Identifier
Values
[1,0,1,0] => [1,2] => [[1,2]] => {{1,2}} => 2
[1,1,0,0] => [2,1] => [[1],[2]] => {{1},{2}} => 0
[1,0,1,0,1,0] => [1,2,3] => [[1,2,3]] => {{1,2,3}} => 3
[1,0,1,1,0,0] => [1,3,2] => [[1,2],[3]] => {{1,2},{3}} => 1
[1,1,0,0,1,0] => [2,1,3] => [[1,3],[2]] => {{1,3},{2}} => 1
[1,1,0,1,0,0] => [2,3,1] => [[1,3],[2]] => {{1,3},{2}} => 1
[1,1,1,0,0,0] => [3,2,1] => [[1],[2],[3]] => {{1},{2},{3}} => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [[1,2,3,4]] => {{1,2,3,4}} => 4
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [[1,2,3],[4]] => {{1,2,3},{4}} => 2
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [[1,2,4],[3]] => {{1,2,4},{3}} => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [[1,2,4],[3]] => {{1,2,4},{3}} => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [[1,2],[3],[4]] => {{1,2},{3},{4}} => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[1,3,4],[2]] => {{1,3,4},{2}} => 2
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[1,3],[2,4]] => {{1,3},{2,4}} => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[1,3,4],[2]] => {{1,3,4},{2}} => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[1,3,4],[2]] => {{1,3,4},{2}} => 2
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [[1,3],[2],[4]] => {{1,3},{2},{4}} => 0
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 1
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [[1],[2],[3],[4]] => {{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}} => 5
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [[1,2,3,4],[5]] => {{1,2,3,4},{5}} => 3
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [[1,2,3,5],[4]] => {{1,2,3,5},{4}} => 3
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [[1,2,3,5],[4]] => {{1,2,3,5},{4}} => 3
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [[1,2,3],[4],[5]] => {{1,2,3},{4},{5}} => 2
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [[1,2,4,5],[3]] => {{1,2,4,5},{3}} => 3
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [[1,2,4],[3,5]] => {{1,2,4},{3,5}} => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [[1,2,4,5],[3]] => {{1,2,4,5},{3}} => 3
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [[1,2,4,5],[3]] => {{1,2,4,5},{3}} => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [[1,2,4],[3],[5]] => {{1,2,4},{3},{5}} => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [[1,2,5],[3],[4]] => {{1,2,5},{3},{4}} => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [[1,2,5],[3],[4]] => {{1,2,5},{3},{4}} => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [[1,2,5],[3],[4]] => {{1,2,5},{3},{4}} => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => {{1,2},{3},{4},{5}} => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 3
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[1,3,4],[2,5]] => {{1,3,4},{2,5}} => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[1,3,5],[2,4]] => {{1,3,5},{2,4}} => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[1,3,5],[2,4]] => {{1,3,5},{2,4}} => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => {{1,3},{2,4},{5}} => 0
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 3
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[1,3,4],[2,5]] => {{1,3,4},{2,5}} => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 3
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[1,3,4],[2],[5]] => {{1,3,4},{2},{5}} => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[1,3,5],[2],[4]] => {{1,3,5},{2},{4}} => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[1,3,5],[2],[4]] => {{1,3,5},{2},{4}} => 1
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [[1,3,5],[2],[4]] => {{1,3,5},{2},{4}} => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[1,3],[2],[4],[5]] => {{1,3},{2},{4},{5}} => 0
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => {{1,4},{2,5},{3}} => 0
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[1,4],[2,5],[3]] => {{1,4},{2,5},{3}} => 0
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 2
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 2
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 2
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [[1,4],[2],[3],[5]] => {{1,4},{2},{3},{5}} => 0
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 1
