Identifier
Values
[1,0,1,0] => [2,1] => [[1],[2]] => {{1},{2}} => 1
[1,1,0,0] => [1,2] => [[1,2]] => {{1,2}} => 0
[1,0,1,0,1,0] => [3,2,1] => [[1],[2],[3]] => {{1},{2},{3}} => 3
[1,0,1,1,0,0] => [2,3,1] => [[1,2],[3]] => {{1,2},{3}} => 2
[1,1,0,0,1,0] => [3,1,2] => [[1,3],[2]] => {{1,3},{2}} => 1
[1,1,0,1,0,0] => [2,1,3] => [[1,3],[2]] => {{1,3},{2}} => 1
[1,1,1,0,0,0] => [1,2,3] => [[1,2,3]] => {{1,2,3}} => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [[1],[2],[3],[4]] => {{1},{2},{3},{4}} => 6
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [[1,2],[3],[4]] => {{1,2},{3},{4}} => 5
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [[1,3],[2],[4]] => {{1,3},{2},{4}} => 4
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [[1,3],[2],[4]] => {{1,3},{2},{4}} => 4
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[1,2,3],[4]] => {{1,2,3},{4}} => 3
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 3
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[1,2],[3,4]] => {{1,2},{3,4}} => 2
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 3
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 3
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [[1,2,4],[3]] => {{1,2,4},{3}} => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[1,3,4],[2]] => {{1,3,4},{2}} => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [[1,3,4],[2]] => {{1,3,4},{2}} => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [[1,3,4],[2]] => {{1,3,4},{2}} => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [[1,2,3,4]] => {{1,2,3,4}} => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => {{1},{2},{3},{4},{5}} => 10
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[1,2],[3],[4],[5]] => {{1,2},{3},{4},{5}} => 9
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[1,3],[2],[4],[5]] => {{1,3},{2},{4},{5}} => 8
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [[1,3],[2],[4],[5]] => {{1,3},{2},{4},{5}} => 8
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[1,2,3],[4],[5]] => {{1,2,3},{4},{5}} => 7
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[1,4],[2],[3],[5]] => {{1,4},{2},{3},{5}} => 7
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[1,2],[3,4],[5]] => {{1,2},{3,4},{5}} => 6
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [[1,4],[2],[3],[5]] => {{1,4},{2},{3},{5}} => 7
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [[1,4],[2],[3],[5]] => {{1,4},{2},{3},{5}} => 7
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [[1,2,4],[3],[5]] => {{1,2,4},{3},{5}} => 6
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[1,3,4],[2],[5]] => {{1,3,4},{2},{5}} => 5
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [[1,3,4],[2],[5]] => {{1,3,4},{2},{5}} => 5
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [[1,3,4],[2],[5]] => {{1,3,4},{2},{5}} => 5
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[1,2,3,4],[5]] => {{1,2,3,4},{5}} => 4
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 6
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[1,2],[3,5],[4]] => {{1,2},{3,5},{4}} => 5
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 4
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 4
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[1,2,3],[4,5]] => {{1,2,3},{4,5}} => 3
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 6
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [[1,2],[3,5],[4]] => {{1,2},{3,5},{4}} => 5
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 6
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 6
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [[1,2,5],[3],[4]] => {{1,2,5},{3},{4}} => 5
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [[1,3,5],[2],[4]] => {{1,3,5},{2},{4}} => 4
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [[1,3,5],[2],[4]] => {{1,3,5},{2},{4}} => 4
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [[1,3,5],[2],[4]] => {{1,3,5},{2},{4}} => 4
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [[1,2,3,5],[4]] => {{1,2,3,5},{4}} => 3
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 3
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 2
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 3
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 3
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 2
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 3
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 3
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 3
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [[1,2,4,5],[3]] => {{1,2,4,5},{3}} => 2
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => {{1,2,3,4,5}} => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => {{1},{2},{3},{4},{5},{6}} => 15
