Identifier
Values
[1,0] => [1] => [1] => {{1}} => 0
[1,0,1,0] => [1,2] => [1,2] => {{1},{2}} => 2
[1,1,0,0] => [2,1] => [2,1] => {{1,2}} => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => {{1},{2},{3}} => 2
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => {{1},{2,3}} => 2
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => {{1,2},{3}} => 2
[1,1,0,1,0,0] => [2,3,1] => [3,1,2] => {{1,3},{2}} => 2
[1,1,1,0,0,0] => [3,1,2] => [2,3,1] => {{1,2,3}} => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => {{1},{2},{3},{4}} => 2
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => {{1},{2},{3,4}} => 2
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => {{1},{2,3},{4}} => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,2,3] => {{1},{2,4},{3}} => 2
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [1,3,4,2] => {{1},{2,3,4}} => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => {{1,2},{3},{4}} => 2
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => {{1,2},{3,4}} => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => {{1,3},{2},{4}} => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,1,2,3] => {{1,4},{2},{3}} => 3
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [3,1,4,2] => {{1,3,4},{2}} => 2
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [2,3,1,4] => {{1,2,3},{4}} => 2
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [2,4,1,3] => {{1,2,4},{3}} => 2
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [3,4,1,2] => {{1,3},{2,4}} => 2
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [2,3,4,1] => {{1,2,3,4}} => 1
[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}} => 2
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => 2
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => {{1},{2},{3,4},{5}} => 2
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,3,4] => {{1},{2},{3,5},{4}} => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [1,2,4,5,3] => {{1},{2},{3,4,5}} => 2
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => {{1},{2,3},{4},{5}} => 2
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => {{1},{2,3},{4,5}} => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,2,3,5] => {{1},{2,4},{3},{5}} => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,2,3,4] => {{1},{2,5},{3},{4}} => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,4,2,5,3] => {{1},{2,4,5},{3}} => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [1,3,4,2,5] => {{1},{2,3,4},{5}} => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [1,3,5,2,4] => {{1},{2,3,5},{4}} => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [1,4,5,2,3] => {{1},{2,4},{3,5}} => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [1,3,4,5,2] => {{1},{2,3,4,5}} => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => 2
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => {{1,2},{3},{4,5}} => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => {{1,2},{3,4},{5}} => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,3,4] => {{1,2},{3,5},{4}} => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [2,1,4,5,3] => {{1,2},{3,4,5}} => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,2,4,5] => {{1,3},{2},{4},{5}} => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,1,2,5,4] => {{1,3},{2},{4,5}} => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => {{1,4},{2},{3},{5}} => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => {{1,5},{2},{3},{4}} => 3
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [4,1,2,5,3] => {{1,4,5},{2},{3}} => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [3,1,4,2,5] => {{1,3,4},{2},{5}} => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [3,1,5,2,4] => {{1,3,5},{2},{4}} => 2
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [4,1,5,2,3] => {{1,4},{2},{3,5}} => 3
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [3,1,4,5,2] => {{1,3,4,5},{2}} => 2
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => 2
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [2,3,1,5,4] => {{1,2,3},{4,5}} => 2
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [2,4,1,3,5] => {{1,2,4},{3},{5}} => 2
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [2,5,1,3,4] => {{1,2,5},{3},{4}} => 3
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [2,4,1,5,3] => {{1,2,4,5},{3}} => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [3,4,1,2,5] => {{1,3},{2,4},{5}} => 2
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [3,5,1,2,4] => {{1,3},{2,5},{4}} => 3
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [4,5,1,2,3] => {{1,4},{2,5},{3}} => 3
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [3,4,1,5,2] => {{1,3},{2,4,5}} => 2
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [2,3,4,1,5] => {{1,2,3,4},{5}} => 2
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [2,3,5,1,4] => {{1,2,3,5},{4}} => 2
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [2,4,5,1,3] => {{1,2,4},{3,5}} => 2
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [3,4,5,1,2] => {{1,3,5},{2,4}} => 2
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [2,3,4,5,1] => {{1,2,3,4,5}} => 1
[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}} => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => {{1},{2},{3},{4,6},{5}} => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => {{1},{2},{3,5},{4},{6}} => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => {{1},{2},{3,6},{4},{5}} => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => {{1},{2},{3,5,6},{4}} => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [1,2,4,6,3,5] => {{1},{2},{3,4,6},{5}} => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}} => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => {{1},{2,3},{4,6},{5}} => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => {{1},{2,4},{3},{5},{6}} => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => {{1},{2,4},{3},{5,6}} => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => {{1},{2,5},{3},{4},{6}} => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => {{1},{2,6},{3},{4},{5}} => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [1,5,2,3,6,4] => {{1},{2,5,6},{3},{4}} => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => {{1},{2,4,5},{3},{6}} => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [1,4,2,6,3,5] => {{1},{2,4,6},{3},{5}} => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [1,5,2,6,3,4] => {{1},{2,5},{3},{4,6}} => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => {{1},{2,4,5,6},{3}} => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [1,3,5,2,4,6] => {{1},{2,3,5},{4},{6}} => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [1,3,6,2,4,5] => {{1},{2,3,6},{4},{5}} => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [1,3,5,2,6,4] => {{1},{2,3,5,6},{4}} => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}} => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [1,4,6,2,3,5] => {{1},{2,4},{3,6},{5}} => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [1,5,6,2,3,4] => {{1},{2,5},{3,6},{4}} => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => {{1},{2,4},{3,5,6}} => 2
>>> Load all 738 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [1,3,4,6,2,5] => {{1},{2,3,4,6},{5}} => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [1,3,5,6,2,4] => {{1},{2,3,5},{4,6}} => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => {{1},{2,4,6},{3,5}} => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => {{1,2},{3},{4,6},{5}} => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => {{1,2},{3,5},{4},{6}} => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => {{1,2},{3,6},{4},{5}} => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => {{1,2},{3,5,6},{4}} => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [2,1,4,6,3,5] => {{1,2},{3,4,6},{5}} => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,1,5,6,3,4] => {{1,2},{3,5},{4,6}} => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => {{1,3},{2},{4},{5},{6}} => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => {{1,3},{2},{4},{5,6}} => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => {{1,3},{2},{4,5},{6}} => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => {{1,3},{2},{4,6},{5}} => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [3,1,2,5,6,4] => {{1,3},{2},{4,5,6}} => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => {{1,4},{2},{3},{5},{6}} => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => {{1,4},{2},{3},{5,6}} => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => {{1,5},{2},{3},{4},{6}} => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => {{1,6},{2},{3},{4},{5}} => 3