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => {{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}} => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => {{1,2,3,4,5},{6}} => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => {{1,2,3,4,6},{5}} => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [[1,2,3,4,6],[5]] => {{1,2,3,4,6},{5}} => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => {{1,2,3,4},{5},{6}} => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [[1,2,3,5],[4],[6]] => {{1,2,3,5},{4},{6}} => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => {{1,2,3,6},{4},{5}} => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [[1,2,3,6],[4],[5]] => {{1,2,3,6},{4},{5}} => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [[1,2,3,6],[4],[5]] => {{1,2,3,6},{4},{5}} => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => {{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] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => {{1,2,4},{3,5},{6}} => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [[1,2,4,5],[3],[6]] => {{1,2,4,5},{3},{6}} => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [[1,2,4,6],[3],[5]] => {{1,2,4,6},{3},{5}} => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [[1,2,4,6],[3],[5]] => {{1,2,4,6},{3},{5}} => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [[1,2,4,6],[3],[5]] => {{1,2,4,6},{3},{5}} => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [[1,2,4],[3],[5],[6]] => {{1,2,4},{3},{5},{6}} => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => {{1,2,5,6},{3},{4}} => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => {{1,2,5},{3,6},{4}} => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [[1,2,5,6],[3],[4]] => {{1,2,5,6},{3},{4}} => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [[1,2,5,6],[3],[4]] => {{1,2,5,6},{3},{4}} => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [[1,2,5],[3,6],[4]] => {{1,2,5},{3,6},{4}} => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [[1,2,5,6],[3],[4]] => {{1,2,5,6},{3},{4}} => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [[1,2,5,6],[3],[4]] => {{1,2,5,6},{3},{4}} => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [[1,2,5,6],[3],[4]] => {{1,2,5,6},{3},{4}} => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [[1,2,5],[3],[4],[6]] => {{1,2,5},{3},{4},{6}} => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => {{1,2,6},{3},{4},{5}} => 2
>>> Load all 743 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [[1,2,6],[3],[4],[5]] => {{1,2,6},{3},{4},{5}} => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [[1,2,6],[3],[4],[5]] => {{1,2,6},{3},{4},{5}} => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [[1,2,6],[3],[4],[5]] => {{1,2,6},{3},{4},{5}} => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => {{1,2},{3},{4},{5},{6}} => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 4
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => {{1,3,4},{2,5},{6}} => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => {{1,3,5},{2,4,6}} => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [[1,3,5],[2,4],[6]] => {{1,3,5},{2,4},{6}} => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => {{1,3,6},{2,4},{5}} => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[1,3,6],[2,4],[5]] => {{1,3,6},{2,4},{5}} => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [[1,3,6],[2,4],[5]] => {{1,3,6},{2,4},{5}} => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => {{1,3},{2,4},{5},{6}} => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [[1,3,4],[2,5],[6]] => {{1,3,4},{2,5},{6}} => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[1,3,4,5],[2],[6]] => {{1,3,4,5},{2},{6}} => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [[1,3,4,6],[2],[5]] => {{1,3,4,6},{2},{5}} => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [[1,3,4,6],[2],[5]] => {{1,3,4,6},{2},{5}} => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [[1,3,4,6],[2],[5]] => {{1,3,4,6},{2},{5}} => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[1,3,4],[2],[5],[6]] => {{1,3,4},{2},{5},{6}} => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [[1,3,5],[2,6],[4]] => {{1,3,5},{2,6},{4}} => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [[1,3,5],[2,6],[4]] => {{1,3,5},{2,6},{4}} => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [[1,3,5],[2],[4],[6]] => {{1,3,5},{2},{4},{6}} => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [[1,3,6],[2],[4],[5]] => {{1,3,6},{2},{4},{5}} => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [[1,3,6],[2],[4],[5]] => {{1,3,6},{2},{4},{5}} => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [[1,3,6],[2],[4],[5]] => {{1,3,6},{2},{4},{5}} => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [[1,3,6],[2],[4],[5]] => {{1,3,6},{2},{4},{5}} => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => {{1,3},{2},{4},{5},{6}} => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => {{1,4,5},{2,6},{3}} => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => {{1,4,6},{2,5},{3}} => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [[1,4,6],[2,5],[3]] => {{1,4,6},{2,5},{3}} => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => {{1,4},{2,5},{3,6}} => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[1,4,5],[2,6],[3]] => {{1,4,5},{2,6},{3}} => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [[1,4,5],[2,6],[3]] => {{1,4,5},{2,6},{3}} => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[1,4,6],