Identifier
Values
[1,0] => {{1}} => {{1}} => [1] => 0
[1,0,1,0] => {{1},{2}} => {{1},{2}} => [1,2] => 0
[1,1,0,0] => {{1,2}} => {{1,2}} => [2,1] => 0
[1,0,1,0,1,0] => {{1},{2},{3}} => {{1},{2},{3}} => [1,2,3] => 0
[1,0,1,1,0,0] => {{1},{2,3}} => {{1},{2,3}} => [1,3,2] => 0
[1,1,0,0,1,0] => {{1,2},{3}} => {{1,2},{3}} => [2,1,3] => 0
[1,1,0,1,0,0] => {{1,3},{2}} => {{1,3},{2}} => [3,2,1] => 1
[1,1,1,0,0,0] => {{1,2,3}} => {{1,2,3}} => [2,3,1] => 0
[1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}} => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => {{1},{2},{3,4}} => [1,2,4,3] => 0
[1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => {{1},{2,3},{4}} => [1,3,2,4] => 0
[1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => {{1},{2,4},{3}} => [1,4,3,2] => 1
[1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => {{1},{2,3,4}} => [1,3,4,2] => 0
[1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => {{1,2},{3},{4}} => [2,1,3,4] => 0
[1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => {{1,2},{3,4}} => [2,1,4,3] => 0
[1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => {{1,3},{2},{4}} => [3,2,1,4] => 1
[1,1,0,1,0,1,0,0] => {{1,4},{2},{3}} => {{1,4},{2},{3}} => [4,2,3,1] => 2
[1,1,0,1,1,0,0,0] => {{1,3,4},{2}} => {{1,3,4},{2}} => [3,2,4,1] => 1
[1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => {{1,2,3},{4}} => [2,3,1,4] => 0
[1,1,1,0,0,1,0,0] => {{1,4},{2,3}} => {{1,3},{2,4}} => [3,4,1,2] => 1
[1,1,1,0,1,0,0,0] => {{1,2,4},{3}} => {{1,2,4},{3}} => [2,4,3,1] => 1
[1,1,1,1,0,0,0,0] => {{1,2,3,4}} => {{1,2,3,4}} => [2,3,4,1] => 0
[1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => {{1},{2},{3},{4,5}} => [1,2,3,5,4] => 0
[1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => {{1},{2},{3,4},{5}} => [1,2,4,3,5] => 0
[1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => {{1},{2},{3,5},{4}} => [1,2,5,4,3] => 1
[1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => {{1},{2},{3,4,5}} => [1,2,4,5,3] => 0
[1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => {{1},{2,3},{4},{5}} => [1,3,2,4,5] => 0
[1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1},{2,3},{4,5}} => [1,3,2,5,4] => 0
[1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}} => [1,4,3,2,5] => 1
[1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => {{1},{2,5},{3},{4}} => [1,5,3,4,2] => 2
[1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => {{1},{2,4,5},{3}} => [1,4,3,5,2] => 1
[1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => {{1},{2,3,4},{5}} => [1,3,4,2,5] => 0
[1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => {{1},{2,4},{3,5}} => [1,4,5,2,3] => 1
[1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => {{1},{2,3,5},{4}} => [1,3,5,4,2] => 1
[1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => {{1},{2,3,4,5}} => [1,3,4,5,2] => 0
[1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => {{1,2},{3},{4},{5}} => [2,1,3,4,5] => 0
[1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => {{1,2},{3},{4,5}} => [2,1,3,5,4] => 0
[1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => {{1,2},{3,4},{5}} => [2,1,4,3,5] => 0
[1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => {{1,2},{3,5},{4}} => [2,1,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2},{3,4,5}} => [2,1,4,5,3] => 0
[1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => {{1,3},{2},{4},{5}} => [3,2,1,4,5] => 1
[1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => {{1,3},{2},{4,5}} => [3,2,1,5,4] => 1
[1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => {{1,4},{2},{3},{5}} => [4,2,3,1,5] => 2
[1,1,0,1,0,1,0,1,0,0] => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 3
[1,1,0,1,0,1,1,0,0,0] => {{1,4,5},{2},{3}} => {{1,4,5},{2},{3}} => [4,2,3,5,1] => 2
[1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => {{1,3,4},{2},{5}} => [3,2,4,1,5] => 1
[1,1,0,1,1,0,0,1,0,0] => {{1,5},{2},{3,4}} => {{1,4},{2},{3,5}} => [4,2,5,1,3] => 2
[1,1,0,1,1,0,1,0,0,0] => {{1,3,5},{2},{4}} => {{1,3,5},{2},{4}} => [3,2,5,4,1] => 2
[1,1,0,1,1,1,0,0,0,0] => {{1,3,4,5},{2}} => {{1,3,4,5},{2}} => [3,2,4,5,1] => 1
[1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => {{1,2,3},{4},{5}} => [2,3,1,4,5] => 0
[1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => {{1,2,3},{4,5}} => [2,3,1,5,4] => 0
[1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => {{1,3},{2,4},{5}} => [3,4,1,2,5] => 1
[1,1,1,0,0,1,0,1,0,0] => {{1,5},{2,3},{4}} => {{1,3},{2,5},{4}} => [3,5,1,4,2] => 2
[1,1,1,0,0,1,1,0,0,0] => {{1,4,5},{2,3}} => {{1,3},{2,4,5}} => [3,4,1,5,2] => 1
[1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => {{1,2,4},{3},{5}} => [2,4,3,1,5] => 1
[1,1,1,0,1,0,0,1,0,0] => {{1,5},{2,4},{3}} => {{1,4},{2,5},{3}} => [4,5,3,1,2] => 3
[1,1,1,0,1,0,1,0,0,0] => {{1,2,5},{3},{4}} => {{1,2,5},{3},{4}} => [2,5,3,4,1] => 2
[1,1,1,0,1,1,0,0,0,0] => {{1,2,4,5},{3}} => {{1,2,4,5},{3}} => [2,4,3,5,1] => 1
[1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => {{1,2,3,4},{5}} => [2,3,4,1,5] => 0
[1,1,1,1,0,0,0,1,0,0] => {{1,5},{2,3,4}} => {{1,3,5},{2,4}} => [3,4,5,2,1] => 1
[1,1,1,1,0,0,1,0,0,0] => {{1,2,5},{3,4}} => {{1,2,4},{3,5}} => [2,4,5,1,3] => 1
[1,1,1,1,0,1,0,0,0,0] => {{1,2,3,5},{4}} => {{1,2,3,5},{4}} => [2,3,5,4,1] => 1
[1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => {{1,2,3,4,5}} => [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => {{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => {{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => {{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => {{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => {{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => {{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => {{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => {{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => {{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => {{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => {{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => {{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => {{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => {{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => {{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => {{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => {{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => {{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => {{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => {{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => {{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => {{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => {{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => {{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => {{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => {{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => {{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => {{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => {{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => {{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => {{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => 1