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [5,1,2,3,6,4] => {{1,5,6},{2},{3},{4}} => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [4,1,2,5,3,6] => {{1,4,5},{2},{3},{6}} => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [4,1,2,6,3,5] => {{1,4,6},{2},{3},{5}} => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [5,1,2,6,3,4] => {{1,5},{2},{3},{4,6}} => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [4,1,2,5,6,3] => {{1,4,5,6},{2},{3}} => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [3,1,4,2,5,6] => {{1,3,4},{2},{5},{6}} => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => {{1,3,4},{2},{5,6}} => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [3,1,5,2,4,6] => {{1,3,5},{2},{4},{6}} => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [3,1,6,2,4,5] => {{1,3,6},{2},{4},{5}} => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => {{1,3,5,6},{2},{4}} => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [4,1,5,2,3,6] => {{1,4},{2},{3,5},{6}} => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [4,1,6,2,3,5] => {{1,4},{2},{3,6},{5}} => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [5,1,6,2,3,4] => {{1,5},{2},{3,6},{4}} => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [4,1,5,2,6,3] => {{1,4},{2},{3,5,6}} => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [3,1,4,5,2,6] => {{1,3,4,5},{2},{6}} => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [3,1,4,6,2,5] => {{1,3,4,6},{2},{5}} => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [3,1,5,6,2,4] => {{1,3,5},{2},{4,6}} => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [4,1,5,6,2,3] => {{1,4,6},{2},{3,5}} => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [3,1,4,5,6,2] => {{1,3,4,5,6},{2}} => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [2,3,1,6,4,5] => {{1,2,3},{4,6},{5}} => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [2,4,1,3,5,6] => {{1,2,4},{3},{5},{6}} => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [2,4,1,3,6,5] => {{1,2,4},{3},{5,6}} => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [2,5,1,3,4,6] => {{1,2,5},{3},{4},{6}} => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [2,6,1,3,4,5] => {{1,2,6},{3},{4},{5}} => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [2,5,1,3,6,4] => {{1,2,5,6},{3},{4}} => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [2,4,1,5,3,6] => {{1,2,4,5},{3},{6}} => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [2,4,1,6,3,5] => {{1,2,4,6},{3},{5}} => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [2,5,1,6,3,4] => {{1,2,5},{3},{4,6}} => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [2,4,1,5,6,3] => {{1,2,4,5,6},{3}} => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [3,4,1,2,6,5] => {{1,3},{2,4},{5,6}} => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [3,5,1,2,4,6] => {{1,3},{2,5},{4},{6}} => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [3,6,1,2,4,5] => {{1,3},{2,6},{4},{5}} => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [3,5,1,2,6,4] => {{1,3},{2,5,6},{4}} => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [4,5,1,2,3,6] => {{1,4},{2,5},{3},{6}} => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [4,6,1,2,3,5] => {{1,4},{2,6},{3},{5}} => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [5,6,1,2,3,4] => {{1,5},{2,6},{3},{4}} => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [4,5,1,2,6,3] => {{1,4},{2,5,6},{3}} => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [3,4,1,5,2,6] => {{1,3},{2,4,5},{6}} => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [3,4,1,6,2,5] => {{1,3},{2,4,6},{5}} => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [3,5,1,6,2,4] => {{1,3},{2,5},{4,6}} => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [4,5,1,6,2,3] => {{1,4,6},{2,5},{3}} => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [3,4,1,5,6,2] => {{1,3},{2,4,5,6}} => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [2,3,5,1,4,6] => {{1,2,3,5},{4},{6}} => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [2,3,6,1,4,5] => {{1,2,3,6},{4},{5}} => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [2,3,5,1,6,4] => {{1,2,3,5,6},{4}} => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [2,4,5,1,3,6] => {{1,2,4},{3,5},{6}} => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [2,4,6,1,3,5] => {{1,2,4},{3,6},{5}} => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [2,5,6,1,3,4] => {{1,2,5},{3,6},{4}} => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [2,4,5,1,6,3] => {{1,2,4},{3,5,6}} => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [3,4,5,1,2,6] => {{1,3,5},{2,4},{6}} => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [3,4,6,1,2,5] => {{1,3,6},{2,4},{5}} => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [3,5,6,1,2,4] => {{1,3,6},{2,5},{4}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [3,4,5,1,6,2] => {{1,3,5,6},{2,4}} => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [2,3,4,6,1,5] => {{1,2,3,4,6},{5}} => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [2,3,5,6,1,4] => {{1,2,3,5},{4,6}} => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [2,4,5,6,1,3] => {{1,2,4,6},{3,5}} => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => 1
[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}} => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}} => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,7},{6}} => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}} => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}} => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => {{1},{2},{3},{4,6},{5},{7}} => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => {{1},{2},{3},{4,7},{5},{6}} => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [1,2,3,6,4,7,5] => {{1},{2},{3},{4,6,7},{5}} => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [1,2,3,5,7,4,6] => {{1},{2},{3},{4,5,7},{6}} => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => {{1},{2},{3},{4,6},{5,7}} => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}} => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}} => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}} => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,7},{6}} => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => {{1},{2},{3,5},{4},{6},{7}} => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => {{1},{2},{3,5},{4},{6,7}} => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => {{1},{2},{3,6},{4},{5},{7}} => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => {{1},{2},{3,7},{4},{5},{6}} => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [1,2,6,3,4,7,5] => {{1},{2},{3,6,7},{4},{5}} => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [1,2,5,3,6,4,7] => {{1},{2},{3,5,6},{4},{7}} => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [1,2,5,3,7,4,6] => {{1},{2},{3,5,7},{4},{6}} => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [1,2,6,3,7,4,5] => {{1},{2},{3,6},{4},{5,7}} => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [1,2,5,3,6,7,4] => {{1},{2},{3,5,6,7},{4}} => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [1,2,4,6,3,5,7] => {{1},{2},{3,4,6},{5},{7}} => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [1,2,4,7,3,5,6] => {{1},{2},{3,4,7},{5},{6}} => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [1,2,4,6,3,7,5] => {{1},{2},{3,4,6,7},{5}} => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [1,2,5,6,3,4,7] => {{1},{2},{3,5},{4,6},{7}} => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [1,2,5,7,3,4,6] => {{1},{2},{3,5},{4,7},{6}} => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [1,2,6,7,3,4,5] => {{1},{2},{3,6},{4,7},{5}} => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [1,2,5,6,3,7,4] => {{1},{2},{3,5},{4,6,7}} => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [1,2,4,5,7,3,6] => {{1},{2},{3,4,5,7},{6}} => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [1,2,4,6,7,3,5] => {{1},{2},{3,4,6},{5,7}} => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [1,2,5,6,7,3,4] => {{1},{2},{3,5,7},{4,6}} => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}} => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}} => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => {{1},{2,3},{4},{5,6},{7}} => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => {{1},{2,3},{4},{5,7},{6}} => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}} => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}} => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => {{1},{2,3},{4,6},{5},{7}} => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => {{1},{2,3},{4,7},{5},{6}} => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [1,3,2,6,4,7,5] => {{1},{2,3},{4,6,7},{5}} => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [1,3,2,5,7,4,6] => {{1},{2,3},{4,5,7},{6}} => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [1,3,2,6,7,4,5] => {{1},{2,3},{4,6},{5,7}} => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => {{1},{2,4},{3},{5},{6},{7}} => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => {{1},{2,4},{3},{5},{6,7}} => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => {{1},{2,4},{3},{5,6},{7}} => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => {{1},{2,4},{3},{5,7},{6}} => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [1,4,2,3,6,7,5] => {{1},{2,4},{3},{5,6,7}} => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => {{1},{2,5},{3},{4},{6},{7}} => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => {{1},{2,5},{3},{4},{6,7}} => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => {{1},{2,6},{3},{4},{5},{7}} => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => {{1},{2,7},{3},{4},{5},{6}} => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [1,6,2,3,4,7,5] => {{1},{2,6,7},{3},{4},{5}} => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [1,5,2,3,6,4,7] => {{1},{2,5,6},{3},{4},{7}} => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [1,5,2,3,7,4,6] => {{1},{2,5,7},{3},{4},{6}} => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [1,6,2,3,7,4,5] => {{1},{2,6},{3},{4},{5,7}} => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [1,5,2,3,6,7,4] => {{1},{2,5,6,7},{3},{4}} => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [1,4,2,5,3,6,7] => {{1},{2,4,5},{3},{6},{7}} => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [1,4,2,5,3,7,6] => {{1},{2,4,5},{3},{6,7}} => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [1,4,2,6,3,5,7] => {{1},{2,4,6},{3},{5},{7}} => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [1,4,2,7,3,5,6] => {{1},{2,4,7},{3},{5},{6}} => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [1,4,2,6,3,7,5] => {{1},{2,4,6,7},{3},{5}} => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [1,5,2,6,3,4,7] => {{1},{2,5},{3},{4,6},{7}} => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [1,5,2,7,3,4,6] => {{1},{2,5},{3},{4,7},{6}} => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [1,6,2,7,3,4,5] => {{1},{2,6},{3},{4,7},{5}} => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [1,5,2,6,3,7,4] => {{1},{2,5},{3},{4,6,7}} => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [1,4,2,5,6,3,7] => {{1},{2,4,5,6},{3},{7}} => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [1,4,2,5,7,3,6] => {{1},{2,4,5,7},{3},{6}} => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [1,4,2,6,7,3,5] => {{1},{2,4,6},{3},{5,7}} => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [1,5,2,6,7,3,4] => {{1},{2,5,7},{3},{4,6}} => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [1,4,2,5,6,7,3] => {{1},{2,4,5,6,7},{3}} => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [1,3,4,2,7,5,6] => {{1},{2,3,4},{5,7},{6}} => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [1,3,5,2,4,6,7] => {{1},{2,3,5},{4},{6},{7}} => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [1,3,5,2,4,7,6] => {{1},{2,3,5},{4},{6,7}} => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [1,3,6,2,4,5,7] => {{1},{2,3,6},{4},{5},{7}} => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [1,3,7,2,4,5,6] => {{1},{2,3,7},{4},{5},{6}} => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [1,3,6,2,4,7,5] => {{1},{2,3,6,7},{4},{5}} => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [1,3,5,2,6,4,7] => {{1},{2,3,5,6},{4},{7}} => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [1,3,5,2,7,4,6] => {{1},{2,3,5,7},{4},{6}} => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [1,3,6,2,7,4,5] => {{1},{2,3,6},{4},{5,7}} => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [1,3,5,2,6,7,4] => {{1},{2,3,5,6,7},{4}} => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [1,4,5,2,3,6,7] => {{1},{2,4},{3,5},{6},{7}} => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [1,4,5,2,3,7,6] => {{1},{2,4},{3,5},{6,7}} => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [1,4,6,2,3,5,7] => {{1},{2,4},{3,6},{5},{7}} => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [1,4,7,2,3,5,6] => {{1},{2,4},{3,7},{5},{6}} => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [1,4,6,2,3,7,5] => {{1},{2,4},{3,6,7},{5}} => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [1,5,6,2,3,4,7] => {{1},{2,5},{3,6},{4},{7}} => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [1,5,7,2,3,4,6] => {{1},{2,5},{3,7},{4},{6}} => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [1,6,7,2,3,4,5] => {{1},{2,6},{3,7},{4},{5}} => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [1,5,6,2,3,7,4] => {{1},{2,5},{3,6,7},{4}} => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [1,4,5,2,6,3,7] => {{1},{2,4},{3,5,6},{7}} => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [1,4,5,2,7,3,6] => {{1},{2,4},{3,5,7},{6}} => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [1,4,6,2,7,3,5] => {{1},{2,4},{3,6},{5,7}} => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [1,5,6,2,7,3,4] => {{1},{2,5,7},{3,6},{4}} => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [1,4,5,2,6,7,3] => {{1},{2,4},{3,5,6,7}} => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [1,3,4,6,2,5,7] => {{1},{2,3,4,6},{5},{7}} => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [1,3,4,7,2,5,6] => {{1},{2,3,4,7},{5},{6}} => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [1,3,4,6,2,7,5] => {{1},{2,3,4,6,7},{5}} => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [1,3,5,6,2,4,7] => {{1},{2,3,5},{4,6},{7}} => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [1,3,5,7,2,4,6] => {{1},{2,3,5},{4,7},{6}} => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [1,3,6,7,2,4,5] => {{1},{2,3,6},{4,7},{5}} => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [1,3,5,6,2,7,4] => {{1},{2,3,5},{4,6,7}} => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [1,4,5,6,2,3,7] => {{1},{2,4,6},{3,5},{7}} => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [1,4,5,7,2,3,6] => {{1},{2,4,7},{3,5},{6}} => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [1,4,6,7,2,3,5] => {{1},{2,4,7},{3,6},{5}} => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [1,5,6,7,2,3,4] => {{1},{2,5},{3,6},{4,7}} => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [1,4,5,6,2,7,3] => {{1},{2,4,6,7},{3,5}} => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [1,3,4,5,7,2,6] => {{1},