Identifier
Values
[1,0] => [2,1] => {{1,2}} => 2
[1,0,1,0] => [3,1,2] => {{1,2,3}} => 3
[1,1,0,0] => [2,3,1] => {{1,2,3}} => 3
[1,0,1,0,1,0] => [4,1,2,3] => {{1,2,3,4}} => 4
[1,0,1,1,0,0] => [3,1,4,2] => {{1,2,3,4}} => 4
[1,1,0,0,1,0] => [2,4,1,3] => {{1,2,3,4}} => 4
[1,1,0,1,0,0] => [4,3,1,2] => {{1,2,3,4}} => 4
[1,1,1,0,0,0] => [2,3,4,1] => {{1,2,3,4}} => 4
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => {{1,2,3,4,5}} => 5
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => {{1,2,3,4,5}} => 5
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => {{1,2,3,4,5}} => 5
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => {{1,2,3,4,5}} => 5
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => {{1,2,3,4,5}} => 5
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => {{1,2,3,4,5}} => 5
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => {{1,2,3,4,5}} => 5
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => {{1,2,3,4,5}} => 5
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => {{1,3,5},{2,4}} => 2
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => {{1,2,3,4,5}} => 5
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => {{1,2,3,4,5}} => 5
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => {{1,2,3,4,5}} => 5
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => {{1,2,3,4,5}} => 5
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => 5
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => {{1,2,3,4,5,6}} => 6
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => {{1,2,3,4,5,6}} => 6
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => {{1,2,3,4,5,6}} => 6
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => {{1,2,3,4,5,6}} => 6
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => {{1,2,3,4,5,6}} => 6
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => {{1,2,3,4,5,6}} => 6
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => {{1,2,3,4,5,6}} => 6
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => {{1,2,3,4,5,6}} => 6
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => {{1,2,4,6},{3,5}} => 2
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => {{1,2,3,4,5,6}} => 6
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => {{1,2,3,4,5,6}} => 6
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => {{1,2,3,4,5,6}} => 6
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => {{1,2,3,4,5,6}} => 6
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => {{1,2,3,4,5,6}} => 6
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => {{1,2,3,4,5,6}} => 6
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => {{1,2,3,4,5,6}} => 6
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => {{1,2,3,4,5,6}} => 6
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => {{1,2,3,4,5,6}} => 6
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => {{1,2,3,4,5,6}} => 6
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => {{1,2,3,4,5,6}} => 6
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => {{1,2,3,4,5,6}} => 6
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => {{1,3,5,6},{2,4}} => 2
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => {{1,3,5},{2,4,6}} => 3
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => {{1,3,5,6},{2,4}} => 2
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => {{1,2,3,4,5,6}} => 6
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => {{1,2,3,4,5,6}} => 6
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => {{1,3,6},{2,4,5}} => 3
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => {{1,2,3,4,5,6}} => 6
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => {{1,2,3,4,5,6}} => 6
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => {{1,2,3,4,5,6}} => 6
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => {{1,2,3,4,5,6}} => 6
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => {{1,2,4,6},{3,5}} => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => {{1,2,3,4,5,6}} => 6
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => {{1,2,3,4,5,6}} => 6
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => {{1,4,6},{2,3,5}} => 3
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => {{1,3,4,6},{2,5}} => 2
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => {{1,2,3,4,5,6}} => 6
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => {{1,2,3,4,5,6}} => 6
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => {{1,2,3,4,5,6}} => 6
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => {{1,2,3,4,5,6}} => 6
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => {{1,2,3,4,5,6}} => 6
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => 6
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => {{1,2,3,5,7},{4,6}} => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => {{1,2,4,6,7},{3,5}} => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => {{1,2,4,6},{3,5,7}} => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => {{1,2,4,6,7},{3,5}} => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => {{1,2,4,7},{3,5,6}} => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => {{1,2,3,5,7},{4,6}} => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => {{1,2,5,7},{3,4,6}} => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => {{1,2,4,5,7},{3,6}} => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => {{1,2,3,4,5,6,7}} => 7
>>> Load all 518 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => {{1,2,3,5,7},{4,6}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => {{1,3,5,6,7},{2,4}} => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => {{1,3,5,6,7},{2,4}} => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => {{1,3,5},{2,4,6,7}} => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => {{1,3,5,7},{2,4,6}} => 3
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => {{1,3,5},{2,4,6,7}} => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => {{1,3,5,6,7},{2,4}} => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => {{1,3,5,6,7},{2,4}} => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => {{1,3,5,6},{2,4,7}} => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => {{1,3,5,6,7},{2,4}} => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => {{1,2,3,5,7},{4,6}} => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => {{1,3,6,7},{2,4,5}} => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => {{1,3,6},{2,4,5,7}} => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => {{1,3,6,7},{2,4,5}} => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => {{1,3,7},{2,4,5,6}} => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => {{1,2,4,6,7},{3,5}} => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => {{1,2,4,6},{3,5,7}} => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => {{1,2,4,6,7},{3,5}} => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => {{1,4,6,7},{2,3,5}} => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => {{1,4,6},{2,3,5,7}} => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => {{1,4,6,7},{2,3,5}} => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => {{1,3,4,6,7},{2,5}} => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => {{1,3,4,6},{2,5,7}} => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => {{1,3,4,6,7},{2,5}} => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => {{1,4,7},{2,3,5,6}} => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => {{1,2,3,5,7},{4,6}} => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => {{1,2,4,5,7},{3,6}} => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => {{1,5,7},{2,3,4,6}} => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => {{1,4,5,7},{2,3,6}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => {{1,3,4,5,7},{2,6}} => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => {{1,2,3,4,5,6,7}} => 7