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => {{1,2},{3},{4},{5},{6}} => 14
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[1,3],[2],[4],[5],[6]] => {{1,3},{2},{4},{5},{6}} => 13
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [[1,3],[2],[4],[5],[6]] => {{1,3},{2},{4},{5},{6}} => 13
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => {{1,2,3},{4},{5},{6}} => 12
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => {{1,4},{2},{3},{5},{6}} => 12
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[1,2],[3,4],[5],[6]] => {{1,2},{3,4},{5},{6}} => 11
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [[1,4],[2],[3],[5],[6]] => {{1,4},{2},{3},{5},{6}} => 12
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [[1,4],[2],[3],[5],[6]] => {{1,4},{2},{3},{5},{6}} => 12
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [[1,2,4],[3],[5],[6]] => {{1,2,4},{3},{5},{6}} => 11
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[1,3,4],[2],[5],[6]] => {{1,3,4},{2},{5},{6}} => 10
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [[1,3,4],[2],[5],[6]] => {{1,3,4},{2},{5},{6}} => 10
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[1,3,4],[2],[5],[6]] => {{1,3,4},{2},{5},{6}} => 10
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => {{1,2,3,4},{5},{6}} => 9
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [[1,5],[2],[3],[4],[6]] => {{1,5},{2},{3},{4},{6}} => 11
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[1,2],[3,5],[4],[6]] => {{1,2},{3,5},{4},{6}} => 10
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[1,3],[2,5],[4],[6]] => {{1,3},{2,5},{4},{6}} => 9
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [[1,3],[2,5],[4],[6]] => {{1,3},{2,5},{4},{6}} => 9
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[1,2,3],[4,5],[6]] => {{1,2,3},{4,5},{6}} => 8
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [[1,5],[2],[3],[4],[6]] => {{1,5},{2},{3},{4},{6}} => 11
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [[1,2],[3,5],[4],[6]] => {{1,2},{3,5},{4},{6}} => 10
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => {{1,5},{2},{3},{4},{6}} => 11
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => {{1,5},{2},{3},{4},{6}} => 11
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [[1,2,5],[3],[4],[6]] => {{1,2,5},{3},{4},{6}} => 10
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [[1,3,5],[2],[4],[6]] => {{1,3,5},{2},{4},{6}} => 9
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [[1,3,5],[2],[4],[6]] => {{1,3,5},{2},{4},{6}} => 9
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => {{1,3,5},{2},{4},{6}} => 9
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [[1,2,3,5],[4],[6]] => {{1,2,3,5},{4},{6}} => 8
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[1,4,5],[2],[3],[6]] => {{1,4,5},{2},{3},{6}} => 8
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[1,2,5],[3,4],[6]] => {{1,2,5},{3,4},{6}} => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [[1,4,5],[2],[3],[6]] => {{1,4,5},{2},{3},{6}} => 8
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [[1,4,5],[2],[3],[6]] => {{1,4,5},{2},{3},{6}} => 8
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [[1,2,5],[3,4],[6]] => {{1,2,5},{3,4},{6}} => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]] => {{1,4,5},{2},{3},{6}} => 8
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[1,4,5],[2],[3],[6]] => {{1,4,5},{2},{3},{6}} => 8
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]] => {{1,4,5},{2},{3},{6}} => 8
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [[1,2,4,5],[3],[6]] => {{1,2,4,5},{3},{6}} => 7
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => {{1,3,4,5},{2},{6}} => 6
>>> Load all 671 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [[1,3,4,5],[2],[6]] => {{1,3,4,5},{2},{6}} => 6
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [[1,3,4,5],[2],[6]] => {{1,3,4,5},{2},{6}} => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => {{1,3,4,5},{2},{6}} => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => {{1,2,3,4,5},{6}} => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 10
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]] => {{1,2},{3,6},{4},{5}} => 9
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[1,3],[2,6],[4],[5]] => {{1,3},{2,6},{4},{5}} => 8
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [[1,3],[2,6],[4],[5]] => {{1,3},{2,6},{4},{5}} => 8
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[1,2,3],[4,6],[5]] => {{1,2,3},{4,6},{5}} => 7
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 7