{2,3,4,5,7},{6}} => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [1,3,4,6,7,2,5] => {{1},{2,3,4,6},{5,7}} => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [1,3,5,6,7,2,4] => {{1},{2,3,5,7},{4,6}} => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [1,4,5,6,7,2,3] => {{1},{2,4,6},{3,5,7}} => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}} => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => {{1,2},{3},{4},{5},{6,7}} => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}} => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => {{1,2},{3},{4},{5,7},{6}} => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [2,1,3,4,6,7,5] => {{1,2},{3},{4},{5,6,7}} => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => {{1,2},{3},{4,5},{6},{7}} => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}} => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => {{1,2},{3},{4,6},{5},{7}} => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => {{1,2},{3},{4,7},{5},{6}} => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [2,1,3,6,4,7,5] => {{1,2},{3},{4,6,7},{5}} => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [2,1,3,5,6,4,7] => {{1,2},{3},{4,5,6},{7}} => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [2,1,3,5,7,4,6] => {{1,2},{3},{4,5,7},{6}} => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [2,1,3,6,7,4,5] => {{1,2},{3},{4,6},{5,7}} => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [2,1,3,5,6,7,4] => {{1,2},{3},{4,5,6,7}} => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}} => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}} => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => {{1,2},{3,4},{5,7},{6}} => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [2,1,4,3,6,7,5] => {{1,2},{3,4},{5,6,7}} => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => {{1,2},{3,5},{4},{6},{7}} => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => {{1,2},{3,5},{4},{6,7}} => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => {{1,2},{3,6},{4},{5},{7}} => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => {{1,2},{3,7},{4},{5},{6}} => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [2,1,6,3,4,7,5] => {{1,2},{3,6,7},{4},{5}} => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [2,1,5,3,6,4,7] => {{1,2},{3,5,6},{4},{7}} => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [2,1,5,3,7,4,6] => {{1,2},{3,5,7},{4},{6}} => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [2,1,6,3,7,4,5] => {{1,2},{3,6},{4},{5,7}} => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [2,1,5,3,6,7,4] => {{1,2},{3,5,6,7},{4}} => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [2,1,4,5,3,6,7] => {{1,2},{3,4,5},{6},{7}} => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [2,1,4,5,3,7,6] => {{1,2},{3,4,5},{6,7}} => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [2,1,4,6,3,5,7] => {{1,2},{3,4,6},{5},{7}} => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [2,1,4,7,3,5,6] => {{1,2},{3,4,7},{5},{6}} => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [2,1,4,6,3,7,5] => {{1,2},{3,4,6,7},{5}} => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [2,1,5,6,3,4,7] => {{1,2},{3,5},{4,6},{7}} => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [2,1,5,7,3,4,6] => {{1,2},{3,5},{4,7},{6}} => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [2,1,6,7,3,4,5] => {{1,2},{3,6},{4,7},{5}} => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [2,1,5,6,3,7,4] => {{1,2},{3,5},{4,6,7}} => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [2,1,4,5,6,3,7] => {{1,2},{3,4,5,6},{7}} => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [2,1,4,5,7,3,6] => {{1,2},{3,4,5,7},{6}} => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [2,1,4,6,7,3,5] => {{1,2},{3,4,6},{5,7}} => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [2,1,5,6,7,3,4] => {{1,2},{3,5,7},{4,6}} => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [2,1,4,5,6,7,3] => {{1,2},{3,4,5,6,7}} => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => {{1,3},{2},{4},{5},{6,7}} => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => {{1,3},{2},{4},{5,6},{7}} => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => {{1,3},{2},{4},{5,7},{6}} => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [3,1,2,4,6,7,5] => {{1,3},{2},{4},{5,6,7}} => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => {{1,3},{2},{4,5},{6},{7}} => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => {{1,3},{2},{4,5},{6,7}} => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => {{1,3},{2},{4,6},{5},{7}} => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => {{1,3},{2},{4,7},{5},{6}} => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [3,1,2,6,4,7,5] => {{1,3},{2},{4,6,7},{5}} => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [3,1,2,5,6,4,7] => {{1,3},{2},{4,5,6},{7}} => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [3,1,2,5,7,4,6] => {{1,3},{2},{4,5,7},{6}} => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [3,1,2,6,7,4,5] => {{1,3},{2},{4,6},{5,7}} => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [3,1,2,5,6,7,4] => {{1,3},{2},{4,5,6,7}} => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => {{1,4},{2},{3},{5},{6,7}} => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => {{1,4},{2},{3},{5,6},{7}} => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => {{1,4},{2},{3},{5,7},{6}} => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [4,1,2,3,6,7,5] => {{1,4},{2},{3},{5,6,7}} => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => {{1,5},{2},{3},{4},{6,7}} => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [6,1,2,3,4,7,5] => {{1,6,7},{2},{3},{4},{5}} => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [5,1,2,3,6,4,7] => {{1,5,6},{2},{3},{4},{7}} => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [5,1,2,3,7,4,6] => {{1,5,7},{2},{3},{4},{6}} => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [6,1,2,3,7,4,5] => {{1,6},{2},{3},{4},{5,7}} => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [5,1,2,3,6,7,4] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [4,1,2,5,3,6,7] => {{1,4,5},{2},{3},{6},{7}} => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [4,1,2,5,3,7,6] => {{1,4,5},{2},{3},{6,7}} => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [4,1,2,6,3,5,7] => {{1,4,6},{2},{3},{5},{7}} => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [4,1,2,7,3,5,6] => {{1,4,7},{2},{3},{5},{6}} => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [4,1,2,6,3,7,5] => {{1,4,6,7},{2},{3},{5}} => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [5,1,2,6,3,4,7] => {{1,5},{2},{3},{4,6},{7}} => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [5,1,2,7,3,4,6] => {{1,5},{2},{3},{4,7},{6}} => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [6,1,2,7,3,4,5] => {{1,6},{2},{3},{4,7},{5}} => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [5,1,2,6,3,7,4] => {{1,5},{2},{3},{4,6,7}} => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [4,1,2,5,6,3,7] => {{1,4,5,6},{2},{3},{7}} => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [4,1,2,5,7,3,6] => {{1,4,5,7},{2},{3},{6}} => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [4,1,2,6,7,3,5] => {{1,4,6},{2},{3},{5,7}} => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [5,1,2,6,7,3,4] => {{1,5,7},{2},{3},{4,6}} => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [4,1,2,5,6,7,3] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [3,1,4,2,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [3,1,4,2,5,7,6] => {{1,3,4},{2},{5},{6,7}} => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [3,1,4,2,6,5,7] => {{1,3,4},{2},{5,6},{7}} => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [3,1,4,2,7,5,6] => {{1,3,4},{2},{5,7},{6}} => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [3,1,4,2,6,7,5] => {{1,3,4},{2},{5,6,7}} => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [3,1,5,2,4,6,7] => {{1,3,5},{2},