Identifier
Values
[1,1,0,0,1,0] => [3,1,2] => [1,2] => [1,0,1,0] => 1
[1,1,1,0,0,0] => [1,2,3] => [1,2] => [1,0,1,0] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [2,3,1] => [1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [2,3,1] => [1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [2,3,1] => [1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3] => [1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3] => [1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
>>> Load all 552 entries. <<<
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [6,7,4,5,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [4,5,6,7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [6,7,5,3,4,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [5,6,7,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [6,4,5,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [6,7,3,4,5,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [6,3,4,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,2,1] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [6,7,5,4,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [5,6,7,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [6,7,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [4,5,6,7,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [6,5,7,3,2,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [5,6,7,3,2,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [6,4,5,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [6,5,3,4,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [6,7,5,2,3,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [5,6,7,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [5,6,7,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [6,7,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [6,4,5,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [4,5,6,7,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [6,7,2,3,4,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [5,2,3,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [4,2,3,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [6,5,7,4,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [5,6,7,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [4,5,6,7,3,1,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [6,7,5,3,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [6,5,7,3,4,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [5,6,7,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [6,5,7,4,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [5,6,7,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [6,7,4,5,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [5,6,4,7,3,1,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [5,4,6,7,3,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [5,4,6,3,7,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [5,6,3,4,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [4,3,5,6,7,1,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [6,4,3,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [5,4,3,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [4,5,3,6,7,1,2] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [6,3,4,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [4,3,5,6,7,1,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [5,6,7,4,2,1,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [4,5,6,7,2,1,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [5,6,7,3,2,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [6,7,4,3,2,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [6,7,3,4,2,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [5,6,7,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [6,7,5,2,3,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [5,6,7,2,3,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [6,7,4,2,3,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [6,7,5,4,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [5,6,7,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [6,7,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [5,6,4,7,2,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [6,7,3,2,4,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [6,5,7,3,2,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [5,6,7,3,2,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [6,7,3,4,2,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [5,6,3,4,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [6,7,2,3,4,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [6,7,5,2,3,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [6,5,7,2,3,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [5,6,7,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [6,7,5,4,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [6,5,7,4,1,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [6,7,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [6,7,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [6,5,4,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [4,5,6,7,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [6,7,5,3,1,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [5,6,7,3,1,2,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [6,7,4,3,1,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [6,7,3,4,1,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [4,3,5,6,1,2,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [3,4,5,6,1,2,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [6,7,5,2,1,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [6,5,7,2,1,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [5,6,7,2,1,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [6,7,4,2,1,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [6,5,4,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [6,7,3,2,1,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [6,3,4,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [6,7,2,3,1,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [6,5,2,3,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [5,6,2,3,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [4,2,3,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [6,7,4,1,2,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [6,4,5,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [5,6,4,7,1,2,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [5,4,6,7,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [6,7,3,1,2,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [5,6,7,3,1,2,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [5,6,4,3,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [5,4,6,3,1,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [5,4,3,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [6,7,2,1,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [5,6,2,1,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [5,6,7,2,1,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [6,4,2,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [5,6,4,2,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [5,4,6,2,1,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [5,6,3,2,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [4,5,2,3,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [5,2,3,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [6,5,1,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [6,4,3,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [6,2,3,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [6,4,1,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [5,3,1,2,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [3,4,1,2,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
search for individual values
searching the database for the individual values of this statistic
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.