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 7
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 7
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [[1,2,4],[3,6],[5]] => {{1,2,4},{3,6},{5}} => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[1,3,4],[2,6],[5]] => {{1,3,4},{2,6},{5}} => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [[1,3,4],[2,6],[5]] => {{1,3,4},{2,6},{5}} => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [[1,3,4],[2,6],[5]] => {{1,3,4},{2,6},{5}} => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 10
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [[1,2],[3,6],[4],[5]] => {{1,2},{3,6},{4},{5}} => 9
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [[1,3],[2,6],[4],[5]] => {{1,3},{2,6},{4},{5}} => 8
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [[1,3],[2,6],[4],[5]] => {{1,3},{2,6},{4},{5}} => 8
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [[1,2,3],[4,6],[5]] => {{1,2,3},{4,6},{5}} => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 10
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [[1,2],[3,6],[4],[5]] => {{1,2},{3,6},{4},{5}} => 9
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 10
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 10
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [[1,2,6],[3],[4],[5]] => {{1,2,6},{3},{4},{5}} => 9
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [[1,3,6],[2],[4],[5]] => {{1,3,6},{2},{4},{5}} => 8
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [[1,3,6],[2],[4],[5]] => {{1,3,6},{2},{4},{5}} => 8
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [[1,3,6],[2],[4],[5]] => {{1,3,6},{2},{4},{5}} => 8
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [[1,2,3,6],[4],[5]] => {{1,2,3,6},{4},{5}} => 7
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 7
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [[1,2,6],[3,4],[5]] => {{1,2,6},{3,4},{5}} => 6
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 7
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 7
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [[1,2,6],[3,4],[5]] => {{1,2,6},{3,4},{5}} => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 7
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => 7
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => {{1,2,4,6},{3},{5}} => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [[1,3,4,6],[2],[5]] => {{1,3,4,6},{2},{5}} => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => {{1,3,4,6},{2},{5}} => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [[1,3,4,6],[2],[5]] => {{1,3,4,6},{2},{5}} => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => {{1,3,4,6},{2},{5}} => 5
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => {{1,2,3,4,6},{5}} => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[1,2,6],[3,5],[4]] => {{1,2,6},{3,5},{4}} => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [[1,2,6],[3,5],[4]] => {{1,2,6},{3,5},{4}} => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [[1,2,6],[3,5],[4]] => {{1,2,6},{3,5},{4}} => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [[1,2,6],[3,5],[4]] => {{1,2,6},{3,5},{4}} => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [[1,2,6],[3,5],[4]] => {{1,2,6},{3,5},{4}} => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [[1,2,5,6],[3],[4]] => {{1,2,5,6},{3},{4}} => 5
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => {{1,2,3,4,5,6}} => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => {{1},{2},{3},{4},{5},{6},{7}} => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => {{1,2},{3},{4},{5},{6},{7}} => 20
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => {{1,3},{2},{4},{5},{6},{7}} => 19
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => {{1,3},{2},{4},{5},{6},{7}} => 19
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => {{1,2,3},{4},{5},{6},{7}} => 18
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => {{1,4},{2},{3},{5},{6},{7}} => 18
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [[1,2],[3,4],[5],[6],[7]] => {{1,2},{3,4},{5},{6},{7}} => 17
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => {{1,4},{2},{3},{5},{6},{7}} => 18
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => {{1,4},{2},{3},{5},{6},{7}} => 18
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => {{1,2,4},{3},{5},{6},{7}} => 17
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => {{1,3,4},{2},{5},{6},{7}} => 16
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => {{1,3,4},{2},{5},{6},{7}} => 16
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => {{1,3,4},{2},{5},{6},{7}} => 16
