Identifier
-
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00284: Standard tableaux —rows⟶ Set partitions
St000248: Set partitions ⟶ ℤ
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] => [[1,2],[3]] => {{1,2},{3}} => 1
[1,1,1,0,0,0] => [3,1,2] => [[1,3],[2]] => {{1,3},{2}} => 1
[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] => [[1,2,3],[4]] => {{1,2,3},{4}} => 2
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [[1,2,4],[3]] => {{1,2,4},{3}} => 2
[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] => [[1,2,4],[3]] => {{1,2,4},{3}} => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[1,2,3],[4]] => {{1,2,3},{4}} => 2
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [[1,2],[3,4]] => {{1,2},{3,4}} => 2
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [[1,3,4],[2]] => {{1,3,4},{2}} => 2
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [[1,3],[2,4]] => {{1,3},{2,4}} => 0
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [[1,2],[3,4]] => {{1,2},{3,4}} => 2
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [[1,3,4],[2]] => {{1,3,4},{2}} => 2
[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] => [[1,2,3,4],[5]] => {{1,2,3,4},{5}} => 3
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [[1,2,3,5],[4]] => {{1,2,3,5},{4}} => 3
[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] => [[1,2,3,5],[4]] => {{1,2,3,5},{4}} => 3
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [[1,2,3,4],[5]] => {{1,2,3,4},{5}} => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [[1,2,3],[4,5]] => {{1,2,3},{4,5}} => 3
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [[1,2,4,5],[3]] => {{1,2,4,5},{3}} => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [[1,2,4],[3,5]] => {{1,2,4},{3,5}} => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [[1,2,3],[4,5]] => {{1,2,3},{4,5}} => 3
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [[1,2,4,5],[3]] => {{1,2,4,5},{3}} => 3
[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] => [[1,3,4],[2,5]] => {{1,3,4},{2,5}} => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [[1,3,5],[2,4]] => {{1,3,5},{2,4}} => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[1,2,4,5],[3]] => {{1,2,4,5},{3}} => 3
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[1,2,4],[3,5]] => {{1,2,4},{3,5}} => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[1,2,3,5],[4]] => {{1,2,3,5},{4}} => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[1,2,3,4],[5]] => {{1,2,3,4},{5}} => 3
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [[1,2,3],[4,5]] => {{1,2,3},{4,5}} => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 3
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [[1,2,4],[3,5]] => {{1,2,4},{3,5}} => 1
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [[1,2,3],[4,5]] => {{1,2,3},{4,5}} => 3
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 3
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 3
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [[1,3,4],[2,5]] => {{1,3,4},{2,5}} => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [[1,3,5],[2,4]] => {{1,3,5},{2,4}} => 1
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [[1,3,4],[2,5]] => {{1,3,4},{2,5}} => 1
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [[1,3,5],[2,4]] => {{1,3,5},{2,4}} => 1
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 3
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [[1,2,4],[3,5]] => {{1,2,4},{3,5}} => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [[1,2,3],[4,5]] => {{1,2,3},{4,5}} => 3
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 3
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 3
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [[1,3,4],[2,5]] => {{1,3,4},{2,5}} => 1
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [[1,3,5],[2,4]] => {{1,3,5},{2,4}} => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 3
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 3
[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] => [[1,2,3,4,5],[6]] => {{1,2,3,4,5},{6}} => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => {{1,2,3,4,6},{5}} => 4
[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] => [[1,2,3,4,6],[5]] => {{1,2,3,4,6},{5}} => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => {{1,2,3,4,5},{6}} => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => 4
[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] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [[1,2,3,4,6],[5]] => {{1,2,3,4,6},{5}} => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => {{1,2,3,4,5},{6}} => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 4
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => 4
>>> Load all 1032 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => 4
[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] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[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] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [[1,3,4],[2,5,6]] => {{1,3,4},{2,5,6}} => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [[1,3,5],[2,4,6]] => {{1,3,5},{2,4,6}} => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => {{1,3,4},{2,5,6}} => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => {{1,2,3,4,6},{5}} => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => {{1,2,3,4,5},{6}} => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [[1,2,5],[3,4,6]] => {{1,2,5},{3,4,6}} => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [[1,2,4],[3,5,6]] => {{1,2,4},{3,5,6}} => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [[1,2,5],[3,4,6]] => {{1,2,5},{3,4,6}} => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [[1,2,4],[3,5,6]] => {{1,2,4},{3,5,6}} => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [[1,3,5],[2,4,6]] => {{1,3,5},{2,4,6}} => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [[1,3,4],[2,5,6]] => {{1,3,4},{2,5,6}} => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [[1,3,5],[2,4,6]] => {{1,3,5},{2,4,6}} => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [[1,3,4],[2,5,6]] => {{1,3,4},{2,5,6}} => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [[1,2,5],[3,4,6]] => {{1,2,5},{3,4,6}} => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [[1,2,4],[3,5,6]] => {{1,2,4},{3,5,6}} => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [[1,2,5],[3,4,6]] => {{1,2,5},{3,4,6}} => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [[1,2,4],[3,5,6]] => {{1,2,4},{3,5,6}} => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [[1,3,5],[2,4,6]] => {{1,3,5},{2,4,6}} => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [[1,3,4],[2,5,6]] => {{1,3,4},{2,5,6}} => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [[1,2,5],[3,4,6]] => {{1,2,5},{3,4,6}} => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [[1,2,4],[3,5,6]] => {{1,2,4},{3,5,6}} => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 4
[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] => [[1,2,3,4,5,6],[7]] => {{1,2,3,4,5,6},{7}} => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => 5
[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] => [[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => {{1,2,3,4,5,6},{7}} => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => 5
[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] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,5,6] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [[1,2,3,4,5,6],[7]] => {{1,2,3,4,5,6},{7}} => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,3,5,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,3,7,5] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,3,5] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,3,6,4,7] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,3,6,7,4] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,3,7,4,6] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,3,7,4] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,3,4] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 5
[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] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,5,6] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[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] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,4,5,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,7,5] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,4,5] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,4,5,6] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,5,6] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [[1,2,3,4,5,6],[7]] => {{1,2,3,4,5,6},{7}} => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,2,5,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,2,7,5] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,2,5] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,2,4,6,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,2,4,7,6] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,2,6,4,7] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,7,4,6] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,2,4,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,2,7,4] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,2,4] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,2,4,7,5] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,4,5] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,2,4,5] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,2,3,5,7,6] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,7] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,2,3,6,7,5] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,2,3,7,5,6] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,3,6,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,7,6] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,2,5,6,3,7] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,2,5,7,3,6] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,6,3,5,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,7,5] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,7,3,5] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,7,3,5,6] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,2,3,7,6] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,2,6,3,7] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,2,6,7,3] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,2,7,3,6] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,2,3,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,2,7,3] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,2,3] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,2,3,7,5] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,2,7,3,5] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,2,3,6,4,7] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,3,6,7,4] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,2,3,7,4,6] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,6,3,4,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,7,4] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,2,6,7,3,4] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,2,3,4,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,2,3,7,4] