Identifier
Values
[1,0] => [1] => [1] => {{1}} => 0
[1,0,1,0] => [1,2] => [1,2] => {{1},{2}} => 0
[1,1,0,0] => [2,1] => [2,1] => {{1,2}} => 0
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => {{1},{2},{3}} => 0
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => {{1},{2,3}} => 0
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => {{1,2},{3}} => 0
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => {{1,3},{2}} => 0
[1,1,1,0,0,0] => [3,2,1] => [2,3,1] => {{1,2,3}} => 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] => [1,2,4,3] => [1,2,4,3] => {{1},{2},{3,4}} => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => {{1},{2,3},{4}} => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => {{1},{2,4},{3}} => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,3,4,2] => {{1},{2,3,4}} => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => {{1,2},{3},{4}} => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => {{1,2},{3,4}} => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,1,4] => {{1,3},{2},{4}} => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,2,3,1] => {{1,4},{2},{3}} => 0
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,2,4,1] => {{1,3,4},{2}} => 0
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,3,1,4] => {{1,2,3},{4}} => 0
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [4,3,2,1] => {{1,4},{2,3}} => 0
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [3,4,2,1] => {{1,3},{2,4}} => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [2,3,4,1] => {{1,2,3,4}} => 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] => [1,2,3,5,4] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => 0
[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}} => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => {{1},{2},{3,5},{4}} => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,4,5,3] => {{1},{2},{3,4,5}} => 0
[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}} => 0
[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}} => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,3,2,5] => {{1},{2,4},{3},{5}} => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => {{1},{2,5},{3},{4}} => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,4,3,5,2] => {{1},{2,4,5},{3}} => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,3,4,2,5] => {{1},{2,3,4},{5}} => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,4,3,2] => {{1},{2,5},{3,4}} => 0
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [1,4,5,3,2] => {{1},{2,4},{3,5}} => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,3,4,5,2] => {{1},{2,3,4,5}} => 0
[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}} => 0
[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}} => 0
[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}} => 0
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => {{1,2},{3,5},{4}} => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,4,5,3] => {{1,2},{3,4,5}} => 0
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => {{1,3},{2},{4},{5}} => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => {{1,3},{2},{4,5}} => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,2,3,1,5] => {{1,4},{2},{3},{5}} => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => {{1,5},{2},{3},{4}} => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,2,3,5,1] => {{1,4,5},{2},{3}} => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,2,4,1,5] => {{1,3,4},{2},{5}} => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,2,4,3,1] => {{1,5},{2},{3,4}} => 0
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [4,2,5,3,1] => {{1,4},{2},{3,5}} => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [3,2,4,5,1] => {{1,3,4,5},{2}} => 0
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,3,1,5,4] => {{1,2,3},{4,5}} => 0
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,3,2,1,5] => {{1,4},{2,3},{5}} => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,3,2,4,1] => {{1,5},{2,3},{4}} => 0
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [4,3,2,5,1] => {{1,4,5},{2,3}} => 0
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [3,4,2,1,5] => {{1,3},{2,4},{5}} => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [5,4,2,3,1] => {{1,5},{2,4},{3}} => 0
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [4,5,2,3,1] => {{1,4},{2,5},{3}} => 1
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [3,4,5,1,2] => {{1,3,5},{2,4}} => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [2,3,4,1,5] => {{1,2,3,4},{5}} => 0
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [5,3,4,2,1] => {{1,5},{2,3,4}} => 0
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [4,3,5,2,1] => {{1,4},{2,3,5}} => 1
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [2,4,5,3,1] => {{1,2,4},{3,5}} => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [2,3,4,5,1] => {{1,2,3,4,5}} => 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] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => 0
[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}} => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}} => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => 0
[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}} => 0
[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}} => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}} => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => {{1},{2},{3,6},{4},{5}} => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,5,4,6,3] => {{1},{2},{3,5,6},{4}} => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}} => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,2,5,6,4,3] => {{1},{2},{3,5},{4,6}} => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => 0
[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}} => 0
[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}} => 0
[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}} => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}} => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}} => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}} => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => {{1},{2,5},{3},{4},{6}} => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => {{1},{2,6},{3},{4},{5}} => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,5,3,4,6,2] => {{1},{2,5,6},{3},{4}} => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => {{1},{2,4,5},{3},{6}} => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => {{1},{2,6},{3},{4,5}} => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [1,5,3,6,4,2] => {{1},{2,5},{3},{4,6}} => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,4,3,5,6,2] => {{1},{2,4,5,6},{3}} => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}} => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => {{1},{2,6},{3,4},{5}} => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,5,4,3,6,2] => {{1},{2,5,6},{3,4}} => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [1,4,5,3,2,6] => {{1},{2,4},{3,5},{6}} => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,6,5,3,4,2] => {{1},{2,6},{3,5},{4}} => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [1,5,6,3,4,2] => {{1},{2,5},{3,6},{4}} => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [1,4,5,6,2,3] => {{1},{2,4,6},{3,5}} => 2
