Identifier
Values
[1,0] => [1,1,0,0] => [1,0,1,0] => 1
[1,0,1,0] => [1,1,0,1,0,0] => [1,1,0,0,1,0] => 2
[1,1,0,0] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 2
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 10
[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] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 9
[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] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 9
[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] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[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] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[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] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 10
[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] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 8
[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] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 9
[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] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[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] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 7
[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] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[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] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 7
[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] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 7
[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] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 7
[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] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 10
[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] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 9
[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] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 9
[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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[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] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 7
[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] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 11
[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] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 8
[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] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 9
[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] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 8
[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] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 7
[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] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 8
[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] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 7
[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] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[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] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 6
[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] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 10
[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] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 7
[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] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 9
[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] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 8
[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] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 6
[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] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 8
[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] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 7
[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] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 7
[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] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 6
>>> Load all 376 entries. <<<
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 6
[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] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 6
[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] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 6
[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] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 10
[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] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[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] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 9
[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] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 8
[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] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8
[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] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 10
[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] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 8
[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] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 9
[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] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 7
[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] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 6
[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] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 8
[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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[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] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 6
[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] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[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] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 11
[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] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[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] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 10
[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] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 7
[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] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 7
[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] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 12
[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] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 8
[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] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[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] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 9
[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] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 8
[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] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 8
[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] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 8
[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] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 7
[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] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 7
[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] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 11
[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] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 7
[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] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 9
[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] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 9
[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] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 7
[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] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 8
[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] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 8
[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] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 7
[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] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 6
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[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] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[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] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 6
[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] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 10
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 9
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[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] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 6
[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] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 12
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 9
[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] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 9
[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] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 8
[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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[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] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6
[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] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[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] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 10
[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] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 10
[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] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 7
[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] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 8
[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] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8
[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] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 8
[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] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 7
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[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] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7
[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] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 7
[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] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 6
[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] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[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] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 10
[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] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[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] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9
[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] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 9
[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] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[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] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 8
[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] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8
[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] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 8
[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] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 7
[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] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 7
[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] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 7
[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] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 7
[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] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[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] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[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] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[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] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6
[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] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 8
[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] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 9
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 10
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 9
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 10
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 8
[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] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 10
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 9
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 10
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 11
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 10
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 9
[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] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 11
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 9
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 10
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 9
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 11
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 10
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 12
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 9
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 9
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 11
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 9
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 11
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 10
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 10
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 9
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 9
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 11
[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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 9
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 10
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 7
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 12
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 11
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 13
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 10
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 9
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 9
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 12
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 10
[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] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 10
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 9
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8
[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] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 7
[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] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 11
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 13
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 10
[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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 10
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 9
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 9
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 12
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11
[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] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 11
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 9
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 9
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 8
[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] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 10
[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] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[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] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8
[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] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 8
[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] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[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] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 7
[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] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
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Description
The sum of the semi-lengths of tunnels before a valley of a Dyck path.
For each valley $v$ in a Dyck path $D$ there is a corresponding tunnel, which
is the factor $T_v = s_i\dots s_j$ of $D$ where $s_i$ is the step after the first intersection of $D$ with the line $y = ht(v)$ to the left of $s_j$. This statistic is
$$ \sum_v (j_v-i_v)/2. $$
Map
swap returns and last descent
Description
Return a Dyck path with number of returns and length of the last descent interchanged.
This is the specialisation of the map $\Phi$ in [1] to Dyck paths. It is characterised by the fact that the number of up steps before a down step that is neither a return nor part of the last descent is preserved.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.