{4},{6},{7}} => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [3,1,5,2,4,7,6] => {{1,3,5},{2},{4},{6,7}} => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [3,1,6,2,4,5,7] => {{1,3,6},{2},{4},{5},{7}} => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [3,1,7,2,4,5,6] => {{1,3,7},{2},{4},{5},{6}} => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [3,1,6,2,4,7,5] => {{1,3,6,7},{2},{4},{5}} => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [3,1,5,2,6,4,7] => {{1,3,5,6},{2},{4},{7}} => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [3,1,5,2,7,4,6] => {{1,3,5,7},{2},{4},{6}} => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [3,1,6,2,7,4,5] => {{1,3,6},{2},{4},{5,7}} => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => [3,1,5,2,6,7,4] => {{1,3,5,6,7},{2},{4}} => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [4,1,5,2,3,6,7] => {{1,4},{2},{3,5},{6},{7}} => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [4,1,5,2,3,7,6] => {{1,4},{2},{3,5},{6,7}} => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [4,1,6,2,3,5,7] => {{1,4},{2},{3,6},{5},{7}} => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [4,1,7,2,3,5,6] => {{1,4},{2},{3,7},{5},{6}} => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [4,1,6,2,3,7,5] => {{1,4},{2},{3,6,7},{5}} => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [5,1,6,2,3,4,7] => {{1,5},{2},{3,6},{4},{7}} => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [5,1,7,2,3,4,6] => {{1,5},{2},{3,7},{4},{6}} => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [6,1,7,2,3,4,5] => {{1,6},{2},{3,7},{4},{5}} => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [5,1,6,2,3,7,4] => {{1,5},{2},{3,6,7},{4}} => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [4,1,5,2,6,3,7] => {{1,4},{2},{3,5,6},{7}} => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [4,1,5,2,7,3,6] => {{1,4},{2},{3,5,7},{6}} => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [4,1,6,2,7,3,5] => {{1,4},{2},{3,6},{5,7}} => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [5,1,6,2,7,3,4] => {{1,5,7},{2},{3,6},{4}} => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [4,1,5,2,6,7,3] => {{1,4},{2},{3,5,6,7}} => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [3,1,4,5,2,6,7] => {{1,3,4,5},{2},{6},{7}} => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [3,1,4,5,2,7,6] => {{1,3,4,5},{2},{6,7}} => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [3,1,4,6,2,5,7] => {{1,3,4,6},{2},{5},{7}} => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [3,1,4,7,2,5,6] => {{1,3,4,7},{2},{5},{6}} => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => [3,1,4,6,2,7,5] => {{1,3,4,6,7},{2},{5}} => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [3,1,5,6,2,4,7] => {{1,3,5},{2},{4,6},{7}} => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [3,1,5,7,2,4,6] => {{1,3,5},{2},{4,7},{6}} => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [3,1,6,7,2,4,5] => {{1,3,6},{2},{4,7},{5}} => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [3,1,5,6,2,7,4] => {{1,3,5},{2},{4,6,7}} => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [4,1,5,6,2,3,7] => {{1,4,6},{2},{3,5},{7}} => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [4,1,5,7,2,3,6] => {{1,4,7},{2},{3,5},{6}} => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [4,1,6,7,2,3,5] => {{1,4,7},{2},{3,6},{5}} => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [5,1,6,7,2,3,4] => {{1,5},{2},{3,6},{4,7}} => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => [4,1,5,6,2,7,3] => {{1,4,6,7},{2},{3,5}} => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [3,1,4,5,6,2,7] => {{1,3,4,5,6},{2},{7}} => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => [3,1,4,5,7,2,6] => {{1,3,4,5,7},{2},{6}} => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [3,1,4,6,7,2,5] => {{1,3,4,6},{2},{5,7}} => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [3,1,5,6,7,2,4] => {{1,3,5,7},{2},{4,6}} => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [4,1,5,6,7,2,3] => {{1,4,6},{2},{3,5,7}} => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [3,1,4,5,6,7,2] => {{1,3,4,5,6,7},{2}} => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [2,3,1,4,5,7,6] => {{1,2,3},{4},{5},{6,7}} => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [2,3,1,4,6,5,7] => {{1,2,3},{4},{5,6},{7}} => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [2,3,1,4,7,5,6] => {{1,2,3},{4},{5,7},{6}} => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [2,3,1,4,6,7,5] => {{1,2,3},{4},{5,6,7}} => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [2,3,1,5,4,6,7] => {{1,2,3},{4,5},{6},{7}} => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [2,3,1,5,4,7,6] => {{1,2,3},{4,5},{6,7}} => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [2,3,1,6,4,5,7] => {{1,2,3},{4,6},{5},{7}} => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [2,3,1,7,4,5,6] => {{1,2,3},{4,7},{5},{6}} => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [2,3,1,6,4,7,5] => {{1,2,3},{4,6,7},{5}} => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [2,3,1,5,6,4,7] => {{1,2,3},{4,5,6},{7}} => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [2,3,1,5,7,4,6] => {{1,2,3},{4,5,7},{6}} => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [2,3,1,6,7,4,5] => {{1,2,3},{4,6},{5,7}} => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [2,3,1,5,6,7,4] => {{1,2,3},{4,5,6,7}} => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [2,4,1,3,5,6,7] => {{1,2,4},{3},{5},{6},{7}} => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [2,4,1,3,5,7,6] => {{1,2,4},{3},{5},{6,7}} => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [2,4,1,3,6,5,7] => {{1,2,4},{3},{5,6},{7}} => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [2,4,1,3,7,5,6] => {{1,2,4},{3},{5,7},{6}} => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [2,4,1,3,6,7,5] => {{1,2,4},{3},{5,6,7}} => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [2,5,1,3,4,6,7] => {{1,2,5},{3},{4},{6},{7}} => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [2,5,1,3,4,7,6] => {{1,2,5},{3},{4},{6,7}} => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [2,6,1,3,4,5,7] => {{1,2,6},{3},{4},{5},{7}} => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [2,7,1,3,4,5,6] => {{1,2,7},{3},{4},{5},{6}} => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [2,6,1,3,4,7,5] => {{1,2,6,7},{3},{4},{5}} => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [2,5,1,3,6,4,7] => {{1,2,5,6},{3},{4},{7}} => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [2,5,1,3,7,4,6] => {{1,2,5,7},{3},{4},{6}} => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [2,6,1,3,7,4,5] => {{1,2,6},{3},{4},{5,7}} => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => [2,5,1,3,6,7,4] => {{1,2,5,6,7},{3},{4}} => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [2,4,1,5,3,6,7] => {{1,2,4,5},{3},{6},{7}} => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [2,4,1,5,3,7,6] => {{1,2,4,5},{3},{6,7}} => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [2,4,1,6,3,5,7] => {{1,2,4,6},{3},{5},{7}} => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [2,4,1,7,3,5,6] => {{1,2,4,7},{3},{5},{6}} => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => [2,4,1,6,3,7,5] => {{1,2,4,6,7},{3},{5}} => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [2,5,1,6,3,4,7] => {{1,2,5},{3},{4,6},{7}} => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [2,5,1,7,3,4,6] => {{1,2,5},{3},{4,7},{6}} => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [2,6,1,7,3,4,5] => {{1,2,6},{3},{4,7},{5}} => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [2,5,1,6,3,7,4] => {{1,2,5},{3},{4,6,7}} => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [2,4,1,5,6,3,7] => {{1,2,4,5,6},{3},{7}} => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => [2,4,1,5,7,3,6] => {{1,2,4,5,7},{3},{6}} => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [2,4,1,6,7,3,5] => {{1,2,4,