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[1,2,3,4],[5],[6],[7]] => {{1,2,3,4},{5},{6},{7}} => 15
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [[1,5],[2],[3],[4],[6],[7]] => {{1,5},{2},{3},{4},{6},{7}} => 17
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [[1,2],[3,5],[4],[6],[7]] => {{1,2},{3,5},{4},{6},{7}} => 16
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [[1,3],[2,5],[4],[6],[7]] => {{1,3},{2,5},{4},{6},{7}} => 15
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [[1,3],[2,5],[4],[6],[7]] => {{1,3},{2,5},{4},{6},{7}} => 15
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [[1,2,3],[4,5],[6],[7]] => {{1,2,3},{4,5},{6},{7}} => 14
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [[1,5],[2],[3],[4],[6],[7]] => {{1,5},{2},{3},{4},{6},{7}} => 17
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [[1,2],[3,5],[4],[6],[7]] => {{1,2},{3,5},{4},{6},{7}} => 16
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [[1,5],[2],[3],[4],[6],[7]] => {{1,5},{2},{3},{4},{6},{7}} => 17
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [[1,5],[2],[3],[4],[6],[7]] => {{1,5},{2},{3},{4},{6},{7}} => 17
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => {{1,2,5},{3},{4},{6},{7}} => 16
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [[1,3,5],[2],[4],[6],[7]] => {{1,3,5},{2},{4},{6},{7}} => 15
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => {{1,3,5},{2},{4},{6},{7}} => 15
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => {{1,3,5},{2},{4},{6},{7}} => 15
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [[1,2,3,5],[4],[6],[7]] => {{1,2,3,5},{4},{6},{7}} => 14
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => {{1,4,5},{2},{3},{6},{7}} => 14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [[1,2,5],[3,4],[6],[7]] => {{1,2,5},{3,4},{6},{7}} => 13
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => {{1,4,5},{2},{3},{6},{7}} => 14
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => {{1,4,5},{2},{3},{6},{7}} => 14
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [[1,2,5],[3,4],[6],[7]] => {{1,2,5},{3,4},{6},{7}} => 13
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => {{1,4,5},{2},{3},{6},{7}} => 14
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => {{1,4,5},{2},{3},{6},{7}} => 14
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => {{1,4,5},{2},{3},{6},{7}} => 14
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [[1,2,4,5],[3],[6],[7]] => {{1,2,4,5},{3},{6},{7}} => 13
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [[1,3,4,5],[2],[6],[7]] => {{1,3,4,5},{2},{6},{7}} => 12
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [[1,3,4,5],[2],[6],[7]] => {{1,3,4,5},{2},{6},{7}} => 12
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => {{1,3,4,5},{2},{6},{7}} => 12
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => {{1,3,4,5},{2},{6},{7}} => 12
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [[1,2,3,4,5],[6],[7]] => {{1,2,3,4,5},{6},{7}} => 11
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [[1,6],[2],[3],[4],[5],[7]] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [[1,2],[3,6],[4],[5],[7]] => {{1,2},{3,6},{4},{5},{7}} => 15
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => {{1,3},{2,6},{4},{5},{7}} => 14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => {{1,3},{2,6},{4},{5},{7}} => 14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [[1,2,3],[4,6],[5],[7]] => {{1,2,3},{4,6},{5},{7}} => 13
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => {{1,4},{2,6},{3},{5},{7}} => 13
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [[1,2],[3,4],[5,6],[7]] => {{1,2},{3,4},{5,6},{7}} => 12
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => {{1,4},{2,6},{3},{5},{7}} => 13
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => {{1,4},{2,6},{3},{5},{7}} => 13
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [[1,2,4],[3,6],[5],[7]] => {{1,2,4},{3,6},{5},{7}} => 12
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [[1,3,4],[2,6],[5],[7]] => {{1,3,4},{2,6},{5},{7}} => 11
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [[1,3,4],[2,6],[5],[7]] => {{1,3,4},{2,6},{5},{7}} => 11
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [[1,3,4],[2,6],[5],[7]] => {{1,3,4},{2,6},{5},{7}} => 11
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [[1,2,3,4],[5,6],[7]] => {{1,2,3,4},{5,6},{7}} => 10
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [[1,6],[2],[3],[4],[5],[7]] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => {{1,2},{3,6},{4},{5},{7}} => 15
