Identifier
Values
[1,0] => [1] => {{1}} => [1] => 0
[1,0,1,0] => [2,1] => {{1,2}} => [2,1] => 1
[1,1,0,0] => [1,2] => {{1},{2}} => [1,2] => 0
[1,0,1,0,1,0] => [2,3,1] => {{1,2,3}} => [2,3,1] => 0
[1,0,1,1,0,0] => [2,1,3] => {{1,2},{3}} => [2,1,3] => 1
[1,1,0,0,1,0] => [1,3,2] => {{1},{2,3}} => [1,3,2] => 1
[1,1,0,1,0,0] => [3,1,2] => {{1,2,3}} => [2,3,1] => 0
[1,1,1,0,0,0] => [1,2,3] => {{1},{2},{3}} => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [2,3,4,1] => {{1,2,3,4}} => [2,3,4,1] => 0
[1,0,1,0,1,1,0,0] => [2,3,1,4] => {{1,2,3},{4}} => [2,3,1,4] => 0
[1,0,1,1,0,0,1,0] => [2,1,4,3] => {{1,2},{3,4}} => [2,1,4,3] => 2
[1,0,1,1,0,1,0,0] => [2,4,1,3] => {{1,2,3,4}} => [2,3,4,1] => 0
[1,0,1,1,1,0,0,0] => [2,1,3,4] => {{1,2},{3},{4}} => [2,1,3,4] => 1
[1,1,0,0,1,0,1,0] => [1,3,4,2] => {{1},{2,3,4}} => [1,3,4,2] => 0
[1,1,0,0,1,1,0,0] => [1,3,2,4] => {{1},{2,3},{4}} => [1,3,2,4] => 1
[1,1,0,1,0,0,1,0] => [3,1,4,2] => {{1,2,3,4}} => [2,3,4,1] => 0
[1,1,0,1,0,1,0,0] => [3,4,1,2] => {{1,3},{2,4}} => [3,4,1,2] => 0
[1,1,0,1,1,0,0,0] => [3,1,2,4] => {{1,2,3},{4}} => [2,3,1,4] => 0
[1,1,1,0,0,0,1,0] => [1,2,4,3] => {{1},{2},{3,4}} => [1,2,4,3] => 1
[1,1,1,0,0,1,0,0] => [1,4,2,3] => {{1},{2,3,4}} => [1,3,4,2] => 0
[1,1,1,0,1,0,0,0] => [4,1,2,3] => {{1,2,3,4}} => [2,3,4,1] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => {{1},{2},{3},{4}} => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 0
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => {{1,2,3},{4,5}} => [2,3,1,5,4] => 1
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => [2,3,1,4,5] => 0
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => {{1,2},{3,4,5}} => [2,1,4,5,3] => 1
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}} => [2,1,4,3,5] => 2
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => {{1,2,4},{3,5}} => [2,4,5,1,3] => 0
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 0
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => {{1,2},{3},{4,5}} => [2,1,3,5,4] => 2
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => {{1,2},{3,4,5}} => [2,1,4,5,3] => 1
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => [2,1,3,4,5] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 0
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => {{1},{2,3,4},{5}} => [1,3,4,2,5] => 0
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}} => [1,3,2,5,4] => 2
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 0
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => {{1},{2,3},{4},{5}} => [1,3,2,4,5] => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 0
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => {{1,3},{2,4,5}} => [3,4,1,5,2] => 0
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => {{1,3},{2,4},{5}} => [3,4,1,2,5] => 0
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => {{1,2,3},{4,5}} => [2,3,1,5,4] => 1
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => {{1,3},{2,4,5}} => [3,4,1,5,2] => 0
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => {{1,2,3},{4},{5}} => [2,3,1,4,5] => 0
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => {{1},{2},{3,4,5}} => [1,2,4,5,3] => 0
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => {{1},{2},{3,4},{5}} => [1,2,4,3,5] => 1
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 0
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => {{1},{2,4},{3,5}} => [1,4,5,2,3] => 0
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => {{1},{2,3,4},{5}} => [1,3,4,2,5] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => {{1,2,4},{3,5}} => [2,4,5,1,3] => 0
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 0
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => [1,2,3,5,4] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => {{1},{2},{3,4,5}} => [1,2,4,5,3] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 0
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => {{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => {{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => {{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
>>> Load all 325 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => {{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => {{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => {{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => {{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => {{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => {{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => {{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => {{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => {{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => {{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => {{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => {{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => {{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => {{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => {{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => {{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => {{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => {{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => {{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => {{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => {{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => {{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => {{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => {{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => {{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => {{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => {{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => {{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => {{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => {{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => {{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => {{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => {{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => {{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => {{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => {{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => {{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
[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},{7}} => [1,2,3,4,5,6,7] => 0
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Description
The number of transpositions swapping cyclically adjacent numbers in a permutation.
Put differently, this is the number of adjacent two-cycles in the chord diagram of a permutation.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
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].