6},{3},{5,7}} => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => [2,5,1,6,7,3,4] => {{1,2,5,7},{3},{4,6}} => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => [2,4,1,5,6,7,3] => {{1,2,4,5,6,7},{3}} => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [3,4,1,2,5,6,7] => {{1,3},{2,4},{5},{6},{7}} => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [3,4,1,2,5,7,6] => {{1,3},{2,4},{5},{6,7}} => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [3,4,1,2,6,5,7] => {{1,3},{2,4},{5,6},{7}} => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [3,4,1,2,7,5,6] => {{1,3},{2,4},{5,7},{6}} => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [3,4,1,2,6,7,5] => {{1,3},{2,4},{5,6,7}} => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [3,5,1,2,4,6,7] => {{1,3},{2,5},{4},{6},{7}} => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [3,5,1,2,4,7,6] => {{1,3},{2,5},{4},{6,7}} => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [3,6,1,2,4,5,7] => {{1,3},{2,6},{4},{5},{7}} => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [3,7,1,2,4,5,6] => {{1,3},{2,7},{4},{5},{6}} => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [3,6,1,2,4,7,5] => {{1,3},{2,6,7},{4},{5}} => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [3,5,1,2,6,4,7] => {{1,3},{2,5,6},{4},{7}} => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [3,5,1,2,7,4,6] => {{1,3},{2,5,7},{4},{6}} => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [3,6,1,2,7,4,5] => {{1,3},{2,6},{4},{5,7}} => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [3,5,1,2,6,7,4] => {{1,3},{2,5,6,7},{4}} => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [4,5,1,2,3,6,7] => {{1,4},{2,5},{3},{6},{7}} => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [4,5,1,2,3,7,6] => {{1,4},{2,5},{3},{6,7}} => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [4,6,1,2,3,5,7] => {{1,4},{2,6},{3},{5},{7}} => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [4,7,1,2,3,5,6] => {{1,4},{2,7},{3},{5},{6}} => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [4,6,1,2,3,7,5] => {{1,4},{2,6,7},{3},{5}} => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [5,6,1,2,3,4,7] => {{1,5},{2,6},{3},{4},{7}} => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [5,7,1,2,3,4,6] => {{1,5},{2,7},{3},{4},{6}} => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [6,7,1,2,3,4,5] => {{1,6},{2,7},{3},{4},{5}} => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [5,6,1,2,3,7,4] => {{1,5},{2,6,7},{3},{4}} => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [4,5,1,2,6,3,7] => {{1,4},{2,5,6},{3},{7}} => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [4,5,1,2,7,3,6] => {{1,4},{2,5,7},{3},{6}} => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [4,6,1,2,7,3,5] => {{1,4},{2,6},{3},{5,7}} => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [5,6,1,2,7,3,4] => {{1,5,7},{2,6},{3},{4}} => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [4,5,1,2,6,7,3] => {{1,4},{2,5,6,7},{3}} => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [3,4,1,5,2,6,7] => {{1,3},{2,4,5},{6},{7}} => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [3,4,1,5,2,7,6] => {{1,3},{2,4,5},{6,7}} => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [3,4,1,6,2,5,7] => {{1,3},{2,4,6},{5},{7}} => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [3,4,1,7,2,5,6] => {{1,3},{2,4,7},{5},{6}} => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [3,4,1,6,2,7,5] => {{1,3},{2,4,6,7},{5}} => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [3,5,1,6,2,4,7] => {{1,3},{2,5},{4,6},{7}} => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [3,5,1,7,2,4,6] => {{1,3},{2,5},{4,7},{6}} => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [3,6,1,7,2,4,5] => {{1,3},{2,6},{4,7},{5}} => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [3,5,1,6,2,7,4] => {{1,3},{2,5},{4,6,7}} => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [4,5,1,6,2,3,7] => {{1,4,6},{2,5},{3},{7}} => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [4,5,1,7,2,3,6] => {{1,4,7},{2,5},{3},{6}} => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [4,6,1,7,2,3,5] => {{1,4,7},{2,6},{3},{5}} => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [5,6,1,7,2,3,4] => {{1,5},{2,6},{3},{4,7}} => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [4,5,1,6,2,7,3] => {{1,4,6,7},{2,5},{3}} => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [3,4,1,5,6,2,7] => {{1,3},{2,4,5,6},{7}} => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [3,4,1,5,7,2,6] => {{1,3},{2,4,5,7},{6}} => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [3,4,1,6,7,2,5] => {{1,3},{2,4,6},{5,7}} => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [3,5,1,6,7,2,4] => {{1,3},{2,5,7},{4,6}} => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => [4,5,1,6,7,2,3] => {{1,4,6},{2,5,7},{3}} => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [3,4,1,5,6,7,2] => {{1,3},{2,4,5,6,7}} => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [2,3,4,1,5,7,6] => {{1,2,3,4},{5},{6,7}} => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [2,3,4,1,6,5,7] => {{1,2,3,4},{5,6},{7}} => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [2,3,4,1,7,5,6] => {{1,2,3,4},{5,7},{6}} => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [2,3,4,1,6,7,5] => {{1,2,3,4},{5,6,7}} => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [2,3,5,1,4,6,7] => {{1,2,3,5},{4},{6},{7}} => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [2,3,5,1,4,7,6] => {{1,2,3,5},{4},{6,7}} => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [2,3,6,1,4,5,7] => {{1,2,3,6},{4},{5},{7}} => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [2,3,7,1,4,5,6] => {{1,2,3,7},{4},{5},{6}} => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => [2,3,6,1,4,7,5] => {{1,2,3,6,7},{4},{5}} => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [2,3,5,1,6,4,7] => {{1,2,3,5,6},{4},{7}} => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => [2,3,5,1,7,4,6] => {{1,2,3,5,7},{4},{6}} => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [2,3,6,1,7,4,5] => {{1,2,3,6},{4},{5,7}} => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => [2,3,5,1,6,7,4] => {{1,2,3,5,6,7},{4}} => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [2,4,5,1,3,6,7] => {{1,2,4},{3,5},{6},{7}} => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [2,4,5,1,3,7,6] => {{1,2,4},{3,5},{6,7}} => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [2,4,6,1,3,5,7] => {{1,2,4},{3,6},{5},{7}} => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [2,4,7,1,3,5,6] => {{1,2,4},{3,7},{5},{6}} => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [2,4,6,1,3,7,5] => {{1,2,4},{3,6,7},{5}} => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [2,5,6,1,3,4,7] => {{1,2,5},{3,6},{4},{7}} => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [2,5,7,1,3,4,6] => {{1,2,5},{3,7},{4},{6}} => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [2,6,7,1,3,4,5] => {{1,2,6},{3,7},{4},{5}} => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => [2,5,6,1,3,7,4] => {{1,2,5},{3,6,7},{4}} => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [2,4,5,1,6,3,7] => {{1,2,4},{3,5,6},{7}} => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [2,4,5,1,7,3,6] => {{1,2,4},{3,5,7},{6}} => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [2,4,6,1,7,3,5] => {{1,2,4},{3,6},{5,7}} => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [2,5,6,1,7,3,4] => {{1,2,5,7},{3,6},{4}} => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [2,4,5,1,6,7,3] => {{1,2,4},{3,5,6,7}} => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [3,4,5,1,2,6,7] => {{1,3,5},{2,4},{6},{7}} => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [3,4,5,1,2,7,6] => {{1,3,5},{2,4},{6,7}} => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [3,4,6,1,2,5,7] => {{1,3,6},{2,4},{5},{7}} => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [3,4,7,1,2,5,6] => {{1,3,7},{2,4},{5},{6}} => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => [3,4,6,1,2,7,5] => {{1,3,6,7},{2,4},{5}} => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [3,5,6,1,2,4,7] => {{1,3,6},{2,5},{4},{7}} => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [3,5,7,1,2,4,6] => {{1,3,7},{2,5},{4},{6}} => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [3,6,7,1,2,4,5] => {{1,3,7},{2,6},{4},{5}} => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [3,5,6,1,2,7,4] => {{1,3,6,7},{2,5},{4}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [4,5,6,1,2,3,7] => {{1,4},{2,5},{3,6},{7}} => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [4,5,7,1,2,3,6] => {{1,4},{2,5},{3,7},{6}} => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [4,6,7,1,2,3,5] => {{1,4},{2,6},{3,7},{5}} => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [5,6,7,1,2,3,4] => {{1,5},{2,6},{3,7},{4}} => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [4,5,6,1,2,7,3] => {{1,4},{2,5},{3,6,7}} => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [3,4,5,1,6,2,7] => {{1,3,5,6},{2,4},{7}} => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => [3,4,5,1,7,2,6] => {{1,3,5,7},{2,4},{6}} => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [3,4,6,1,7,2,5] => {{1,3,6},{2,4},{5,7}} => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => [3,5,6,1,7,2,4] => {{1,3,6},{2,5,7},{4}} => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [4,5,6,1,7,2,3] => {{1,4},{2,5,7},{3,6}} => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => [3,4,5,1,6,7,2] => {{1,3,5,6,7},{2,4}} => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [2,3,4,5,1,7,6] => {{1,2,3,4,5},{6,7}} => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [2,3,4,6,1,5,7] => {{1,2,3,4,6},{5},{7}} => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [2,3,4,7,1,5,6] => {{1,2,3,4,7},{5},{6}} => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => [2,3,4,6,1,7,5] => {{1,2,3,4,6,7},{5}} => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [2,3,5,6,1,4,7] => {{1,2,3,5},{4,6},{7}} => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [2,3,5,7,1,4,6] => {{1,2,3,5},{4,7},{6}} => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [2,3,6,7,1,4,5] => {{1,2,3,6},{4,7},{5}} => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [2,3,5,6,1,7,4] => {{1,2,3,5},{4,6,7}} => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [2,4,5,6,1,3,7] => {{1,2,4,6},{3,5},{7}} => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => [2,4,5,7,1,3,6] => {{1,2,4,7},{3,5},{6}} => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [2,4,6,7,1,3,5] => {{1,2,4,7},{3,6},{5}} => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [2,5,6,7,1,3,4] => {{1,2,5},{3,6},{4,7}} => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => [2,4,5,6,1,7,3] => {{1,2,4,6,7},{3,5}} => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [3,4,5,6,1,2,7] => {{1,3,5},{2,4,6},{7}} => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [3,4,5,7,1,2,6] => {{1,3,5},{2,4,7},{6}} => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => [3,4,6,7,1,2,5] => {{1,3,6},{2,4,7},{5}} => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [3,5,6,7,1,2,4] => {{1,3,6},{2,5},{4,7}} => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => [4,5,6,7,1,2,3] => {{1,4,7},{2,5},{3,6}} => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [3,4,5,6,1,7,2] => {{1,3,5},{2,4,6,7}} => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [2,3,4,5,7,1,6] => {{1,2,3,4,5,7},{6}} => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [2,3,4,6,7,1,5] => {{1,2,3,4,6},{5,7}} => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [2,3,5,6,7,1,4] => {{1,2,3,5,7},{4,6}} => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [2,4,5,6,7,1,3] => {{1,2,4,6},{3,5,7}} => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => [3,4,5,6,7,1,2] => {{1,3,5,7},{2,4,6}} => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}} => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}} => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => {{1},{2},{3},{4},{5},{6,8},{7}} => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,7,8,6] => {{1},{2},{3},{4},{5},{6,7,8}} => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7] => {{1},{2},{3},{4},{5,8},{6},{7}} => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,6,7,8,5] => {{1},{2},{3},{4},{5,6,7,8}} => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => {{1},{2},{3},{4,8},{5},{6},{7}} => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,2,3,5,6,7,8,4] => {{1},{2},{3},{4,5,6,7,8}} => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,2,5,6,3,7,8,4] => {{1},{2},{3,5},{4,6,7,8}} => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,3,8,4,5,6] => [1,2,4,6,7,8,3,5] => {{1},{2},{3,4,6,8},{5,7}} => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,5,6,7,8,3,4] => {{1},{2},{3,5,7},{4,6,8}} => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,4,5,6,7,8,3] => {{1},{2},{3,4,5,6,7,8}} => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => {{1},{2,8},{3},{4},{5},{6},{7}} => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,8,6] => [1,4,2,6,3,8,5,7] => {{1},{2,4,6,8},{3},{5},{7}} => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,2,8,4,5,6] => [1,4,2,6,7,8,3,5] => {{1},{2,4,6,8},{3},{5,7}} => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [1,4,2,5,6,7,8,3] => {{1},{2,4,5,6,7,8},{3}} => 2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,2,8,3,5,7] => [1,4,6,2,7,3,8,5] => {{1},{2,4},{3,6},{5,7,8}} => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,2,8,3,5,6] => [1,4,6,2,7,8,3,5] => {{1},{2,4},{3,6,8},{5,7}} => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,5,6,7,8,2,3,4] => {{1},{2,5,8},{3,6},{4,7}} => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [1,3,4,5,6,7,8,2] => {{1},{2,3,4,5,6,7,8}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}} => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,5,7] => [2,1,4,3,7,5,8,6] => {{1,2},{3,4},{5,7,8},{6}} => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,6,8,5,7] => {{1,2},{3,4},{5,6,8},{7}} => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,7,8,5,6] => {{1,2},{3,4},{5,7},{6,8}} => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,3,6,7] => [2,1,6,3,4,7,8,5] => {{1,2},{3,6,7,8},{4},{5}} => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,3,5,8,7] => [2,1,5,3,6,4,8,7] => {{1,2},{3,5,6},{4},{7,8}} => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7] => [2,1,4,6,3,5,8,7] => {{1,2},{3,4,6},{5},{7,8}} => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6] => [2,1,4,6,3,8,5,7] => {{1,2},{3,4,6,8},{5},{7}} => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => [2,1,5,6,3,4,8,7] => {{1,2},{3,5},{4,6},{7,8}} => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => [2,1,5,7,3,8,4,6] => {{1,2},{3,5},{4,7},{6,8}} => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,8,5] => [2,1,4,6,8,3,5,7] => {{1,2},{3,4,6},{5,8},{7}} => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,3,8,4,5] => [2,1,5,7,8,3,4,6] => {{1,2},{3,5,8},{4,7},{6}} => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,3,4,5] => [2,1,6,7,8,3,4,5] => {{1,2},{3,6},{4,7},{5,8}} => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [2,1,4,5,6,7,8,3] => {{1,2},{3,4,5,6,7,8}} => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => 3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,1,5,6,7] => [5,1,2,3,6,7,8,4] => {{1,5,6,7,8},{2},{3},{4}} => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,1,4,5,8,7] => [4,1,2,5,6,3,8,7] => {{1,4,5,6},{2},{3},{7,8}} => 3
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,1,8,4,5,7] => [4,1,2,6,7,3,8,5] => {{1,4,6},{2},{3},{5,7,8}} => 3