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [[1,3],[2,6],[4],[5],[7]] => {{1,3},{2,6},{4},{5},{7}} => 14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [[1,3],[2,6],[4],[5],[7]] => {{1,3},{2,6},{4},{5},{7}} => 14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [[1,2,3],[4,6],[5],[7]] => {{1,2,3},{4,6},{5},{7}} => 13
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [[1,6],[2],[3],[4],[5],[7]] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [[1,2],[3,6],[4],[5],[7]] => {{1,2},{3,6},{4},{5},{7}} => 15
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5],[7]] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [[1,6],[2],[3],[4],[5],[7]] => {{1,6},{2},{3},{4},{5},{7}} => 16
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => {{1,2,6},{3},{4},{5},{7}} => 15
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [[1,3,6],[2],[4],[5],[7]] => {{1,3,6},{2},{4},{5},{7}} => 14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => {{1,3,6},{2},{4},{5},{7}} => 14
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => {{1,3,6},{2},{4},{5},{7}} => 14
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [[1,2,3,6],[4],[5],[7]] => {{1,2,3,6},{4},{5},{7}} => 13
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [[1,4,6],[2],[3],[5],[7]] => {{1,4,6},{2},{3},{5},{7}} => 13
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [[1,2,6],[3,4],[5],[7]] => {{1,2,6},{3,4},{5},{7}} => 12
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => {{1,4,6},{2},{3},{5},{7}} => 13
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => {{1,4,6},{2},{3},{5},{7}} => 13
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [[1,2,6],[3,4],[5],[7]] => {{1,2,6},{3,4},{5},{7}} => 12
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => {{1,4,6},{2},{3},{5},{7}} => 13
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => {{1,4,6},{2},{3},{5},{7}} => 13
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => {{1,4,6},{2},{3},{5},{7}} => 13
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => {{1,2,4,6},{3},{5},{7}} => 12
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [[1,3,4,6],[2],[5],[7]] => {{1,3,4,6},{2},{5},{7}} => 11
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[1,3,4,6],[2],[5],[7]] => {{1,3,4,6},{2},{5},{7}} => 11
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => {{1,3,4,6},{2},{5},{7}} => 11
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => {{1,3,4,6},{2},{5},{7}} => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [[1,2,3,4,6],[5],[7]] => {{1,2,3,4,6},{5},{7}} => 10
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [[1,2,6],[3,5],[4],[7]] => {{1,2,6},{3,5},{4},{7}} => 11
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [[1,3,6],[2,5],[4],[7]] => {{1,3,6},{2,5},{4},{7}} => 10
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [[1,3,6],[2,5],[4],[7]] => {{1,3,6},{2,5},{4},{7}} => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [[1,2,3],[4,5,6],[7]] => {{1,2,3},{4,5,6},{7}} => 9
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [[1,2,6],[3,5],[4],[7]] => {{1,2,6},{3,5},{4},{7}} => 11
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [[1,2,6],[3,5],[4],[7]] => {{1,2,6},{3,5},{4},{7}} => 11
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [[1,3,6],[2,5],[4],[7]] => {{1,3,6},{2,5},{4},{7}} => 10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [[1,3,6],[2,5],[4],[7]] => {{1,3,6},{2,5},{4},{7}} => 10
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [[1,3,6],[2,5],[4],[7]] => {{1,3,6},{2,5},{4},{7}} => 10
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [[1,2,3,6],[4,5],[7]] => {{1,2,3,6},{4,5},{7}} => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [[1,2,6],[3,5],[4],[7]] => {{1,2,6},{3,5},{4},{7}} => 11
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [[1,2,6],[3,5],[4],[7]] => {{1,2,6},{3,5},{4},{7}} => 11
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => 12
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [[1,2,5,6],[3],[4],[7]] => {{1,2,5,6},{3},{4},{7}} => 11
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [[1,3,5,6],[2],[4],[7]] => {{1,3,5,6},{2},{4},{7}} => 10
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[1,3,5,6],[2],[4],[7]] => {{1,3,5,6},{2},{4},{7}} => 10
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => {{1,3,5,6},{2},{4},{7}} => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => {{1,3,5,6},{2},{4},{7}} => 10
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [[1,2,3,5,6],[4],[7]] => {{1,2,3,5,6},{4},{7}} => 9
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [[1,2,5,6],[3,4],[7]] => {{1,2,5,6},{3,4},{7}} => 8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [[1,2,5,6],[3,4],[7]] => {{1,2,5,6},{3,4},{7}} => 8