[2,5],[3]] => {{1,4,6},{2,5},{3}} => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[1,4,6],[2,5],[3]] => {{1,4,6},{2,5},{3}} => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [[1,4,6],[2,5],[3]] => {{1,4,6},{2,5},{3}} => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [[1,4],[2,5],[3],[6]] => {{1,4},{2,5},{3},{6}} => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [[1,4,5],[2,6],[3]] => {{1,4,5},{2,6},{3}} => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [[1,4,5],[2,6],[3]] => {{1,4,5},{2,6},{3}} => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [[1,4,5],[2],[3],[6]] => {{1,4,5},{2},{3},{6}} => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [[1,4],[2],[3],[5],[6]] => {{1,4},{2},{3},{5},{6}} => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => {{1,5},{2,6},{3},{4}} => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [[1,5],[2,6],[3],[4]] => {{1,5},{2,6},{3},{4}} => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [[1,5],[2,6],[3],[4]] => {{1,5},{2,6},{3},{4}} => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [[1,5],[2],[3],[4],[6]] => {{1,5},{2},{3},{4},{6}} => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => {{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}} => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => {{1,2,3,4,5,6},{7}} => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]] => {{1,2,3,4,5},{6},{7}} => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [[1,2,3,4,6],[5],[7]] => {{1,2,3,4,6},{5},{7}} => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]] => {{1,2,3,4,7},{5},{6}} => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [[1,2,3,4,7],[5],[6]] => {{1,2,3,4,7},{5},{6}} => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [[1,2,3,4,7],[5],[6]] => {{1,2,3,4,7},{5},{6}} => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [[1,2,3,4],[5],[6],[7]] => {{1,2,3,4},{5},{6},{7}} => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]] => {{1,2,3,5},{4,6},{7}} => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [[1,2,3,5,6],[4],[7]] => {{1,2,3,5,6},{4},{7}} => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [[1,2,3,5,7],[4],[6]] => {{1,2,3,5,7},{4},{6}} => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [[1,2,3,5,7],[4],[6]] => {{1,2,3,5,7},{4},{6}} => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [[1,2,3,5,7],[4],[6]] => {{1,2,3,5,7},{4},{6}} => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [[1,2,3,5],[4],[6],[7]] => {{1,2,3,5},{4},{6},{7}} => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]] => {{1,2,3,6,7},{4},{5}} => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]] => {{1,2,3,6},{4,7},{5}} => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [[1,2,3,6,7],[4],[5]] => {{1,2,3,6,7},{4},{5}} => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [[1,2,3,6,7],[4],[5]] => {{1,2,3,6,7},{4},{5}} => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [[1,2,3,6],[4,7],[5]] => {{1,2,3,6},{4,7},{5}} => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [[1,2,3,6,7],[4],[5]] => {{1,2,3,6,7},{4},{5}} => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [[1,2,3,6,7],[4],[5]] => {{1,2,3,6,7},{4},{5}} => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [[1,2,3,6,7],[4],[5]] => {{1,2,3,6,7},{4},{5}} => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [[1,2,3,6],[4],[5],[7]] => {{1,2,3,6},{4},{5},{7}} => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [[1,2,3,7],[4],[5],[6]] => {{1,2,3,7},{4},{5},{6}} => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [[1,2,3,7],[4],[5],[6]] => {{1,2,3,7},{4},{5},{6}} => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [[1,2,3,7],[4],[5],[6]] => {{1,2,3,7},{4},{5},{6}} => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [[1,2,3,7],[4],[5],[6]] => {{1,2,3,7},{4},{5},{6}} => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]] => {{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] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => {{1,2,4,5},{3,6},{7}} => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [[1,2,4,6],[3,5],[7]] => {{1,2,4,6},{3,5},{7}} => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => {{1,2,4,7},{3,5},{6}} => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [[1,2,4,7],[3,5],[6]] => {{1,2,4,7},{3,5},{6}} => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [[1,2,4,7],[3,5],[6]] => {{1,2,4,7},{3,5},{6}} => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => {{1,2,4},{3,5},{6},{7}} => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [[1,2,4,5],[3,6],[7]] => {{1,2,4,5},{3,6},{7}} => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [[1,2,4,5,6],[3],[7]] => {{1,2,4,5,6},{3},{7}} => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [[1,2,4,5,7],[3],[6]] => {{1,2,4,5,7},{3},{6}} => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [[1,2,4,5,7],[3],[6]] => {{