>>> Load all 668 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,4,5,3,2] => {{1},{2,6},{3,4,5}} => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [1,5,4,6,3,2] => {{1},{2,5},{3,4,6}} => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [1,3,5,6,4,2] => {{1},{2,3,5},{4,6}} => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => 0
[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}} => 0
[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}} => 0
[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}} => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}} => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => 0
[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}} => 0
[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}} => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}} => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => {{1,2},{3,6},{4},{5}} => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,5,4,6,3] => {{1,2},{3,5,6},{4}} => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => {{1,2},{3,6},{4,5}} => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [2,1,5,6,4,3] => {{1,2},{3,5},{4,6}} => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}} => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}} => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}} => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => {{1,3},{2},{4,5,6}} => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => {{1,4},{2},{3},{5},{6}} => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => {{1,4},{2},{3},{5,6}} => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => {{1,5},{2},{3},{4},{6}} => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => {{1,6},{2},{3},{4},{5}} => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,2,3,4,6,1] => {{1,5,6},{2},{3},{4}} => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,2,3,5,1,6] => {{1,4,5},{2},{3},{6}} => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => {{1,6},{2},{3},{4,5}} => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [5,2,3,6,4,1] => {{1,5},{2},{3},{4,6}} => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [4,2,3,5,6,1] => {{1,4,5,6},{2},{3}} => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}} => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,4,1,6,5] => {{1,3,4},{2},{5,6}} => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => {{1,5},{2},{3,4},{6}} => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => {{1,6},{2},{3,4},{5}} => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [5,2,4,3,6,1] => {{1,5,6},{2},{3,4}} => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [4,2,5,3,1,6] => {{1,4},{2},{3,5},{6}} => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [6,2,5,3,4,1] => {{1,6},{2},{3,5},{4}} => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [5,2,6,3,4,1] => {{1,5},{2},{3,6},{4}} => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [4,2,5,6,1,3] => {{1,4,6},{2},{3,5}} => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,2,4,5,1,6] => {{1,3,4,5},{2},{6}} => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,2,4,5,3,1] => {{1,6},{2},{3,4,5}} => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [5,2,4,6,3,1] => {{1,5},{2},{3,4,6}} => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [3,2,5,6,4,1] => {{1,3,5},{2},{4,6}} => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [3,2,4,5,6,1] => {{1,3,4,5,6},{2}} => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => {{1,2,3},{4,6},{5}} => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => {{1,4},{2,3},{5,6}} => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => {{1,5},{2,3},{4},{6}} => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => {{1,6},{2,3},{4},{5}} => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [5,3,2,4,6,1] => {{1,5,6},{2,3},{4}} => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [4,3,2,5,1,6] => {{1,4,5},{2,3},{6}} => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => {{1,6},{2,3},{4,5}} => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [5,3,2,6,4,1] => {{1,5},{2,3},{4,6}} => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [4,3,2,5,6,1] => {{1,4,5,6},{2,3}} => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [3,4,2,1,5,6] => {{1,3},{2,4},{5},{6}} => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [3,4,2,1,6,5] => {{1,3},{2,4},{5,6}} => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [5,4,2,3,1,6] => {{1,5},{2,4},{3},{6}} => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [6,4,2,3,5,1] => {{1,6},{2,4},{3},{5}} => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [5,4,2,3,6,1] => {{1,5,6},{2,4},{3}} => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [4,5,2,3,1,6] => {{1,4},{2,5},{3},{6}} => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [6,5,2,3,4,1] => {{1,6},{2,5},{3},{4}} => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [5,6,2,3,4,1] => {{1,5},{2,6},{3},{4}} => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [4,5,1,6,3,2] => {{1,4,6},{2,5},{3}} => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [3,4,5,1,2,6] => {{1,3,5},{2,4},{6}} => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [6,5,4,2,3,1] => {{1,6},{2,5},{3,4}} => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [5,6,4,2,3,1] => {{1,5},{2,6},{3,4}} => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [3,5,6,1,4,2] => {{1,3,6},{2,5},{4}} => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [3,4,5,6,2,1] => {{1,3,5},{2,4,6}} => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,3,4,2,1,6] => {{1,5},{2,3,4},{6}} => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,3,4,2,5,1] => {{1,6},{2,3,4},{5}} => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [5,3,4,2,6,1] => {{1,5,6},{2,3,4}} => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [4,3,5,2,1,6] => {{1,4},{2,3,5},{6}} => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [6,3,5,2,4,1] => {{1,6},{2,3,5},{4}} => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [5,3,6,2,4,1] => {{1,5},{2,3,6},{4}} => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [4,3,5,6,1,2] => {{1,4,6},{2,3,5}} => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [2,4,5,3,1,6] => {{1,2,4},{3,5},{6}} => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [6,4,5,3,2,1] => {{1,6},{2,4},{3,5}} => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [5,4,6,3,2,1] => {{1,5},{2,4},{3,6}} => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [2,5,6,3,4,1] => {{1,2,5},{3,6},{4}} => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [2,4,5,6,1,3] => {{1,2,4,6},{3,5}} => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [6,3,4,5,2,1] => {{1,6},{2,3,4,5}} => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [5,3,4,6,2,1] => {{1,5},{2,3,4,6}} => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [2,5,4,6,3,1] => {{1,2,5},{3,4,6}} => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [2,4,5,3,6,1] => {{1,2,4},{3,5,6}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => 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] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}} => 0