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [[1,2,5,6],[3,4],[7]] => {{1,2,5,6},{3,4},{7}} => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => 9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => {{1,2,4,5,6},{3},{7}} => 8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => {{1,3,4,5,6},{2},{7}} => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[1,3,4,5,6],[2],[7]] => {{1,3,4,5,6},{2},{7}} => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [[1,3,4,5,6],[2],[7]] => {{1,3,4,5,6},{2},{7}} => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => {{1,3,4,5,6},{2},{7}} => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => {{1,3,4,5,6},{2},{7}} => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => {{1,2,3,4,5,6},{7}} => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 15
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [[1,2],[3,7],[4],[5],[6]] => {{1,2},{3,7},{4},{5},{6}} => 14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => {{1,3},{2,7},{4},{5},{6}} => 13
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => {{1,3},{2,7},{4},{5},{6}} => 13
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [[1,2,3],[4,7],[5],[6]] => {{1,2,3},{4,7},{5},{6}} => 12
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => {{1,4},{2,7},{3},{5},{6}} => 12
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [[1,2],[3,4],[5,7],[6]] => {{1,2},{3,4},{5,7},{6}} => 11
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => {{1,4},{2,7},{3},{5},{6}} => 12
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => {{1,4},{2,7},{3},{5},{6}} => 12
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [[1,2,4],[3,7],[5],[6]] => {{1,2,4},{3,7},{5},{6}} => 11
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [[1,3,4],[2,7],[5],[6]] => {{1,3,4},{2,7},{5},{6}} => 10
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [[1,3,4],[2,7],[5],[6]] => {{1,3,4},{2,7},{5},{6}} => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [[1,3,4],[2,7],[5],[6]] => {{1,3,4},{2,7},{5},{6}} => 10
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [[1,2,3,4],[5,7],[6]] => {{1,2,3,4},{5,7},{6}} => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 11
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [[1,2],[3,5],[4,7],[6]] => {{1,2},{3,5},{4,7},{6}} => 10
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 9
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 9
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [[1,2,3],[4,5],[6,7]] => {{1,2,3},{4,5},{6,7}} => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 11
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [[1,2],[3,5],[4,7],[6]] => {{1,2},{3,5},{4,7},{6}} => 10
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 11
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 11
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [[1,2,5],[3,7],[4],[6]] => {{1,2,5},{3,7},{4},{6}} => 10
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [[1,3,5],[2,7],[4],[6]] => {{1,3,5},{2,7},{4},{6}} => 9
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [[1,3,5],[2,7],[4],[6]] => {{1,3,5},{2,7},{4},{6}} => 9
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [[1,3,5],[2,7],[4],[6]] => {{1,3,5},{2,7},{4},{6}} => 9
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [[1,2,3,5],[4,7],[6]] => {{1,2,3,5},{4,7},{6}} => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [[1,4,5],[2,7],[3],[6]] => {{1,4,5},{2,7},{3},{6}} => 8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]] => {{1,2,5},{3,4},{6,7}} => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [[1,4,5],[2,7],[3],[6]] => {{1,4,5},{2,7},{3},{6}} => 8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [[1,4,5],[2,7],[3],[6]] => {{1,4,5},{2,7},{3},{6}} => 8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [[1,2,5],[3,4],[6,7]] => {{1,2,5},{3,4},{6,7}} => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [[1,4,5],[2,7],[3],[6]] => {{1,4,5},{2,7},{3},{6}} => 8
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [[1,4,5],[2,7],[3],[6]] => {{1,4,5},{2,7},{3},{6}} => 8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [[1,4,5],[2,7],[3],[6]] => {{1,4,5},{2,7},{3},{6}} => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [[1,2,4,5],[3,7],[6]] => {{1,2,4,5},{3,7},{6}} => 7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [[1,3,4,5],[2,7],[6]] => {{1,3,4,5},{2,7},{6}} => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [[1,3,4,5],[2,7],[6]] => {{1,3,4,5},{2,7},{6}} => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => {{1,3,4,5},{2,7},{6}} => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => {{1,3,4,5},{2,7},{6}} => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 15