1,2,4,5,7},{3},{6}} => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [[1,2,4,5,7],[3],[6]] => {{1,2,4,5,7},{3},{6}} => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [[1,2,4,5],[3],[6],[7]] => {{1,2,4,5},{3},{6},{7}} => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [[1,2,4,6,7],[3],[5]] => {{1,2,4,6,7},{3},{5}} => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [[1,2,4,6],[3,7],[5]] => {{1,2,4,6},{3,7},{5}} => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [[1,2,4,6,7],[3],[5]] => {{1,2,4,6,7},{3},{5}} => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [[1,2,4,6,7],[3],[5]] => {{1,2,4,6,7},{3},{5}} => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [[1,2,4,6],[3,7],[5]] => {{1,2,4,6},{3,7},{5}} => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [[1,2,4,6,7],[3],[5]] => {{1,2,4,6,7},{3},{5}} => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [[1,2,4,6,7],[3],[5]] => {{1,2,4,6,7},{3},{5}} => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [[1,2,4,6,7],[3],[5]] => {{1,2,4,6,7},{3},{5}} => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [[1,2,4,6],[3],[5],[7]] => {{1,2,4,6},{3},{5},{7}} => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [[1,2,4,7],[3],[5],[6]] => {{1,2,4,7},{3},{5},{6}} => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [[1,2,4,7],[3],[5],[6]] => {{1,2,4,7},{3},{5},{6}} => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [[1,2,4,7],[3],[5],[6]] => {{1,2,4,7},{3},{5},{6}} => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [[1,2,4,7],[3],[5],[6]] => {{1,2,4,7},{3},{5},{6}} => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [[1,2,4],[3],[5],[6],[7]] => {{1,2,4},{3},{5},{6},{7}} => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]] => {{1,2,5,6},{3,7},{4}} => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]] => {{1,2,5,7},{3,6},{4}} => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [[1,2,5,7],[3,6],[4]] => {{1,2,5,7},{3,6},{4}} => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => {{1,2,5},{3,6},{4,7}} => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [[1,2,5,6],[3,7],[4]] => {{1,2,5,6},{3,7},{4}} => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [[1,2,5,6],[3,7],[4]] => {{1,2,5,6},{3,7},{4}} => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [[1,2,5,7],[3,6],[4]] => {{1,2,5,7},{3,6},{4}} => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [[1,2,5,7],[3,6],[4]] => {{1,2,5,7},{3,6},{4}} => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [[1,2,5,7],[3,6],[4]] => {{1,2,5,7},{3,6},{4}} => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [[1,2,5],[3,6],[4],[7]] => {{1,2,5},{3,6},{4},{7}} => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [[1,2,5,6],[3,7],[4]] => {{1,2,5,6},{3,7},{4}} => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [[1,2,5,6],[3,7],[4]] => {{1,2,5,6},{3,7},{4}} => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [[1,2,5,6],[3],[4],[7]] => {{1,2,5,6},{3},{4},{7}} => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [[1,2,5,7],[3],[4],[6]] => {{1,2,5,7},{3},{4},{6}} => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [[1,2,5,7],[3],[4],[6]] => {{1,2,5,7},{3},{4},{6}} => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [[1,2,5,7],[3],[4],[6]] => {{1,2,5,7},{3},{4},{6}} => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [[1,2,5,7],[3],[4],[6]] => {{1,2,5,7},{3},{4},{6}} => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [[1,2,5],[3],[4],[6],[7]] => {{1,2,5},{3},{4},{6},{7}} => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [[1,2,6],[3,7],[4],[5]] => {{1,2,6},{3,7},{4},{5}} => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [[1,2,6],[3,7],[4],[5]] => {{1,2,6},{3,7},{4},{5}} => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [[1,2,6],[3,7],[4],[5]] => {{1,2,6},{3,7},{4},{5}} => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [[1,2,6],[3],[4],[5],[7]] => {{1,2,6},{3},{4},{5},{7}} => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]] => {{1,2,7},{3},{4},{5},{6}} => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [[1,2,7],[3],[4],[5],[6]] => {{1,2,7},{3},{4},{5},{6}} => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [[1,2,7],[3],[4],[5],[6]] => {{1,2,7},{3},{4},{5},{6}} => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [[1,2,7],[3],[4],[5],[6]] => {{1,2,7},{3},{4},{5},{6}} => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [[1,2,7],[3],[4],[5],[6]] => {{1,2,7},{3},{4},{5},{6}} => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => {{1,2},{3},{4},{5},{6},{7}} => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => {{1,3,4,5},{2,6},{7}} => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [[1,3,4,6],[2,5],[7]] => {{1,3,4,6},{2,5},{7}} => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => {{1,3,4,7},{2,5},{6}} => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [[1,3