[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}} => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => {{1},{2},{3},{4},{5,7},{6}} => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}} => 0
[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}} => 0
[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}} => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}} => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => {{1},{2},{3},{4,7},{5},{6}} => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,6,5,7,4] => {{1},{2},{3},{4,6,7},{5}} => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}} => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => {{1},{2},{3},{4,7},{5,6}} => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [1,2,3,6,7,5,4] => {{1},{2},{3},{4,6},{5,7}} => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}} => 0
[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}} => 0
[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}} => 0
[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}} => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => {{1},{2},{3,4},{5,7},{6}} => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}} => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}} => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => {{1},{2},{3,5},{4},{6,7}} => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => {{1},{2},{3,6},{4},{5},{7}} => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => {{1},{2},{3,7},{4},{5},{6}} => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,6,4,5,7,3] => {{1},{2},{3,6,7},{4},{5}} => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,5,4,6,3,7] => {{1},{2},{3,5,6},{4},{7}} => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => {{1},{2},{3,7},{4},{5,6}} => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [1,2,6,4,7,5,3] => {{1},{2},{3,6},{4},{5,7}} => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,5,4,6,7,3] => {{1},{2},{3,5,6,7},{4}} => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}} => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}} => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => {{1},{2},{3,6},{4,5},{7}} => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => {{1},{2},{3,7},{4,5},{6}} => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,6,5,4,7,3] => {{1},{2},{3,6,7},{4,5}} => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [1,2,5,6,4,3,7] => {{1},{2},{3,5},{4,6},{7}} => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [1,2,7,6,4,5,3] => {{1},{2},{3,7},{4,6},{5}} => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [1,2,6,7,4,5,3] => {{1},{2},{3,6},{4,7},{5}} => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [1,2,5,6,7,3,4] => {{1},{2},{3,5,7},{4,6}} => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}} => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,7,5,6,4,3] => {{1},{2},{3,7},{4,5,6}} => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [1,2,6,5,7,4,3] => {{1},{2},{3,6},{4,5,7}} => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [1,2,4,6,7,5,3] => {{1},{2},{3,4,6},{5,7}} => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}} => 0
[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}} => 0
[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}} => 0
[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}} => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => {{1},{2,3},{4},{5,7},{6}} => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}} => 0
[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}} => 0
[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}} => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => {{1},{2,3},{4,6},{5},{7}} => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => {{1},{2,3},{4,7},{5},{6}} => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,6,5,7,4] => {{1},{2,3},{4,6,7},{5}} => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}} => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => {{1},{2,3},{4,7},{5,6}} => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [1,3,2,6,7,5,4] => {{1},{2,3},{4,6},{5,7}} => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}} => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => {{1},{2,4},{3},{5},{6},{7}} => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => {{1},{2,4},{3},{5},{6,7}} => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => {{1},{2,4},{3},{5,6},{7}} => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => {{1},{2,4},{3},{5,7},{6}} => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,4,3,2,6,7,5] => {{1},{2,4},{3},{5,6,7}} => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => {{1},{2,5},{3},{4},{6},{7}} => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => {{1},{2,5},{3},{4},{6,7}} => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => {{1},{2,6},{3},{4},{5},{7}} => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => {{1},{2,7},{3},{4},{5},{6}} => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,6,3,4,5,7,2] => {{1},{2,6,7},{3},{4},{5}} => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,5,3,4,6,2,7] => {{1},{2,5,6},{3},{4},{7}} => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2] => {{1},{2,7},{3},{4},{5,6}} => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [1,6,3,4,7,5,2] => {{1},{2,6},{3},{4},{5,7}} => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,5,3,4,6,7,2] => {{1},{2,5,6,7},{3},{4}} => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7] => {{1},{2,4,5},{3},{6},{7}} => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,4,3,5,2,7,6] => {{1},{2,4,5},{3},{6,7}} => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7] => {{1},{2,6},{3},{4,5},{7}} => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2] => {{1},{2,7},{3},{4,5},{6}} => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,6,3,5,4,7,2] => {{1},{2,6,7},{3},{4,5}} => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [1,5,3,6,4,2,7] => {{1},{2,5},{3},{4,6},{7}} => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [1,7,3,6,4,5,2] => {{1},{2,7},{3},{4,6},{5}} => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [1,6,3,7,4,5,2] => {{1},{2,6},{3},{4,7},{5}} => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [1,5,3,6,7,2,4] => {{1},{2,5,7},{3},{4,6}} => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,4,3,5,6,2,7] => {{1},{2,4,5,6},{3},{7}} => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,7,3,5,6,4,2] => {{1},{2,7},{3},{4,5,6}} => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [1,6,3,5,7,4,2] => {{1},{2,6},{3},{4,5,7}} => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [1,4,3,6,7,5,2] => {{1},{2,4,6},{3},{5,7}} => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,4,3,5,6,7,2] => {{1},{2,4,5,6,7},{3}} => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}} => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}} => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}} => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