => 5
[[],[[]],[[[],[],[]]]] => 5
[[],[[]],[[[],[[]]]]] => 5
[[],[[]],[[[[]],[]]]] => 5
[[],[[]],[[[[],[]]]]] => 6
[[],[[]],[[[[[]]]]]] => 6
[[],[[],[]],[],[],[],[]] => 3
[[],[[[]]],[],[],[],[]] => 4
[[],[[],[]],[],[],[[]]] => 4
[[],[[[]]],[],[],[[]]] => 4
[[],[[],[]],[],[[]],[]] => 4
[[],[[[]]],[],[[]],[]] => 4
[[],[[],[]],[],[[],[]]] => 3
[[],[[],[]],[],[[[]]]] => 5
[[],[[[]]],[],[[],[]]] => 5
[[],[[[]]],[],[[[]]]] => 4
[[],[[],[]],[[]],[],[]] => 4
[[],[[[]]],[[]],[],[]] => 4
[[],[[],[]],[[]],[[]]] => 4
[[],[[[]]],[[]],[[]]] => 4
[[],[[],[]],[[],[]],[]] => 3
[[],[[],[]],[[[]]],[]] => 5
[[],[[[]]],[[],[]],[]] => 5
[[],[[[]]],[[[]]],[]] => 4
[[],[[],[]],[[],[],[]]] => 4
[[],[[],[]],[[],[[]]]] => 5
[[],[[],[]],[[[]],[]]] => 5
[[],[[],[]],[[[],[]]]] => 4
[[],[[],[]],[[[[]]]]] => 6
[[],[[[]]],[[],[],[]]] => 5
[[],[[[]]],[[],[[]]]] => 5
[[],[[[]]],[[[]],[]]] => 5
[[],[[[]]],[[[],[]]]] => 6
[[],[[[]]],[[[[]]]]] => 5
[[],[[],[],[]],[],[],[]] => 3
[[],[[],[[]]],[],[],[]] => 4
[[],[[[]],[]],[],[],[]] => 4
[[],[[[],[]]],[],[],[]] => 4
[[],[[[[]]]],[],[],[]] => 5
[[],[[],[],[]],[],[[]]] => 4
[[],[[],[[]]],[],[[]]] => 4
[[],[[[]],[]],[],[[]]] => 4
[[],[[[],[]]],[],[[]]] => 5
[[],[[[[]]]],[],[[]]] => 5
[[],[[],[],[]],[[]],[]] => 4
[[],[[],[[]]],[[]],[]] => 4
[[],[[[]],[]],[[]],[]] => 4
[[],[[[],[]]],[[]],[]] => 5
[[],[[[[]]]],[[]],[]] => 5
[[],[[],[],[]],[[],[]]] => 4
[[],[[],[],[]],[[[]]]] => 5
[[],[[],[[]]],[[],[]]] => 5
[[],[[],[[]]],[[[]]]] => 5
[[],[[[]],[]],[[],[]]] => 5
[[],[[[]],[]],[[[]]]] => 5
[[],[[[],[]]],[[],[]]] => 4
[[],[[[],[]]],[[[]]]] => 6
[[],[[[[]]]],[[],[]]] => 6
[[],[[[[]]]],[[[]]]] => 5
[[],[[],[],[],[]],[],[]] => 3
[[],[[],[],[[]]],[],[]] => 4
[[],[[],[[]],[]],[],[]] => 4
[[],[[],[[],[]]],[],[]] => 4
[[],[[],[[[]]]],[],[]] => 5
[[],[[[]],[],[]],[],[]] => 4
[[],[[[]],[[]]],[],[]] => 4
[[],[[[],[]],[]],[],[]] => 4
[[],[[[[]]],[]],[],[]] => 5
[[],[[[],[],[]]],[],[]] => 4
[[],[[[],[[]]]],[],[]] => 5
[[],[[[[]],[]]],[],[]] => 5
[[],[[[[],[]]]],[],[]] => 5
[[],[[[[[]]]]],[],[]] => 6
[[],[[],[],[],[]],[[]]] => 4
[[],[[],[],[[]]],[[]]] => 4
[[],[[],[[]],[]],[[]]] => 4
[[],[[],[[],[]]],[[]]] => 5
[[],[[],[[[]]]],[[]]] => 5
[[],[[[]],[],[]],[[]]] => 4
[[],[[[]],[[]]],[[]]] => 4
[[],[[[],[]],[]],[[]]] => 5
[[],[[[[]]],[]],[[]]] => 5
[[],[[[],[],[]]],[[]]] => 5
[[],[[[],[[]]]],[[]]] => 5
[[],[[[[]],[]]],[[]]] => 5