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [[1,2],[3,7],[4],[5],[6]] => {{1,2},{3,7},{4},{5},{6}} => 14
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => {{1,3},{2,7},{4},{5},{6}} => 13
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => {{1,3},{2,7},{4},{5},{6}} => 13
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [[1,2,3],[4,7],[5],[6]] => {{1,2,3},{4,7},{5},{6}} => 12
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => {{1,4},{2,7},{3},{5},{6}} => 12
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [[1,2],[3,4],[5,7],[6]] => {{1,2},{3,4},{5,7},{6}} => 11
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => {{1,4},{2,7},{3},{5},{6}} => 12
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => {{1,4},{2,7},{3},{5},{6}} => 12
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [[1,2,4],[3,7],[5],[6]] => {{1,2,4},{3,7},{5},{6}} => 11
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [[1,3,4],[2,7],[5],[6]] => {{1,3,4},{2,7},{5},{6}} => 10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [[1,3,4],[2,7],[5],[6]] => {{1,3,4},{2,7},{5},{6}} => 10
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [[1,3,4],[2,7],[5],[6]] => {{1,3,4},{2,7},{5},{6}} => 10
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [[1,2,3,4],[5,7],[6]] => {{1,2,3,4},{5,7},{6}} => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 15
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => {{1,2},{3,7},{4},{5},{6}} => 14
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [[1,3],[2,7],[4],[5],[6]] => {{1,3},{2,7},{4},{5},{6}} => 13
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [[1,3],[2,7],[4],[5],[6]] => {{1,3},{2,7},{4},{5},{6}} => 13
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [[1,2,3],[4,7],[5],[6]] => {{1,2,3},{4,7},{5},{6}} => 12
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 15
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [[1,2],[3,7],[4],[5],[6]] => {{1,2},{3,7},{4},{5},{6}} => 14
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 15
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 15
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => {{1,2,7},{3},{4},{5},{6}} => 14
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => 13
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => 13
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => 13
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [[1,2,3,7],[4],[5],[6]] => {{1,2,3,7},{4},{5},{6}} => 12
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 12
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [[1,2,7],[3,4],[5],[6]] => {{1,2,7},{3,4},{5},{6}} => 11
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 12
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 12
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [[1,2,7],[3,4],[5],[6]] => {{1,2,7},{3,4},{5},{6}} => 11
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 12
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 12
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => 12
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [[1,2,4,7],[3],[5],[6]] => {{1,2,4,7},{3},{5},{6}} => 11
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => 10
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => 10
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => 10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [[1,2,3,4,7],[5],[6]] => {{1,2,3,4,7},{5},{6}} => 9
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [[1,2,7],[3,5],[4],[6]] => {{1,2,7},{3,5},{4},{6}} => 10
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [[1,3,7],[2,5],[4],[6]] => {{1,3,7},{2,5},{4},{6}} => 9
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [[1,3,7],[2,5],[4],[6]] => {{1,3,7},{2,5},{4},{6}} => 9
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [[1,2,3],[4,5,7],[6]] => {{1,2,3},{4,5,7},{6}} => 8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [[1,2,7],[3,5],[4],[6]] => {{1,2,7},{3,5},{4},{6}} => 10
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [[1,2,7],[3,5],[4],[6]] => {{1,2,7},{3,5},{4},{6}} => 10
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [[1,3,7],[2,5],[4],[6]] => {{1,3,7},{2,5},{4},{6}} => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [[1,3,7],[2,5],[4],[6]] => {{1,3,7},{2,5},{4},{6}} => 9
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [[1,3,7],[2,5],[4],[6]] => {{1,3,7},{2,5},{4},{6}} => 9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [[1,2,3,7],[4,5],[6]] => {{1,2,3,7},{4,5},{6}} => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [[1,2,7],[3,5],[4],[6]] => {{1,2,7},{3,5},{4},{6}} => 10
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [[1,2,7],[3,5],[4],[6]] => {{1,2,7},{3,5},{4},{6}} => 10
