Identifier
Values
[1,0] => [1,0] => 0
[1,0,1,0] => [1,0,1,0] => 0
[1,1,0,0] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [1,1,0,1,0,0] => 1
[1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,1,0,1,0,0] => [1,0,1,0,1,0] => 0
[1,1,1,0,0,0] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
>>> Load all 625 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
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Description
The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path.
The global dimension is given by St000684The global dimension of the LNakayama algebra associated to a Dyck path. and the dominant dimension is given by St000685The dominant dimension of the LNakayama algebra associated to a Dyck path.. To every Dyck path there is an LNakayama algebra associated as described in St000684The global dimension of the LNakayama algebra associated to a Dyck path..
Dyck paths for which the global dimension and the dominant dimension of the the LNakayama algebra coincide and both dimensions at least $2$ correspond to the LNakayama algebras that are higher Auslander algebras in the sense of [1].
Map
Barnabei-Castronuovo involution
Description
The Barnabei-Castronuovo Schützenberger involution on Dyck paths.
The image of a Dyck path is obtained by reversing the canonical decompositions of the two halves of the Dyck path. More precisely, let $D_1, 1, D_2, 1, \dots$ be the canonical decomposition of the first half, then the canonical decomposition of the first half of the image is $\dots, 1, D_2, 1, D_1$.