[[],[[[[],[]]]],[[]]] => 6
[[],[[[[[]]]]],[[]]] => 6
[[],[[],[],[],[],[]],[]] => 3
[[],[[],[],[],[[]]],[]] => 4
[[],[[],[],[[]],[]],[]] => 4
[[],[[],[],[[],[]]],[]] => 4
[[],[[],[],[[[]]]],[]] => 5
[[],[[],[[]],[],[]],[]] => 4
[[],[[],[[]],[[]]],[]] => 4
[[],[[],[[],[]],[]],[]] => 4
[[],[[],[[[]]],[]],[]] => 5
[[],[[],[[],[],[]]],[]] => 4
[[],[[],[[],[[]]]],[]] => 5
[[],[[],[[[]],[]]],[]] => 5
[[],[[],[[[],[]]]],[]] => 5
[[],[[],[[[[]]]]],[]] => 6
[[],[[[]],[],[],[]],[]] => 4
[[],[[[]],[],[[]]],[]] => 4
[[],[[[]],[[]],[]],[]] => 4
[[],[[[]],[[],[]]],[]] => 5
[[],[[[]],[[[]]]],[]] => 5
[[],[[[],[]],[],[]],[]] => 4
[[],[[[[]]],[],[]],[]] => 5
[[],[[[],[]],[[]]],[]] => 5
[[],[[[[]]],[[]]],[]] => 5
[[],[[[],[],[]],[]],[]] => 4
[[],[[[],[[]]],[]],[]] => 5
[[],[[[[]],[]],[]],[]] => 5
[[],[[[[],[]]],[]],[]] => 5
[[],[[[[[]]]],[]],[]] => 6
[[],[[[],[],[],[]]],[]] => 4
[[],[[[],[],[[]]]],[]] => 5
[[],[[[],[[]],[]]],[]] => 5
[[],[[[],[[],[]]]],[]] => 5
[[],[[[],[[[]]]]],[]] => 6
[[],[[[[]],[],[]]],[]] => 5
[[],[[[[]],[[]]]],[]] => 5
[[],[[[[],[]],[]]],[]] => 5
[[],[[[[[]]],[]]],[]] => 6
[[],[[[[],[],[]]]],[]] => 5
[[],[[[[],[[]]]]],[]] => 6
[[],[[[[[]],[]]]],[]] => 6
[[],[[[[[],[]]]]],[]] => 6
[[],[[[[[[]]]]]],[]] => 7
[[],[[],[],[],[],[],[]]] => 3
[[],[[],[],[],[],[[]]]] => 4
[[],[[],[],[],[[]],[]]] => 4
[[],[[],[],[],[[],[]]]] => 4
[[],[[],[],[],[[[]]]]] => 5
[[],[[],[],[[]],[],[]]] => 4
[[],[[],[],[[]],[[]]]] => 4
[[],[[],[],[[],[]],[]]] => 4
[[],[[],[],[[[]]],[]]] => 5
[[],[[],[],[[],[],[]]]] => 4
[[],[[],[],[[],[[]]]]] => 5
[[],[[],[],[[[]],[]]]] => 5
[[],[[],[],[[[],[]]]]] => 5
[[],[[],[],[[[[]]]]]] => 6
[[],[[],[[]],[],[],[]]] => 4
[[],[[],[[]],[],[[]]]] => 4
[[],[[],[[]],[[]],[]]] => 4
[[],[[],[[]],[[],[]]]] => 5
[[],[[],[[]],[[[]]]]] => 5
[[],[[],[[],[]],[],[]]] => 4
[[],[[],[[[]]],[],[]]] => 5
[[],[[],[[],[]],[[]]]] => 5
[[],[[],[[[]]],[[]]]] => 5
[[],[[],[[],[],[]],[]]] => 4
[[],[[],[[],[[]]],[]]] => 5
[[],[[],[[[]],[]],[]]] => 5
[[],[[],[[[],[]]],[]]] => 5
[[],[[],[[[[]]]],[]]] => 6
[[],[[],[[],[],[],[]]]] => 4
[[],[[],[[],[],[[]]]]] => 5
[[],[[],[[],[[]],[]]]] => 5
[[],[[],[[],[[],[]]]]] => 5
[[],[[],[[],[[[]]]]]] => 6
[[],[[],[[[]],[],[]]]] => 5
[[],[[],[[[]],[[]]]]] => 5
[[],[[],[[[],[]],[]]]] => 5
[[],[[],[[[[]]],[]]]] => 6
[[],[[],[[[],[],[]]]]] => 5
[[],[[],[[[],[[]]]]]] => 6
[[],[[],[[[[]],[]]]]] => 6
[[],[[],[[[[],[]]]]]] => 6