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => 11
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [[1,2,5,7],[3],[4],[6]] => {{1,2,5,7},{3},{4},{6}} => 10
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => 9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => 9
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => 9
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [[1,2,3,5,7],[4],[6]] => {{1,2,3,5,7},{4},{6}} => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [[1,2,5,7],[3,4],[6]] => {{1,2,5,7},{3,4},{6}} => 7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [[1,2,5,7],[3,4],[6]] => {{1,2,5,7},{3,4},{6}} => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [[1,2,5,7],[3,4],[6]] => {{1,2,5,7},{3,4},{6}} => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => {{1,2,4,5,7},{3},{6}} => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => 6
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => 9
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [[1,2,3],[4,6,7],[5]] => {{1,2,3},{4,6,7},{5}} => 7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 6
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 7
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 7
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [[1,2,4],[3,6,7],[5]] => {{1,2,4},{3,6,7},{5}} => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => 9
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [[1,2,3],[4,6,7],[5]] => {{1,2,3},{4,6,7},{5}} => 7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => 9
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => 9
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [[1,2,3,7],[4,6],[5]] => {{1,2,3,7},{4,6},{5}} => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 7
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 7
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 7
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [[1,2,4,7],[3,6],[5]] => {{1,2,4,7},{3,6},{5}} => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[1,3,4,7],[2,6],[5]] => {{1,3,4,7},{2,6},{5}} => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [[1,3,4,7],[2,6],[5]] => {{1,3,4,7},{2,6},{5}} => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => {{1,3,4,7},{2,6},{5}} => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => {{1,3,4,7},{2,6},{5}} => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => 9
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [[1,2,3],[4,6,7],[5]] => {{1,2,3},{4,6,7},{5}} => 7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => 9
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => 9
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [[1,2,3,7],[4,6],[5]] => {{1,2,3,7},{4,6},{5}} => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => 9
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => 9
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => 9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [[1,2,3,6,7],[4],[5]] => {{1,2,3,6,7},{4},{5}} => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [[1,2,6,7],[3,4],[5]] => {{1,2,6,7},{3,4},{5}} => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [[1,2,6,7],[3,4],[5]] => {{1,2,6,7},{3,4},{5}} => 6
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [[1,2,6,7],[3,4],[5]] => {{1,2,6,7},{3,4},{5}} => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => {{1,2,4,6,7},{3},{5}} => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => 5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => {{1,2,3,4,5,6,7}} => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[1,2,3,4,5,6,7],[8]] => {{1,2,3,4,5,6,7},{8}} => 7
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => 6
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => 5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => {{1,2,3,4,5,6,7,8}} => 0
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Description
The rob statistic of a set partition.
Let $S = B_1,\ldots,B_k$ be a set partition with ordered blocks $B_i$ and with $\operatorname{min} B_a < \operatorname{min} B_b$ for $a < b$.
According to [1, Definition 3], a rob (right-opener-bigger) of $S$ is given by a pair $i < j$ such that $j = \operatorname{min} B_b$ and $i \in B_a$ for $a < b$.
This is also the number of occurrences of the pattern {{1}, {2}}, such that 2 is the minimal element of a block.
Map
rows
Description
The set partition whose blocks are the rows of the tableau.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording 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 recording tableau.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].