,3,4,2,7,6,5] => {{1},{2,3,4},{5,7},{6}} => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}} => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7] => {{1},{2,5},{3,4},{6},{7}} => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,5,4,3,2,7,6] => {{1},{2,5},{3,4},{6,7}} => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7] => {{1},{2,6},{3,4},{5},{7}} => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2] => {{1},{2,7},{3,4},{5},{6}} => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,6,4,3,5,7,2] => {{1},{2,6,7},{3,4},{5}} => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,5,4,3,6,2,7] => {{1},{2,5,6},{3,4},{7}} => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => {{1},{2,7},{3,4},{5,6}} => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [1,6,4,3,7,5,2] => {{1},{2,6},{3,4},{5,7}} => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,5,4,3,6,7,2] => {{1},{2,5,6,7},{3,4}} => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [1,4,5,3,2,6,7] => {{1},{2,4},{3,5},{6},{7}} => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [1,4,5,3,2,7,6] => {{1},{2,4},{3,5},{6,7}} => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [1,6,5,3,4,2,7] => {{1},{2,6},{3,5},{4},{7}} => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [1,7,5,3,4,6,2] => {{1},{2,7},{3,5},{4},{6}} => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [1,6,5,3,4,7,2] => {{1},{2,6,7},{3,5},{4}} => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [1,5,6,3,4,2,7] => {{1},{2,5},{3,6},{4},{7}} => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [1,7,6,3,4,5,2] => {{1},{2,7},{3,6},{4},{5}} => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [1,6,7,3,4,5,2] => {{1},{2,6},{3,7},{4},{5}} => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [1,5,6,2,7,4,3] => {{1},{2,5,7},{3,6},{4}} => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [1,4,5,6,2,3,7] => {{1},{2,4,6},{3,5},{7}} => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [1,7,6,5,3,4,2] => {{1},{2,7},{3,6},{4,5}} => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [1,6,7,5,3,4,2] => {{1},{2,6},{3,7},{4,5}} => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [1,4,6,7,2,5,3] => {{1},{2,4,7},{3,6},{5}} => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [1,4,5,6,7,3,2] => {{1},{2,4,6},{3,5,7}} => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}} => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}} => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,6,4,5,3,2,7] => {{1},{2,6},{3,4,5},{7}} => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,7,4,5,3,6,2] => {{1},{2,7},{3,4,5},{6}} => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,6,4,5,3,7,2] => {{1},{2,6,7},{3,4,5}} => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [1,5,4,6,3,2,7] => {{1},{2,5},{3,4,6},{7}} => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [1,7,4,6,3,5,2] => {{1},{2,7},{3,4,6},{5}} => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [1,6,4,7,3,5,2] => {{1},{2,6},{3,4,7},{5}} => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [1,5,4,6,7,2,3] => {{1},{2,5,7},{3,4,6}} => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [1,3,5,6,4,2,7] => {{1},{2,3,5},{4,6},{7}} => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [1,7,5,6,4,3,2] => {{1},{2,7},{3,5},{4,6}} => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [1,6,5,7,4,3,2] => {{1},{2,6},{3,5},{4,7}} => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [1,3,6,7,4,5,2] => {{1},{2,3,6},{4,7},{5}} => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [1,3,5,6,7,2,4] => {{1},{2,3,5,7},{4,6}} => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}} => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,7,4,5,6,3,2] => {{1},{2,7},{3,4,5,6}} => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [1,6,4,5,7,3,2] => {{1},{2,6},{3,4,5,7}} => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [1,3,6,5,7,4,2] => {{1},{2,3,6},{4,5,7}} => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [1,3,5,6,4,7,2] => {{1},{2,3,5},{4,6,7}} => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}} => 0
[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}} => 0
[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}} => 0
[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}} => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => {{1,2},{3},{4},{5,7},{6}} => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,1,3,4,6,7,5] => {{1,2},{3},{4},{5,6,7}} => 0
[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}} => 0
[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}} => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => {{1,2},{3},{4,6},{5},{7}} => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => {{1,2},{3},{4,7},{5},{6}} => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,3,6,5,7,4] => {{1,2},{3},{4,6,7},{5}} => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,1,3,5,6,4,7] => {{1,2},{3},{4,5,6},{7}} => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,3,7,6,5,4] => {{1,2},{3},{4,7},{5,6}} => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [2,1,3,6,7,5,4] => {{1,2},{3},{4,6},{5,7}} => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,3,5,6,7,4] => {{1,2},{3},{4,5,6,7}} => 0
[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}} => 0
[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}} => 0
[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}} => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => {{1,2},{3,4},{5,7},{6}} => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,1,4,3,6,7,5] => {{1,2},{3,4},{5,6,7}} => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => {{1,2},{3,5},{4},{6},{7}} => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => {{1,2},{3,5},{4},{6,7}} => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => {{1,2},{3,6},{4},{5},{7}} => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => {{1,2},{3,7},{4},{5},{6}} => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,6,4,5,7,3] => {{1,2},{3,6,7},{4},{5}} => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,5,4,6,3,7] => {{1,2},{3,5,6},{4},{7}} => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,7,4,6,5,3] => {{1,2},{3,7},{4},{5,6}} => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [2,1,6,4,7,5,3] => {{1,2},{3,6},{4},{5,7}} => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,5,4,6,7,3] => {{1,2},{3,5,6,7},{4}} => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,1,4,5,3,6,7] => {{1,2},{3,4,5},{6},{7}} => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,1,4,5,3,7,6] => {{1,2},{3,4,5},{6,7}} => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,6,5,4,3,7] => {{1,2},{3,6},{4,5},{7}} => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,7,5,4,6,3] => {{1,2},{3,7},{4,5},{6}} => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,6,5,4,7,3] => {{1,2},{3,6,7},{4,5}} => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [2,1,5,6,4,3,7] => {{1,2},{3,5},{4,6},{7}} => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [2,1,7,6,4,5,3] => {{1,2},{3,7},{4,6},{5}} => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [2,1,6,7,4,5,3] => {{1,2},{3,6},{4,7},{5}} => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [2,1,5,6,7,3,4] => {{1,2},{3,5,7},{4,6}} => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,4,5,6,3,7] => {{1,2},{3,4,5,6},{7}} => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,7,5,6,4,3] => {{1,2},{3,7},{4,5,6}} => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [2,1,6,5,7,4,3] => {{1,2},{3,6},{4,5,7}} => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [2,1,4,6,7,5,3] => {{1,2},{3,4,6},{5,7}} => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,4,5,6,7,3] => {{1,2},{3,4,5,6,7}} => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => {{1,3},{2},{4},{5},{6,7}} => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => {{1,3},{2},{4},{5,6},{7}} => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => {{1,3},{2},{4},{5,7},{6}} => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,2,1,4,6,7,5] => {{1,3},{2},{4},{5,6,7}} => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => {{1,3},{2},{4,5},{6},{7}} => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => {{1,3},{2},{4,5},{6,7}} => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => {{1,3},{2},{4,6},{5},{7}} => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => {{1,3},{2},{4,7},{5},{6}} => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,2,1,6,5,7,4] => {{1,3},{2},{4,6,7},{5}} => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,2,1,5,6,4,7] => {{1,3},{2},{4,5,6},{7}} => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,2,1,7,6,5,4] => {{1,3},{2},{4,7},{5,6}} => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [3,2,1,6,7,5,4] => {{1,3},{2},{4,6},{5,7}} => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,1,5,6,7,4] => {{1,3},{2},{4,5,6,7}} => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => {{1,4},{2},{3},{5},{6,7}} => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => {{1,4},{2},{3},{5,6},{7}} => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => {{1,4},{2},{3},{5,7},{6}} => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,3,1,6,7,5] => {{1,4},{2},{3},{5,6,7}} => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,2,3,4,1,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2,3,4,1,7,6] => {{1,5},{2},{3},{4},{6,7}} => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,2,3,4,5,1,7] => {{1,6},{2},{3},{4},{5},{7}} => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => {{1,7},{2},{3},{4},{5},{6}} => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [6,2,3,4,5,7,1] => {{1,6,7},{2},{3},{4},{5}} => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,2,3,4,6,1,7] => {{1,5,6},{2},{3},{4},{7}} => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [7,2,3,4,6,5,1] => {{1,7},{2},{3},{4},{5,6}} => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [6,2,3,4,7,5,1] => {{1,6},{2},{3},{4},{5,7}} => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [5,2,3,4,6,7,1] => {{1,5,6,7},{2},{3},{4}} => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,2,3,5,1,6,7] => {{1,4,5},{2},{3},{6},{7}} => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,2,3,5,1,7,6] => {{1,4,5},{2},{3},{6,7}} => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [6,2,3,5,4,1,7] => {{1,6},{2},{3},{4,5},{7}} => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [7,2,3,5,4,6,1] => {{1,7},{2},{3},{4,5},{6}} => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [6,2,3,5,4,7,1] => {{1,6,7},{2},{3},{4,5}} => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [5,2,3,6,4,1,7] => {{1,5},{2},{3},{4,6},{7}} => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [7,2,3,6,4,5,1] => {{1,7},{2},{3},{4,6},{5}} => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [6,2,3,7,4,5,1] => {{1,6},{2},{3},{4,7},{5}} => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [5,2,3,6,7,1,4] => {{1,5,7},{2},{3},{4,6}} => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,2,3,5,6,1,7] => {{1,4,5,6},{2},{3},{7}} => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [7,2,3,5,6,4,1] => {{1,7},{2},{3},{4,5,6}} => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [6,2,3,5,7,4,1] => {{1,6},{2},{3},{4,5,7}} => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [4,2,3,6,7,5,1] => {{1,4,6},{2},{3},{5,7}} => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [4,2,3,5,6,7,1] => {{1,4,5,6,7},{2},{3}} => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,2,4,1,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,2,4,1,5,7,6] => {{1,3,4},{2},{5},{6,7}} => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,2,4,1,6,5,7] => {{1,3,4},{2},{5,6},{7}} => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,2,4,1,7,6,5] => {{1,3,4},{2},{5,7},{6}} => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,2,4,1,6,7,5] => {{1,3,4},{2},{5,6,7}} => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,2,4,3,1,6,7] => {{1,5},{2},{3,4},{6},{7}} => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [5,2,4,3,1,7,6] => {{1,5},{2},{3,4},{6,7}} => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [6,2,4,3,5,1,7] => {{1,6},{2},{3,4},{5},{7}} => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [7,2,4,3,5,6,1] => {{1,7},{2},{3,4},{5},{6}} => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [6,2,4,3,5,7,1] => {{1,6,7},{2},{3,4},{5}} => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [5,2,4,3,6,1,7] => {{1,5,6},{2},{3,4},{7}} => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [7,2,4,3,6,5,1] => {{1,7},{2},{3,4},{5,6}} => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [6,2,4,3,7,5,1] => {{1,6},{2},{3,4},{5,7}} => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [5,2,4,3,6,7,1] => {{1,5,6,7},{2},{3,4}} => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [4,2,5,3,1,6,7] => {{1,4},{2},{3,5},{6},{7}} => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [4,2,5,3,1,7,6] => {{1,4},{2},{3,5},{6,7}} => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [6,2,5,3,4,1,7] => {{1,6},{2},{3,5},{4},{7}} => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [7,2,5,3,4,6,1] => {{1,7},{2},{3,5},{4},{6}} => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [6,2,5,3,4,7,1] => {{1,6,7},{2},{3,5},{4}} => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [5,2,6,3,4,1,7] => {{1,5},{2},{3,6},{4},{7}} => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [7,2,6,3,4,5,1] => {{1,7},{2},{3,6},{4},{5}} => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [6,2,7,3,4,5,1] => {{1,6},{2},{3,7},{4},{5}} => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [5,2,6,1,7,4,3] => {{1,5,7},{2},{3,6},{4}} => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [4,2,5,6,1,3,7] => {{1,4,6},{2},{3,5},{7}} => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [7,2,6,5,3,4,1] => {{1,7},{2},{3,6},{4,5}} => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [6,2,7,5,3,4,1] => {{1,6},{2},{3,7},{4,5}} => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [4,2,6,7,1,5,3] => {{1,4,7},{2},{3,6},{5}} => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [4,2,5,6,7,3,1] => {{1,4,6},{2},{3,5,7}} => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [3,2,4,5,1,6,7] => {{1,3,4,5},{2},{6},{7}} => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,2,4,5,1,7,6] => {{1,3,4,5},{2},{6,7}} => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [6,2,4,5,3,1,7] => {{1,6},{2},{3,4,5},{7}} => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [7,2,4,5,3,6,1] => {{1,7},{2},{3,4,5},{6}} => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [6,2,4,5,3,7,1] => {{1,6,7},{2},{3,4,5}} => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [5,2,4,6,3,1,7] => {{1,5},{2},{3,4,6},{7}} => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [7,2,4,6,3,5,1] => {{1,7},{2},{3,4,6},{5}} => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [6,2,4,7,3,5,1] => {{1,6},{2},{3,4,7},{5}} => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [5,2,4,6,7,1,3] => {{1,5,7},{2},{3,4,6}} => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [3,2,5,6,4,1,7] => {{1,3,5},{2},{4,6},{7}} => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [7,2,5,6,4,3,1] => {{1,7},{2},{3,5},{4,6}} => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [6,2,5,7,4,3,1] => {{1,6},{2},{3,5},{4,7}} => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [3,2,6,7,4,5,1] => {{1,3,6},{2},{4,7},{5}} => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [3,2,5,6,7,1,4] => {{1,3,5,7},{2},{4,6}} => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [3,2,4,5,6,1,7] => {{1,3,4,5,6},{2},{7}} => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [7,2,4,5,6,3,1] => {{1,7},{2},{3,4,5,6}} => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [6,2,4,5,7,3,1] => {{1,6},{2},{3,4,5,7}} => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [3,2,6,5,7,4,1] => {{1,3,6},{2},{4,5,7}} => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [3,2,5,6,4,7,1] => {{1,3,5},{2},{4,6,7}} => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [3,2,4,5,6,7,1] => {{1,3,4,5,6,7},{2}} => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,3,1,4,5,7,6] => {{1,2,3},{4},{5},{6,7}} => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,3,1,4,6,5,7] => {{1,2,3},{4},{5,6},{7}} => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [2,3,1,4,7,6,5] => {{1,2,3},{4},{5,7},{6}} => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [2,3,1,4,6,7,5] => {{1,2,3},{4},{5,6,7}} => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,3,1,5,4,6,7] => {{1,2,3},{4,5},{6},{7}} => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,3,1,5,4,7,6] => {{1,2,3},{4,5},{6,7}} => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [2,3,1,6,5,4,7] => {{1,2,3},{4,6},{5},{7}} => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [2,3,1,7,5,6,4] => {{1,2,3},{4,7},{5},{6}} => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [2,3,1,6,5,7,4] => {{1,2,3},{4,6,7},{5}} => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [2,3,1,5,6,4,7] => {{1,2,3},{4,5,6},{7}} => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [2,3,1,7,6,5,4] => {{1,2,3},{4,7},{5,6}} => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [2,3,1,6,7,5,4] => {{1,2,3},{4,6},{5,7}} => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,3,1,5,6,7,4] => {{1,2,3},{4,5,6,7}} => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [4,3,2,1,5,7,6] => {{1,4},{2,3},{5},{6,7}} => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [4,3,2,1,6,5,7] => {{1,4},{2,3},{5,6},{7}} => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [4,3,2,1,7,6,5] => {{1,4},{2,3},{5,7},{6}} => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [4,3,2,1,6,7,5] => {{1,4},{2,3},{5,6,7}} => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,3,2,4,1,6,7] => {{1,5},{2,3},{4},{6},{7}} => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [5,3,2,4,1,7,6] => {{1,5},{2,3},{4},{6,7}} => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [6,3,2,4,5,1,7] => {{1,6},{2,3},{4},{5},{7}} => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [7,3,2,4,5,6,1] => {{1,7},{2,3},{4},{5},{6}} => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [6,3,2,4,5,7,1] => {{1,6,7},{2,3},{4},{5}} => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [5,3,2,4,6,1,7] => {{1,5,6},{2,3},{4},{7}} => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [7,3,2,4,6,5,1] => {{1,7},{2,3},{4},{5,6}} => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [6,3,2,4,7,5,1] => {{1,6},{2,3},{4},{5,7}} => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [5,3,2,4,6,7,1] => {{1,5,6,7},{2,3},{4}} => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [4,3,2,5,1,6,7] => {{1,4,5},{2,3},{6},{7}} => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [4,3,2,5,1,7,6] => {{1,4,5},{2,3},{6,7}} => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [6,3,2,5,4,1,7] => {{1,6},{2,3},{4,5},{7}} => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [7,3,2,5,4,6,1] => {{1,7},{2,3},{4,5},{6}} => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [6,3,2,5,4,7,1] => {{1,6,7},{2,3},{4,5}} => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [5,3,2,6,4,1,7] => {{1,5},{2,3},{4,6},{7}} => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [7,3,2,6,4,5,1] => {{1,7},{2,3},{4,6},{5}} => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [6,3,2,7,4,5,1] => {{1,6},{2,3},{4,7},{5}} => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [5,3,2,6,7,1,4] => {{1,5,7},{2,3},{4,6}} => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [4,3,2,5,6,1,7] => {{1,4,5,6},{2,3},{7}} => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [7,3,2,5,6,4,1] => {{1,7},{2,3},{4,5,6}} => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [6,3,2,5,7,4,1] => {{1,6},{2,3},{4,5,7}} => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [4,3,2,6,7,5,1] => {{1,4,6},{2,3},{5,7}} => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [4,3,2,5,6,7,1] => {{1,4,5,6,7},{2,3}} => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [3,4,2,1,5,6,7] => {{1,3},{2,4},{5},{6},{7}} => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [3,4,2,1,5,7,6] => {{1,3},{2,4},{5},{6,7}} => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [3,4,2,1,6,5,7] => {{1,3},{2,4},{5,6},{7}} => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [3,4,2,1,7,6,5] => {{1,3},{2,4},{5,7},{6}} => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [3,4,2,1,6,7,5] => {{1,3},{2,4},{5,6,7}} => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [5,4,2,3,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [5,4,2,3,1,7,6] => {{1,5},{2,4},{3},{6,7}} => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [6,4,2,3,5,1,7] => {{1,6},{2,4},{3},{5},{7}} => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [7,4,2,3,5,6,1] => {{1,7},{2,4},{3},{5},{6}} => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [6,4,2,3,5,7,1] => {{1,6,7},{2,4},{3},{5}} => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [5,4,2,3,6,1,7] => {{1,5,6},{2,4},{3},{7}} => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [7,4,2,3,6,5,1] => {{1,7},{2,4},{3},{5,6}} => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [6,4,2,3,7,5,1] => {{1,6},{2,4},{3},{5,7}} => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [5,4,2,3,6,7,1] => {{1,5,6,7},{2,4},{3}} => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [4,5,2,3,1,6,7] => {{1,4},{2,5},{3},{6},{7}} => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [4,5,2,3,1,7,6] => {{1,4},{2,5},{3},{6,7}} => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [6,5,2,3,4,1,7] => {{1,6},{2,5},{3},{4},{7}} => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [7,5,2,3,4,6,1] => {{1,7},{2,5},{3},{4},{6}} => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [6,5,2,3,4,7,1] => {{1,6,7},{2,5},{3},{4}} => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [5,6,2,3,4,1,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [7,6,2,3,4,5,1] => {{1,7},{2,6},{3},{4},{5}} => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [6,7,2,3,4,5,1] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [5,6,1,3,7,4,2] => {{1,5,7},{2,6},{3},{4}} => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [4,5,1,6,3,2,7] => {{1,4,6},{2,5},{3},{7}} => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [7,6,2,5,3,4,1] => {{1,7},{2,6},{3},{4,5}} => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [6,7,2,5,3,4,1] => {{1,6},{2,7},{3},{4,5}} => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [4,6,1,7,3,5,2] => {{1,4,7},{2,6},{3},{5}} => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [4,5,2,6,7,3,1] => {{1,4,6},{2,5,7},{3}} => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [3,4,5,1,2,6,7] => {{1,3,5},{2,4},{6},{7}} => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [3,4,5,1,2,7,6] => {{1,3,5},{2,4},{6,7}} => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [6,5,4,2,3,1,7] => {{1,6},{2,5},{3,4},{7}} => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [7,5,4,2,3,6,1] => {{1,7},{2,5},{3,4},{6}} => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [6,5,4,2,3,7,1] => {{1,6,7},{2,5},{3,4}} => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [5,6,4,2,3,1,7] => {{1,5},{2,6},{3,4},{7}} => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [7,6,4,2,3,5,1] => {{1,7},{2,6},{3,4},{5}} => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [6,7,4,2,3,5,1] => {{1,6},{2,7},{3,4},{5}} => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [5,6,4,1,7,3,2] => {{1,5,7},{2,6},{3,4}} => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [3,5,6,1,4,2,7] => {{1,3,6},{2,5},{4},{7}} => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [7,6,5,2,4,3,1] => {{1,7},{2,6},{3,5},{4}} => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [6,7,5,2,4,3,1] => {{1,6},{2,7},{3,5},{4}} => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [3,6,7,1,4,5,2] => {{1,3,7},{2,6},{4},{5}} => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [3,5,6,2,7,4,1] => {{1,3,6},{2,5,7},{4}} => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [3,4,5,6,2,1,7] => {{1,3,5},{2,4,6},{7}} => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [7,6,4,5,2,3,1] => {{1,7},{2,6},{3,4,5}} => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [6,7,4,5,2,3,1] => {{1,6},{2,7},{3,4,5}} => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [3,6,7,5,1,4,2] => {{1,3,7},{2,6},{4,5}} => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [3,5,7,6,4,1,2] => {{1,3,7},{2,5},{4,6}} => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [3,4,5,6,7,1,2] => {{1,3,5,7},{2,4,6}} => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [2,3,4,1,5,7,6] => {{1,2,3,4},{5},{6,7}} => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [2,3,4,1,6,5,7] => {{1,2,3,4},{5,6},{7}} => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [2,3,4,1,7,6,5] => {{1,2,3,4},{5,7},{6}} => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [2,3,4,1,6,7,5] => {{1,2,3,4},{5,6,7}} => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [5,3,4,2,1,6,7] => {{1,5},{2,3,4},{6},{7}} => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [5,3,4,2,1,7,6] => {{1,5},{2,3,4},{6,7}} => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [6,3,4,2,5,1,7] => {{1,6},{2,3,4},{5},{7}} => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [7,3,4,2,5,6,1] => {{1,7},{2,3,4},{5},{6}} => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [6,3,4,2,5,7,1] => {{1,6,7},{2,3,4},{5}} => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [5,3,4,2,6,1,7] => {{1,5,6},{2,3,4},{7}} => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [7,3,4,2,6,5,1] => {{1,7},{2,3,4},{5,6}} => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [6,3,4,2,7,5,1] => {{1,6},{2,3,4},{5,7}} => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [5,3,4,2,6,7,1] => {{1,5,6,7},{2,3,4}} => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [4,3,5,2,1,6,7] => {{1,4},{2,3,5},{6},{7}} => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [4,3,5,2,1,7,6] => {{1,4},{2,3,5},{6,7}} => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [6,3,5,2,4,1,7] => {{1,6},{2,3,5},{4},{7}} => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [7,3,5,2,4,6,1] => {{1,7},{2,3,5},{4},{6}} => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [6,3,5,2,4,7,1] => {{1,6,7},{2,3,5},{4}} => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [5,3,6,2,4,1,7] => {{1,5},{2,3,6},{4},{7}} => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [7,3,6,2,4,5,1] => {{1,7},{2,3,6},{4},{5}} => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [6,3,7,2,4,5,1] => {{1,6},{2,3,7},{4},{5}} => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [5,3,6,1,7,4,2] => {{1,5,7},{2,3,6},{4}} => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [4,3,5,6,1,2,7] => {{1,4,6},{2,3,5},{7}} => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [7,3,6,5,2,4,1] => {{1,7},{2,3,6},{4,5}} => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [6,3,7,5,2,4,1] => {{1,6},{2,3,7},{4,5}} => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [4,3,6,7,1,5,2] => {{1,4,7},{2,3,6},{5}} => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [4,3,5,6,7,2,1] => {{1,4,6},{2,3,5,7}} => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [2,4,5,3,1,6,7] => {{1,2,4},{3,5},{6},{7}} => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [2,4,5,3,1,7,6] => {{1,2,4},{3,5},{6,7}} => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [6,4,5,3,2,1,7] => {{1,6},{2,4},{3,5},{7}} => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [7,4,5,3,2,6,1] => {{1,7},{2,4},{3,5},{6}} => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [6,4,5,3,2,7,1] => {{1,6,7},{2,4},{3,5}} => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [5,4,6,3,2,1,7] => {{1,5},{2,4},{3,6},{7}} => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [7,4,6,3,2,5,1] => {{1,7},{2,4},{3,6},{5}} => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [6,4,7,3,2,5,1] => {{1,6},{2,4},{3,7},{5}} => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [5,4,6,1,7,2,3] => {{1,5,7},{2,4},{3,6}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [2,5,6,3,4,1,7] => {{1,2,5},{3,6},{4},{7}} => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [7,5,6,3,4,2,1] => {{1,7},{2,5},{3,6},{4}} => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [6,5,7,3,4,2,1] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [2,6,7,3,4,5,1] => {{1,2,6},{3,7},{4},{5}} => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [2,5,6,1,7,4,3] => {{1,2,5,7},{3,6},{4}} => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [2,4,5,6,1,3,7] => {{1,2,4,6},{3,5},{7}} => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [7,4,5,6,2,3,1] => {{1,7},{2,4,6},{3,5}} => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [6,4,5,7,2,3,1] => {{1,6},{2,4,7},{3,5}} => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [2,6,7,5,3,4,1] => {{1,2,6},{3,7},{4,5}} => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [2,5,7,6,4,3,1] => {{1,2,5},{3,7},{4,6}} => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [2,4,5,6,7,3,1] => {{1,2,4,6},{3,5,7}} => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [2,3,4,5,1,7,6] => {{1,2,3,4,5},{6,7}} => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [6,3,4,5,2,1,7] => {{1,6},{2,3,4,5},{7}} => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [7,3,4,5,2,6,1] => {{1,7},{2,3,4,5},{6}} => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [6,3,4,5,2,7,1] => {{1,6,7},{2,3,4,5}} => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [5,3,4,6,2,1,7] => {{1,5},{2,3,4,6},{7}} => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [7,3,4,6,2,5,1] => {{1,7},{2,3,4,6},{5}} => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [6,3,4,7,2,5,1] => {{1,6},{2,3,4,7},{5}} => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [5,3,4,6,7,1,2] => {{1,5,7},{2,3,4,6}} => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [2,5,4,6,3,1,7] => {{1,2,5},{3,4,6},{7}} => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [7,5,4,6,3,2,1] => {{1,7},{2,5},{3,4,6}} => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [6,5,4,7,3,2,1] => {{1,6},{2,5},{3,4,7}} => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [2,6,4,7,3,5,1] => {{1,2,6},{3,4,7},{5}} => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [2,5,4,6,7,1,3] => {{1,2,5,7},{3,4,6}} => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [2,4,5,3,6,1,7] => {{1,2,4},{3,5,6},{7}} => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [7,4,5,3,6,2,1] => {{1,7},{2,4},{3,5,6}} => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [6,4,5,3,7,2,1] => {{1,6},{2,4},{3,5,7}} => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [2,6,5,3,7,4,1] => {{1,2,6},{3,5,7},{4}} => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [2,5,6,3,4,7,1] => {{1,2,5},{3,6,7},{4}} => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [2,4,5,6,1,7,3] => {{1,2,4,6,7},{3,5}} => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [7,3,4,5,6,2,1] => {{1,7},{2,3,4,5,6}} => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [6,3,4,5,7,2,1] => {{1,6},{2,3,4,5,7}} => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [2,6,4,5,7,3,1] => {{1,2,6},{3,4,5,7}} => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [2,5,4,6,3,7,1] => {{1,2,5},{3,4,6,7}} => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [2,3,5,6,4,7,1] => {{1,2,3,5},{4,6,7}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [1,2,4,5,6,7,8,3] => {{1},{2},{3,4,5,6,7,8}} => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [1,4,3,5,6,7,8,2] => {{1},{2,4,5,6,7,8},{3}} => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,2] => {{1},{2,3,4,5,6,7,8}} => 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] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}} => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => {{1,2},{3,4},{5,8},{6,7}} => 0
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [2,1,4,3,7,8,6,5] => {{1,2},{3,4},{5,7},{6,8}} => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => {{1,2},{3,6},{4,5},{7,8}} => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => {{1,2},{3,8},{4,5},{6,7}} => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [2,1,5,6,4,3,8,7] => {{1,2},{3,5},{4,6},{7,8}} => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [2,1,8,7,6,4,5,3] => {{1,2},{3,8},{4,7},{5,6}} => 0
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [2,1,7,8,6,4,5,3] => {{1,2},{3,7},{4,8},{5,6}} => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => {{1,2},{3,4,5,6,7,8}} => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [4,2,3,5,6,7,8,1] => {{1,4,5,6,7,8},{2},{3}} => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,1] => {{1,3,4,5,6,7,8},{2}} => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}} => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => {{1,4},{2,3},{5,8},{6,7}} => 0
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [4,3,2,1,7,8,6,5] => {{1,4},{2,3},{5,7},{6,8}} => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => {{1,6},{2,3},{4,5},{7,8}} => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => {{1,8},{2,3},{4,5},{6,7}} => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [8,3,2,7,6,4,5,1] => {{1,8},{2,3},{4,7},{5,6}} => 0
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [7,3,2,8,6,4,5,1] => {{1,7},{2,3},{4,8},{5,6}} => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [4,3,2,5,6,7,8,1] => {{1,4,5,6,7,8},{2,3}} => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [3,4,2,1,6,5,8,7] => {{1,3},{2,4},{5,6},{7,8}} => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [3,4,2,1,8,7,6,5] => {{1,3},{2,4},{5,8},{6,7}} => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [3,4,2,1,7,8,6,5] => {{1,3},{2,4},{5,7},{6,8}} => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [6,5,4,2,3,1,8,7] => {{1,6},{2,5},{3,4},{7,8}} => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [8,5,4,2,3,7,6,1] => {{1,8},{2,5},{3,4},{6,7}} => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [5,6,4,2,3,1,8,7] => {{1,5},{2,6},{3,4},{7,8}} => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [8,7,4,2,6,3,5,1] => {{1,8},{2,7},{3,4},{5,6}} => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [8,7,6,5,2,4,3,1] => {{1,8},{2,7},{3,6},{4,5}} => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [8,7,5,6,4,2,3,1] => {{1,8},{2,7},{3,5},{4,6}} => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [8,4,7,3,6,2,5,1] => {{1,8},{2,4},{3,7},{5,6}} => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [8,6,7,5,3,4,2,1] => {{1,8},{2,6},{3,7},{4,5}} => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [7,5,8,6,4,3,2,1] => {{1,7},{2,5},{3,8},{4,6}} => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}} => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}} => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,2] => {{1},{2,3,4,5,6,7,8,9}} => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}} => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,2] => {{1},{2,3,4,5,6,7,8,9,10}} => 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] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => 0
[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}} => 0
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Description
The number of crossings of a set partition.
This is given by the number of $i < i' < j < j'$ such that $i,j$ are two consecutive entries on one block, and $i',j'$ are consecutive entries in another block.
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 non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.