[[],[[],[[[[[]]]]]]] => 7
[[],[[[]],[],[],[],[]]] => 4
[[],[[[]],[],[],[[]]]] => 4
[[],[[[]],[],[[]],[]]] => 4
[[],[[[]],[],[[],[]]]] => 5
[[],[[[]],[],[[[]]]]] => 5
[[],[[[]],[[]],[],[]]] => 4
[[],[[[]],[[]],[[]]]] => 4
[[],[[[]],[[],[]],[]]] => 5
[[],[[[]],[[[]]],[]]] => 5
[[],[[[]],[[],[],[]]]] => 5
[[],[[[]],[[],[[]]]]] => 5
[[],[[[]],[[[]],[]]]] => 5
[[],[[[]],[[[],[]]]]] => 6
[[],[[[]],[[[[]]]]]] => 6
[[],[[[],[]],[],[],[]]] => 4
[[],[[[[]]],[],[],[]]] => 5
[[],[[[],[]],[],[[]]]] => 5
[[],[[[[]]],[],[[]]]] => 5
[[],[[[],[]],[[]],[]]] => 5
[[],[[[[]]],[[]],[]]] => 5
[[],[[[],[]],[[],[]]]] => 4
[[],[[[],[]],[[[]]]]] => 6
[[],[[[[]]],[[],[]]]] => 6
[[],[[[[]]],[[[]]]]] => 5
[[],[[[],[],[]],[],[]]] => 4
[[],[[[],[[]]],[],[]]] => 5
[[],[[[[]],[]],[],[]]] => 5
[[],[[[[],[]]],[],[]]] => 5
[[],[[[[[]]]],[],[]]] => 6
[[],[[[],[],[]],[[]]]] => 5
[[],[[[],[[]]],[[]]]] => 5
[[],[[[[]],[]],[[]]]] => 5
[[],[[[[],[]]],[[]]]] => 6
[[],[[[[[]]]],[[]]]] => 6
[[],[[[],[],[],[]],[]]] => 4
[[],[[[],[],[[]]],[]]] => 5
[[],[[[],[[]],[]],[]]] => 5
[[],[[[],[[],[]]],[]]] => 5
[[],[[[],[[[]]]],[]]] => 6
[[],[[[[]],[],[]],[]]] => 5
[[],[[[[]],[[]]],[]]] => 5
[[],[[[[],[]],[]],[]]] => 5
[[],[[[[[]]],[]],[]]] => 6
[[],[[[[],[],[]]],[]]] => 5
[[],[[[[],[[]]]],[]]] => 6
[[],[[[[[]],[]]],[]]] => 6
[[],[[[[[],[]]]],[]]] => 6
[[],[[[[[[]]]]],[]]] => 7
[[],[[[],[],[],[],[]]]] => 4
[[],[[[],[],[],[[]]]]] => 5
[[],[[[],[],[[]],[]]]] => 5
[[],[[[],[],[[],[]]]]] => 5
[[],[[[],[],[[[]]]]]] => 6
[[],[[[],[[]],[],[]]]] => 5
[[],[[[],[[]],[[]]]]] => 5
[[],[[[],[[],[]],[]]]] => 5
[[],[[[],[[[]]],[]]]] => 6
[[],[[[],[[],[],[]]]]] => 5
[[],[[[],[[],[[]]]]]] => 6
[[],[[[],[[[]],[]]]]] => 6
[[],[[[],[[[],[]]]]]] => 6
[[],[[[],[[[[]]]]]]] => 7
[[],[[[[]],[],[],[]]]] => 5
[[],[[[[]],[],[[]]]]] => 5
[[],[[[[]],[[]],[]]]] => 5
[[],[[[[]],[[],[]]]]] => 6
[[],[[[[]],[[[]]]]]] => 6
[[],[[[[],[]],[],[]]]] => 5
[[],[[[[[]]],[],[]]]] => 6
[[],[[[[],[]],[[]]]]] => 6
[[],[[[[[]]],[[]]]]] => 6
[[],[[[[],[],[]],[]]]] => 5
[[],[[[[],[[]]],[]]]] => 6
[[],[[[[[]],[]],[]]]] => 6
[[],[[[[[],[]]],[]]]] => 6
[[],[[[[[[]]]],[]]]] => 7
[[],[[[[],[],[],[]]]]] => 5
[[],[[[[],[],[[]]]]]] => 6
[[],[[[[],[[]],[]]]]] => 6
[[],[[[[],[[],[]]]]]] => 6
[[],[[[[],[[[]]]]]]] => 7
[[],[[[[[]],[],[]]]]] => 6
[[],[[[[[]],[[]]]]]] => 6
[[],[[[[[],[]],[]]]]] => 6
[[],[[[[[[]]],[]]]]] => 7