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [4,1,2,5,6,7,8,3] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [3,1,4,2,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}} => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,1,3,6,8,5,7] => [3,1,4,2,7,5,8,6] => {{1,3,4},{2},{5,7,8},{6}} => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5,8] => [3,1,5,2,7,4,6,8] => {{1,3,5,7},{2},{4},{6},{8}} => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,1,8,3,5,7] => [4,1,6,2,7,3,8,5] => {{1,4},{2},{3,6},{5,7,8}} => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7] => [5,1,6,2,7,3,8,4] => {{1,5,7,8},{2},{3,6},{4}} => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => [3,1,5,6,2,8,4,7] => {{1,3,5},{2},{4,6,8},{7}} => 2
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,8,4,6] => [3,1,5,7,2,8,4,6] => {{1,3,5},{2},{4,7},{6,8}} => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,1,3,8,4,6] => [4,1,5,7,2,8,3,6] => {{1,4,7},{2},{3,5},{6,8}} => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [3,1,4,5,6,7,8,2] => {{1,3,4,5,6,7,8},{2}} => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7] => [2,4,1,3,6,5,8,7] => {{1,2,4},{3},{5,6},{7,8}} => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => [2,4,1,3,6,8,5,7] => {{1,2,4},{3},{5,6,8},{7}} => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7] => [2,4,1,6,3,5,8,7] => {{1,2,4,6},{3},{5},{7,8}} => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6] => [2,4,1,6,3,8,5,7] => {{1,2,4,6,8},{3},{5},{7}} => 2
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => [2,5,1,7,3,4,8,6] => {{1,2,5},{3},{4,7,8},{6}} => 3
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,1,5,7,8,2,4,6] => [2,6,1,7,3,8,4,5] => {{1,2,6,8},{3},{4,7},{5}} => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,8,5] => [2,4,1,6,8,3,5,7] => {{1,2,4,6},{3},{5,8},{7}} => 3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [2,4,1,5,6,7,8,3] => {{1,2,4,5,6,7,8},{3}} => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [3,4,1,2,6,5,8,7] => {{1,3},{2,4},{5,6},{7,8}} => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => [3,4,1,2,7,8,5,6] => {{1,3},{2,4},{5,7},{6,8}} => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,1,6,2,4,8,7] => [3,5,1,6,2,4,8,7] => {{1,3},{2,5},{4,6},{7,8}} => 3
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,1,6,8,2,4,7] => [3,6,1,7,2,4,8,5] => {{1,3},{2,6},{4,7,8},{5}} => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => [3,5,1,7,2,8,4,6] => {{1,3},{2,5},{4,7},{6,8}} => 3
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,1,2,8,4,6] => [4,5,1,7,2,8,3,6] => {{1,4,7},{2,5},{3},{6,8}} => 3
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,1,7,8,2,4,5] => [3,6,1,7,8,2,4,5] => {{1,3},{2,6},{4,7},{5,8}} => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [3,4,1,5,6,7,8,2] => {{1,3},{2,4,5,6,7,8}} => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,2,8,3,5,6,7] => [2,3,5,1,6,7,8,4] => {{1,2,3,5,6,7,8},{4}} => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7] => [2,4,6,1,3,5,8,7] => {{1,2,4},{3,6},{5},{7,8}} => 3
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,2,6,8,3,7] => [2,4,7,1,3,5,8,6] => {{1,2,4},{3,7,8},{5},{6}} => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,8,6] => [2,4,6,1,3,8,5,7] => {{1,2,4},{3,6,8},{5},{7}} => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => [2,4,6,1,8,3,5,7] => {{1,2,4},{3,6},{5,8},{7}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,1,2,3,8,7] => [4,5,6,1,2,3,8,7] => {{1,4},{2,5},{3,6},{7,8}} => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,5,7,1,2,3,8,6] => [4,5,6,1,2,8,3,7] => {{1,4},{2,5},{3,6,8},{7}} => 3
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,1,2,8,3,6] => [4,5,7,1,2,8,3,6] => {{1,4},{2,5},{3,7},{6,8}} => 3
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,1,8,2,3,5] => [4,6,7,1,8,2,3,5] => {{1,4},{2,6},{3,7},{5,8}} => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,1,2,3,7,4,6,8] => [2,3,4,6,1,7,5,8] => {{1,2,3,4,6,7},{5},{8}} => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4] => [2,4,6,8,1,3,5,7] => {{1,2,4,8},{3,6},{5},{7}} => 3
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,6,2,7,8,3,4] => [2,4,7,8,1,3,5,6] => {{1,2,4,8},{3,7},{5},{6}} => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,6,7,2,3,8,4] => [2,5,6,8,1,3,4,7] => {{1,2,5},{3,6},{4,8},{7}} => 3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,6,7,2,8,3,4] => [2,5,7,8,1,3,4,6] => {{1,2,5},{3,7},{4,8},{6}} => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,6,7,8,2,3,4] => [2,6,7,8,1,3,4,5] => {{1,2,6},{3,7},{4,8},{5}} => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [2,4,5,6,1,7,8,3] => {{1,2,4,6,7,8},{3,5}} => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,1,2,7,3,8,4] => [3,4,6,8,1,2,5,7] => {{1,3,6},{2,4,8},{5},{7}} => 3
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,1,2,7,8,3,4] => [3,4,7,8,1,2,5,6] => {{1,3,7},{2,4,8},{5},{6}} => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,1,7,2,3,8,4] => [3,5,6,8,1,2,4,7] => {{1,3,6},{2,5},{4,8},{7}} => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,6,1,7,2,8,3,4] => [3,5,7,8,1,2,4,6] => {{1,3,7},{2,5},{4,8},{6}} => 4
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,1,7,8,2,3,4] => [3,6,7,8,1,2,4,5] => {{1,3,7},{2,6},{4,8},{5}} => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,1,2,3,4,8] => [4,5,6,7,1,2,3,8] => {{1,4,7},{2,5},{3,6},{8}} => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,1,2,3,8,4] => [4,5,6,8,1,2,3,7] => {{1,4,8},{2,5},{3,6},{7}} => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,1,2,8,3,4] => [4,5,7,8,1,2,3,6] => {{1,4,8},{2,5},{3,7},{6}} => 4
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,1,8,2,3,4] => [4,6,7,8,1,2,3,5] => {{1,4,8},{2,6},{3,7},{5}} => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => [5,6,7,8,1,2,3,4] => {{1,5},{2,6},{3,7},{4,8}} => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2,3,4,8,5,7] => [2,3,4,5,7,1,8,6] => {{1,2,3,4,5,7,8},{6}} => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => [2,3,4,5,6,8,1,7] => {{1,2,3,4,5,6,8},{7}} => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,8,5,6] => [2,3,4,5,7,8,1,6] => {{1,2,3,4,5,7},{6,8}} => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1,2,3,8,4,5,6] => [2,3,4,6,7,8,1,5] => {{1,2,3,4,6,8},{5,7}} => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}} => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [1,3,4,5,6,7,8,9,2] => {{1},{2,3,4,5,6,7,8,9}} => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,10,2] => {{1},{2,3,4,5,6,7,8,9,10}} => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,7,8] => {{1},{2},{3},{4},{5},{6},{7,9},{8}} => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => {{1},{2,9},{3},{4},{5},{6},{7},{8}} => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,8,9,7] => {{1},{2},{3},{4},{5},{6},{7,8,9}} => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => 2
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The length of the longest partition in the vacillating tableau corresponding to a set partition.
To a set partition $\pi$ of $\{1,\dots,r\}$ with at most $n$ blocks we associate a vacillating tableau, following [1], as follows: create a triangular growth diagram by labelling the columns of a triangular grid with row lengths $r-1, \dots, 0$ from left to right $1$ to $r$, and the rows from the shortest to the longest $1$ to $r$. For each arc $(i,j)$ in the standard representation of $\pi$, place a cross into the cell in column $i$ and row $j$.
Next we label the corners of the first column beginning with the corners of the shortest row. The first corner is labelled with the partition $(n)$. If there is a cross in the row separating this corner from the next, label the next corner with the same partition, otherwise with the partition smaller by one. Do the same with the corners of the first row.
Finally, apply Fomin's local rules, to obtain the partitions along the diagonal. These will alternate in size between $n$ and $n-1$.
This statistic is the length of the longest partition on the diagonal of the diagram.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
inverse
Description
Sends a permutation to its inverse.