>>> Load all 306 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => {{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => {{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => {{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => {{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => {{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => {{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => {{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => {{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => {{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => {{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => {{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => {{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => {{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => {{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => {{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => {{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => {{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => {{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => {{1,5,6},{2},{3},{4}} => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => {{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => {{1,6},{2},{3},{4,5}} => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => {{1,4,6},{2},{3},{5}} => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2},{3}} => {{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => {{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => {{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => {{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => {{1,6},{2},{3,4},{5}} => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => {{1,5,6},{2},{3,4}} => {{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => {{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => {{1,6},{2},{3,5},{4}} => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => {{1,3,6},{2},{4},{5}} => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => {{1,3,5,6},{2},{4}} => {{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => {{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => {{1,6},{2},{3,4,5}} => {{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => {{1,3,6},{2},{4,5}} => {{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => {{1,3,4,6},{2},{5}} => {{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => {{1,3,4,5,6},{2}} => {{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => {{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => {{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => {{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => {{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => {{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => {{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => {{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => {{1,6},{2,3},{4},{5}} => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => {{1,5,6},{2,3},{4}} => {{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => {{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => {{1,6},{2,3},{4,5}} => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => {{1,4,6},{2,3},{5}} => {{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => {{1,4,5,6},{2,3}} => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => {{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => {{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => {{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => {{1,6},{2,4},{3},{5}} => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => {{1,5,6},{2,4},{3}} => {{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => {{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => {{1,6},{2,5},{3},{4}} => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 5
[1,1,1,0,1,0,1,0,1,0,0,0] => {{1,2,6},{3},{4},{5}} => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => {{1,2,5,6},{3},{4}} => {{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => {{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => {{1,6},{2,4,5},{3}} => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => {{1,2,6},{3},{4,5}} => {{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => {{1,2,4,6},{3},{5}} => {{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => {{1,2,4,5,6},{3}} => {{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => {{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => {{1,6},{2,3,4},{5}} => {{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => {{1,5,6},{2,3,4}} => {{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => {{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => {{1,6},{2,5},{3,4}} => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => {{1,2,6},{3,4},{5}} => {{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => {{1,2,5,6},{3,4}} => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => {{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => {{1,6},{2,3,5},{4}} => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => {{1,2,6},{3,5},{4}} => {{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => {{1,2,3,6},{4},{5}} => {{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => {{1,2,3,5,6},{4}} => {{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => {{1,6},{2,3,4,5}} => {{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => {{1,2,6},{3,4,5}} => {{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => {{1,2,3,6},{4,5}} => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => {{1,2,3,4,6},{5}} => {{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => {{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => {{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => {{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => {{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => {{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}} => {{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => {{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}} => {{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => {{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}} => {{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => {{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => {{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => {{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}} => {{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => {{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}} => {{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => {{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => {{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}} => {{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}} => {{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}} => {{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}} => {{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}} => {{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => {{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}} => {{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}} => {{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}} => {{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => {{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}} => {{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => {{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}} => {{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}} => {{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}} => {{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}} => {{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => {{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}} => {{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => {{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => {{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => {{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}} => {{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}} => {{1},{2,3},{4,7},{5},{6}} => [1,3,2,7,5,6,4] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => {{1},{2,3},{4,6,7},{5}} => [1,3,2,6,5,7,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => {{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}} => {{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}} => {{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}} => {{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}} => {{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}} => {{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}} => {{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}} => {{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}} => {{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}} => {{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}} => {{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}} => {{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}} => {{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}} => {{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}} => {{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}} => {{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => {{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => {{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => {{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => {{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => {{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}} => {{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}} => {{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}} => {{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}} => {{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}} => {{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}} => {{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}} => {{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}} => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => {{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}} => {{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => {{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => {{1},{2,3,7},{4},{5},{6}} => [1,3,7,4,5,6,2] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => {{1},{2,3,6,7},{4},{5}} => [1,3,6,4,5,7,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}} => {{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}} => {{1},{2,3,6},{4},{5,7}} => [1,3,6,4,7,2,5] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}} => {{1},{2,3,5,7},{4},{6}} => [1,3,5,4,7,6,2] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => {{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}} => {{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => {{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => {{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}} => {{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => {{1},{2,3,5},{4,7},{6}} => [1,3,5,7,2,6,4] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}} => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => {{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}} => {{1},{2,3,6},{4,7},{5}} => [1,3,6,7,5,2,4] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => {{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => {{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => {{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => {{1},{2,3,5,7},{4,6}} => [1,3,5,6,7,4,2] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => {{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => 0
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Description
The number of invisible inversions of a permutation.
A visible inversion of a permutation $\pi$ is a pair $i < j$ such that $\pi(j) \leq \min(i, \pi(i))$. Thus, an invisible inversion satisfies $\pi(i) > \pi(j) > i$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution.
This is defined in [1] and yields the set partition with the number of nestings and crossings exchanged.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.