[[],[[[[[],[],[]]]]]] => 6
[[],[[[[[],[[]]]]]]] => 7
[[],[[[[[[]],[]]]]]] => 7
[[],[[[[[[],[]]]]]]] => 7
[[],[[[[[[[]]]]]]]] => 8
[[[]],[],[],[],[],[],[]] => 3
[[[]],[],[],[],[],[[]]] => 3
[[[]],[],[],[],[[]],[]] => 3
[[[]],[],[],[],[[],[]]] => 4
[[[]],[],[],[],[[[]]]] => 4
[[[]],[],[],[[]],[],[]] => 3
[[[]],[],[],[[]],[[]]] => 3
[[[]],[],[],[[],[]],[]] => 4
[[[]],[],[],[[[]]],[]] => 4
[[[]],[],[],[[],[],[]]] => 4
[[[]],[],[],[[],[[]]]] => 4
[[[]],[],[],[[[]],[]]] => 4
[[[]],[],[],[[[],[]]]] => 5
[[[]],[],[],[[[[]]]]] => 5
[[[]],[],[[]],[],[],[]] => 3
[[[]],[],[[]],[],[[]]] => 3
[[[]],[],[[]],[[]],[]] => 3
[[[]],[],[[]],[[],[]]] => 4
[[[]],[],[[]],[[[]]]] => 4
[[[]],[],[[],[]],[],[]] => 4
[[[]],[],[[[]]],[],[]] => 4
[[[]],[],[[],[]],[[]]] => 4
[[[]],[],[[[]]],[[]]] => 4
[[[]],[],[[],[],[]],[]] => 4
[[[]],[],[[],[[]]],[]] => 4
[[[]],[],[[[]],[]],[]] => 4
[[[]],[],[[[],[]]],[]] => 5
[[[]],[],[[[[]]]],[]] => 5
[[[]],[],[[],[],[],[]]] => 4
[[[]],[],[[],[],[[]]]] => 4
[[[]],[],[[],[[]],[]]] => 4
[[[]],[],[[],[[],[]]]] => 5
[[[]],[],[[],[[[]]]]] => 5
[[[]],[],[[[]],[],[]]] => 4
[[[]],[],[[[]],[[]]]] => 4
[[[]],[],[[[],[]],[]]] => 5
[[[]],[],[[[[]]],[]]] => 5
[[[]],[],[[[],[],[]]]] => 5
[[[]],[],[[[],[[]]]]] => 5
[[[]],[],[[[[]],[]]]] => 5
[[[]],[],[[[[],[]]]]] => 6
[[[]],[],[[[[[]]]]]] => 6
[[[]],[[]],[],[],[],[]] => 3
[[[]],[[]],[],[],[[]]] => 3
[[[]],[[]],[],[[]],[]] => 3
[[[]],[[]],[],[[],[]]] => 4
[[[]],[[]],[],[[[]]]] => 4
[[[]],[[]],[[]],[],[]] => 3
[[[]],[[]],[[]],[[]]] => 3
[[[]],[[]],[[],[]],[]] => 4
[[[]],[[]],[[[]]],[]] => 4
[[[]],[[]],[[],[],[]]] => 4
[[[]],[[]],[[],[[]]]] => 4
[[[]],[[]],[[[]],[]]] => 4
[[[]],[[]],[[[],[]]]] => 5
[[[]],[[]],[[[[]]]]] => 5
[[[]],[[],[]],[],[],[]] => 4
[[[]],[[[]]],[],[],[]] => 4
[[[]],[[],[]],[],[[]]] => 4
[[[]],[[[]]],[],[[]]] => 4
[[[]],[[],[]],[[]],[]] => 4
[[[]],[[[]]],[[]],[]] => 4
[[[]],[[],[]],[[],[]]] => 4
[[[]],[[],[]],[[[]]]] => 5
[[[]],[[[]]],[[],[]]] => 5
[[[]],[[[]]],[[[]]]] => 4
[[[]],[[],[],[]],[],[]] => 4
[[[]],[[],[[]]],[],[]] => 4
[[[]],[[[]],[]],[],[]] => 4
[[[]],[[[],[]]],[],[]] => 5
[[[]],[[[[]]]],[],[]] => 5
[[[]],[[],[],[]],[[]]] => 4
[[[]],[[],[[]]],[[]]] => 4
[[[]],[[[]],[]],[[]]] => 4
[[[]],[[[],[]]],[[]]] => 5
[[[]],[[[[]]]],[[]]] => 5
[[[]],[[],[],[],[]],[]] => 4
[[[]],[[],[],[[]]],[]] => 4
[[[]],[[],[[]],[]],[]] => 4
[[[]],[[],[[],[]]],[]] => 5
[[[]],[[],[[[]]]],[]] => 5