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [4,1,2,8,3,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => {{1,2,3,5,7,8},{4,6}} => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [7,1,2,6,3,4,8,5] => {{1,2,3,5,7,8},{4,6}} => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,1,2,5,3,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [4,1,2,8,6,3,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => {{1,2,3,5,6,8},{4,7}} => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,8,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,8,2,6,7,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,1,4,2,3,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => {{1,2,4,6,7,8},{3,5}} => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,1,5,2,3,4,8,6] => {{1,2,4,6,7,8},{3,5}} => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => {{1,2,4,6,7,8},{3,5}} => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [8,1,5,2,3,7,4,6] => {{1,2,4,6,7,8},{3,5}} => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => {{1,2,4,6,7,8},{3,5}} => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [8,1,4,2,7,3,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,4,2,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,1,4,2,8,7,3,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,4,8,2,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,8,5,2,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => {{1,2,3,5,7,8},{4,6}} => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,7,6,2,4,8,5] => {{1,2,3,5,7,8},{4,6}} => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,6,5,2,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,5,2,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,1,4,5,2,3,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7] => {{1,2,4,5,7,8},{3,6}} => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => {{1,2,4,5,7,8},{3,6}} => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,1,4,5,2,8,3,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,8,6,2,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,1,4,7,6,2,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,8,5,6,2,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,1,8,7,6,2,4,5] => {{1,2,3,5,6,8},{4,7}} => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => {{1,2,4,5,6,8},{3,7}} => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,8,1,3,7,4,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,7,1,3,6,4,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,3,8,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,8,1,3,6,7,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,7,1,5,3,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7] => {{1,2,3,5,7,8},{4,6}} => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,7,1,6,3,4,8,5] => {{1,2,3,5,7,8},{4,6}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,6,1,5,3,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,8,1,5,3,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,6,1,5,3,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,5,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,4,1,7,6,3,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,8,1,5,6,3,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => {{1,2,3,5,6,8},{4,7}} => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,7,1,5,6,3,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,8,7,3,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1,8,6,7,3,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,8,1,5,6,7,3,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,3,1,2,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,3,1,2,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,3,1,2,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,3,1,2,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [8,3,1,2,7,4,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1,2,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,1,2,8,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [8,3,1,2,6,7,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,4,1,2,3,5,8,6] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,4,1,2,3,7,8,5] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,4,1,2,6,3,5,7] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => {{1,3,5,6,7,8},{2,4}} => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,3,1,7,2,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3,1,6,2,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7] => {{1,2,3,5,7,8},{4,6}} => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => {{1,2,3,5,7,8},{4,6}} => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,1,5,2,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [4,3,1,5,7,2,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,1,7,6,2,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => {{1,2,3,5,6,8},{4,7}} => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,3,8,1,4,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,3,8,1,6,4,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,3,5,1,8,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,3,8,1,6,7,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,8,4,1,3,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,4,1,3,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7] => {{1,2,4,6,7,8},{3,5}} => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6] => {{1,2,4,6,7,8},{3,5}} => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => {{1,2,4,6,7,8},{3,5}} => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => {{1,2,4,6,7,8},{3,5}} => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4] => {{1,2,4,6,7,8},{3,5}} => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,5,4,1,7,3,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,5,4,1,8,7,3,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,3,4,1,2,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3,4,1,2,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,5,4,1,2,3,6,7] => {{1,3,4,6,7,8},{2,5}} => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => {{1,3,4,6,7,8},{2,5}} => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7] => {{1,3,4,6,7,8},{2,5}} => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => {{1,3,4,6,7,8},{2,5}} => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => {{1,3,4,6,7,8},{2,5}} => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,3,4,1,7,2,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7,3,4,1,6,2,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [5,3,4,1,6,8,2,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,7,5,1,4,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7] => {{1,2,3,5,7,8},{4,6}} => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => {{1,2,3,5,7,8},{4,6}} => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,6,5,1,8,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => {{1,2,4,5,7,8},{3,6}} => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => {{1,2,4,5,7,8},{3,6}} => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,3,4,5,1,2,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,3,4,5,1,2,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => {{1,3,4,5,7,8},{2,6}} => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => {{1,3,4,5,7,8},{2,6}} => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => {{1,2,3,4,6,8},{5,7}} => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => {{1,2,3,5,6,8},{4,7}} => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => {{1,2,4,5,6,8},{3,7}} => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => {{1,3,4,5,6,8},{2,7}} => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => {{1,2,3,4,5,6,7,8}} => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => 8
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Description
The minimal size of a block of a set partition.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.