,4,7],[2,5],[6]] => {{1,3,4,7},{2,5},{6}} => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [[1,3,4,7],[2,5],[6]] => {{1,3,4,7},{2,5},{6}} => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => {{1,3,4},{2,5},{6},{7}} => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]] => {{1,3,5},{2,4,6},{7}} => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [[1,3,5,6],[2,4],[7]] => {{1,3,5,6},{2,4},{7}} => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [[1,3,5,7],[2,4],[6]] => {{1,3,5,7},{2,4},{6}} => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [[1,3,5,7],[2,4],[6]] => {{1,3,5,7},{2,4},{6}} => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [[1,3,5,7],[2,4],[6]] => {{1,3,5,7},{2,4},{6}} => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [[1,3,5],[2,4],[6],[7]] => {{1,3,5},{2,4},{6},{7}} => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]] => {{1,3,6,7},{2,4},{5}} => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]] => {{1,3,6},{2,4,7},{5}} => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [[1,3,6,7],[2,4],[5]] => {{1,3,6,7},{2,4},{5}} => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [[1,3,6,7],[2,4],[5]] => {{1,3,6,7},{2,4},{5}} => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [[1,3,6],[2,4,7],[5]] => {{1,3,6},{2,4,7},{5}} => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [[1,3,6,7],[2,4],[5]] => {{1,3,6,7},{2,4},{5}} => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [[1,3,6,7],[2,4],[5]] => {{1,3,6,7},{2,4},{5}} => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [[1,3,6,7],[2,4],[5]] => {{1,3,6,7},{2,4},{5}} => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [[1,3,6],[2,4],[5],[7]] => {{1,3,6},{2,4},{5},{7}} => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[1,3,7],[2,4],[5],[6]] => {{1,3,7},{2,4},{5},{6}} => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [[1,3,7],[2,4],[5],[6]] => {{1,3,7},{2,4},{5},{6}} => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [[1,3,7],[2,4],[5],[6]] => {{1,3,7},{2,4},{5},{6}} => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [[1,3,7],[2,4],[5],[6]] => {{1,3,7},{2,4},{5},{6}} => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => {{1,3},{2,4},{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] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => {{1,3,4,5},{2,6},{7}} => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [[1,3,4,6],[2,5],[7]] => {{1,3,4,6},{2,5},{7}} => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => {{1,3,4,7},{2,5},{6}} => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [[1,3,4,7],[2,5],[6]] => {{1,3,4,7},{2,5},{6}} => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [[1,3,4,7],[2,5],[6]] => {{1,3,4,7},{2,5},{6}} => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => {{1,3,4},{2,5},{6},{7}} => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [[1,3,4,5],[2,6],[7]] => {{1,3,4,5},{2,6},{7}} => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [[1,3,4,5,6],[2],[7]] => {{1,3,4,5,6},{2},{7}} => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [[1,3,4,5],[2],[6],[7]] => {{1,3,4,5},{2},{6},{7}} => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [[1,3,4,6],[2,7],[5]] => {{1,3,4,6},{2,7},{5}} => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [[1,3,4,6],[2,7],[5]] => {{1,3,4,6},{2,7},{5}} => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [[1,3,4,6],[2],[5],[7]] => {{1,3,4,6},{2},{5},{7}} => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [[1,3,4],[2],[5],[6],[7]] => {{1,3,4},{2},{5},{6},{7}} => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => {{1,3,5,6},{2,7},{4}} => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => {{1,3,5,7},{2,6},{4}} => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [[1,3,5,7],[2,6],[4]] => {{1,3,5,7},{2,6},{4}} => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => {{1,3,5},{2,6},{4,7}} => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [[1,3,5,6],[2,7],[4]] => {{1,3,5,6},{2,7},{4}} => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [[1,3,5,6],[2,7],[4]] => {{1,3,5,6},{2,7},{4}} => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [[1,3,5,7],[2,6],[4]] => {{1,3,5,7},{2,6},{4}} => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [[1,3,5,7],[2,6],[4]] => {{1,3,5,7},{2,6},{4}} => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [[1,3,5,7],[2,6],[4]] => {{1,3,5,7},{2,6},{4}} => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [[1,3,5],[2,6],[4],[7]] => {{1,3,5},{2,6},{4},{7}} => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [[1,3,5,6],[2,7],[4]] => {{1,3,5,6},{2,7},{4}} => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [[1,3,5,6],[2,7],[4]] => {{1,3,5,6},{2,7},{4}} => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [[1,3,5,6],[2],[4],[7]] => {{1,3,5,6},{2},{4},{7}} => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [[1,3,5],[2],[4],[6],[7]] => {{1,3,5},{2},{4},{6},{7}} => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [[1,3,6],[2,7],[4],[5]] => {{1,3,6},{2,7},{4},{5}} => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [[1,3,6],[2,7],[4],[5]] => {{1,3,6},{2,7},{4},{5}} => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [[1,3,6],[2,7],[4],[5]] => {{1,3,6},{2,7},{4},{5}} => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [[1,3,6],[2],[4],[5],[7]] => {{1,3,6},{2},{4},{5},{7}} => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7]] => {{1,3},{2},{4},{5},{6},{7}} => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => {{1,4,5},{2,6},{3,7}} => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]] => {{1,4,6},{2,5,7},{3}} => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [[1,4,6],[2,5],[3,7]] => {{1,4,6},{2,5},{3,7}} => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => {{1,4,7},{2,5},{3,6}} => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [[1,4,7],[2,5],[3,6]] => {{1,4,7},{2,5},{3,6}} => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [[1,4,7],[2,5],[3,6]] => {{1,4,7},{2,5},{3,6}} => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => {{1,4},{2,5},{3,6},{7}} => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [[1,4,5],[2,6],[3,7]] => {{1,4,5},{2,6},{3,7}} => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [[1,4,5],[2,6],[3],[7]] => {{1,4,5},{2,6},{3},{7}} => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [[1,4,6],[2,5,7],[3]] => {{1,4,6},{2,5,7},{3}} => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [[1,4,6],[2,5,7],[3]] => {{1,4,6},{2,5,7},{3}} => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [[1,4,6],[2,5],[3],[7]] => {{1,4,6},{2,5},{3},{7}} => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [[1,4,7],[2,5],[3],[6]] => {{1,4,7},{2,5},{3},{6}} => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [[1,4,7],[2,5],[3],[6]] => {{1,4,7},{2,5},{3},{6}} => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [[1,4,7],[2,5],[3],[6]] => {{1,4,7},{2,5},{3},{6}} => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [[1,4,7],[2,5],[3],[6]] => {{1,4,7},{2,5},{3},{6}} => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [[1,4],[2,5],[3],[6],[7]] => {{1,4},{2,5},{3},{6},{7}} => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [[1,4,5],[2,6],[3,7]] => {{1,4,5},{2,6},{3,7}} => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [[1,4,5],[2,6],[3],[7]] => {{1,4,5},{2,6},{3},{7}} => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => {{1,4,5},{2},{3},{6},{7}} => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [[1,4,6],[2,7],[3],[5]] => {{1,4,6},{2,7},{3},{5}} => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [[1,4,6],[2,7],[3],[5]] => {{1,4,6},{2,7},{3},{5}} => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [[1,4,6],[2,7],[3],[5]] => {{1,4,6},{2,7},{3},{5}} => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [[1,4,6],[2],[3],[5],[7]] => {{1,4,6},{2},{3},{5},{7}} => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7]] => {{1,4},{2},{3},{5},{6},{7}} => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => {{1,5},{2,6},{3,7},{4}} => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [[1,5],[2,6],[3,7],[4]] => {{1,5},{2,6},{3,7},{4}} => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [[1,5],[2,6],[3],[4],[7]] => {{1,5},{2,6},{3},{4},{7}} => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7]] => {{1,5},{2},{3},{4},{6},{7}} => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => {{1,6},{2,7},{3},{4},{5}} => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [[1,6],[2,7],[3],[4],[5]] => {{1,6},{2,7},{3},{4},{5}} => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [[1,6],[2,7],[3],[4],[5]] => {{1,6},{2,7},{3},{4},{5}} => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [[1,6],[2,7],[3],[4],[5]] => {{1,6},{2,7},{3},{4},{5}} => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [[1,6],[2],[3],[4],[5],[7]] => {{1,6},{2},{3},{4},{5},{7}} => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => {{1},{2},{3},{4},{5},{6},{7}} => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => {{1,2,3,4,5,6,7,8}} => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => {{1,2,3,4,5,6,7},{8}} => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => 6
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 5
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Description
The number of anti-singletons of a set partition.
An anti-singleton of a set partition $S$ is an index $i$ such that $i$ and $i+1$ (considered cyclically) are both in the same block of $S$.
For noncrossing set partitions, this is also the number of singletons of the image of $S$ under the Kreweras complement.
Map
rows
Description
The set partition whose blocks are the rows of the tableau.
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.