[[[]],[[[]],[],[]],[]] => 4
[[[]],[[[]],[[]]],[]] => 4
[[[]],[[[],[]],[]],[]] => 5
[[[]],[[[[]]],[]],[]] => 5
[[[]],[[[],[],[]]],[]] => 5
[[[]],[[[],[[]]]],[]] => 5
[[[]],[[[[]],[]]],[]] => 5
[[[]],[[[[],[]]]],[]] => 6
[[[]],[[[[[]]]]],[]] => 6
[[[]],[[],[],[],[],[]]] => 4
[[[]],[[],[],[],[[]]]] => 4
[[[]],[[],[],[[]],[]]] => 4
[[[]],[[],[],[[],[]]]] => 5
[[[]],[[],[],[[[]]]]] => 5
[[[]],[[],[[]],[],[]]] => 4
[[[]],[[],[[]],[[]]]] => 4
[[[]],[[],[[],[]],[]]] => 5
[[[]],[[],[[[]]],[]]] => 5
[[[]],[[],[[],[],[]]]] => 5
[[[]],[[],[[],[[]]]]] => 5
[[[]],[[],[[[]],[]]]] => 5
[[[]],[[],[[[],[]]]]] => 6
[[[]],[[],[[[[]]]]]] => 6
[[[]],[[[]],[],[],[]]] => 4
[[[]],[[[]],[],[[]]]] => 4
[[[]],[[[]],[[]],[]]] => 4
[[[]],[[[]],[[],[]]]] => 5
[[[]],[[[]],[[[]]]]] => 5
[[[]],[[[],[]],[],[]]] => 5
[[[]],[[[[]]],[],[]]] => 5
[[[]],[[[],[]],[[]]]] => 5
[[[]],[[[[]]],[[]]]] => 5
[[[]],[[[],[],[]],[]]] => 5
[[[]],[[[],[[]]],[]]] => 5
[[[]],[[[[]],[]],[]]] => 5
[[[]],[[[[],[]]],[]]] => 6
[[[]],[[[[[]]]],[]]] => 6
[[[]],[[[],[],[],[]]]] => 5
[[[]],[[[],[],[[]]]]] => 5
[[[]],[[[],[[]],[]]]] => 5
[[[]],[[[],[[],[]]]]] => 6
[[[]],[[[],[[[]]]]]] => 6
[[[]],[[[[]],[],[]]]] => 5
[[[]],[[[[]],[[]]]]] => 5
[[[]],[[[[],[]],[]]]] => 6
[[[]],[[[[[]]],[]]]] => 6
[[[]],[[[[],[],[]]]]] => 6
[[[]],[[[[],[[]]]]]] => 6
[[[]],[[[[[]],[]]]]] => 6
[[[]],[[[[[],[]]]]]] => 7
[[[]],[[[[[[]]]]]]] => 7
[[[],[]],[],[],[],[],[]] => 3
[[[[]]],[],[],[],[],[]] => 4
[[[],[]],[],[],[],[[]]] => 4
[[[[]]],[],[],[],[[]]] => 4
[[[],[]],[],[],[[]],[]] => 4
[[[[]]],[],[],[[]],[]] => 4
[[[],[]],[],[],[[],[]]] => 3
[[[],[]],[],[],[[[]]]] => 5
[[[[]]],[],[],[[],[]]] => 5
[[[[]]],[],[],[[[]]]] => 4
[[[],[]],[],[[]],[],[]] => 4
[[[[]]],[],[[]],[],[]] => 4
[[[],[]],[],[[]],[[]]] => 4
[[[[]]],[],[[]],[[]]] => 4
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of distinct subtrees of an ordered tree.
A subtree is specified by a node of the tree. Thus, the tree consisting of a single path has as many subtrees as nodes, whereas the tree of height two, having all leaves attached to the root, has only two distinct subtrees. Because we consider ordered trees, the tree $[[[[]], []], [[], [[]]]]$ on nine nodes has five distinct subtrees.
Code
def statistic(T):
    return len(set(T.subtrees()))
Created
Jun 02, 2016 at 08:53 by Martin Rubey
Updated
Jun 02, 2016 at 08:53 by Martin Rubey