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[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] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[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] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,4,6] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,4,5,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,4,7,5] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,4,5] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[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] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,5,6] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,3,6] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,3,5,7] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,3,7,5] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,3,5] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,3,5,6] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,3,4,7,6] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4,7] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,7,4,6] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,3,4,7] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,3,7,4] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,3,4] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,3,4,7,5] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,7,4,5] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,3,4,5] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,5,6] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => {{1,2,3,4,5,6},{7}} => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,1,5,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,1,4,6,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,1,4,7,6] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,1,6,4,7] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,7,4,6] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,1,4,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,1,7,4] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,1,4,7,5] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,4,5] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,1,3,5,7,6] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,1,3,6,5,7] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,1,3,6,7,5] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,1,3,7,5,6] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,5,3,6,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,1,5,3,7,6] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,1,5,6,3,7] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,1,5,7,3,6] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,1,6,3,5,7] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,1,6,3,7,5] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,7,3,5] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,1,7,3,5,6] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,1,3,6,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,1,6,3,7] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,1,6,7,3] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,1,7,3,6] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,1,3,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,1,3] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,7] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,1,3,7,5] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,1,7,3,5] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,1,3,5] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,1,3,5,6] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1,3,6,4,7] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,1,3,6,7,4] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,1,3,7,4,6] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1,6,3,4,7] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,1,6,3,7,4] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,1,6,7,3,4] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,1,7,3,4,6] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,1,3,4,7] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,1,7,3,4] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,1,3,4] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,7,5] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,1,3,7,4,5] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,4,6,5,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,4,6,7,5] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,4,7,5,6] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,5,4,6,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,5,6,4,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,5,6,7,4] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,5,7,4,6] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,6,4,5,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,2,6,4,7,5] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,6,7,4,5] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,2,7,4,5,6] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,4,2,5,7,6] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,7] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,4,2,6,7,5] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,7,5,6] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2,6,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,2,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,4,5,7,2,6] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,4,6,2,5,7] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,4,6,2,7,5] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,4,7,2,5,6] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,5,2,4,7,6] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4,7] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,5,2,6,7,4] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,7,4,6] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,6,2,4,7] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,6,2,7,4] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,6,7,2,4] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,6,2,4,7,5] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,7,4,5] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,6,7,2,4,5] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,5,7,6] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,7] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,1,2,6,7,5] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,7,5,6] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,1,5,2,6,7] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,1,5,6,2,7] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,1,5,7,2,6] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,1,6,2,5,7] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,1,6,2,7,5] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,7,2,5] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,1,7,2,5,6] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,1,2,6,7] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,1,2,7,6] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,1,7,2,6] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,1,2,7] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,1,7,2] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,7] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,1,2,7,5] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,1,7,2,5] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,1,2,5,6] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,6,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,6,4,7] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,1,2,6,7,4] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,1,2,7,4,6] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,1,6,2,4,7] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,6,2,7,4] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,1,6,7,2,4] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,1,7,2,4,6] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,1,2,7,4] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,7,5] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,1,2,7,4,5] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,1,7,2,4,5] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,1,2,4,5] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,3,6,7,5] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,7,5,6] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,2,5,3,6,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,2,5,6,3,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,3] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2,5,7,3,6] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,6,3,5,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,7,5] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,6,7,3,5] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,1,2,7,3,5,6] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,5,2,3,7,6] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3,7] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,5,2,6,7,3] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,5,2,7,3,6] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,5,6,2,3,7] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,5,6,2,7,3] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,5,6,7,2,3] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,1,6,2,3,7,5] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,7,3,5] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,7,2,3,5] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,1,2,3,6,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,1,2,6,3,7] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,1,2,6,7,3] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,1,2,7,3,6] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,1,6,2,7,3] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,1,6,7,2,3] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,1,2,7,3] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,1,7,2,3] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => 5
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,1,2,3,6] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,1,2,7,3,5] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,7,2,3,5] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,1,2,3,5] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,1,2,3,5,6] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,2,6,3,7,4] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,2,6,7,3,4] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,1,2,7,3,4,6] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,6,2,7,3,4] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,6,7,2,3,4] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,1,7,2,3,4,6] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,1,2,7,3,4] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,1,7,2,3,4] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1,7,2,3,4,5] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 5
[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] => [[1,2,3,4,5,6,7],[8]] => {{1,2,3,4,5,6,7},{8}} => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[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] => [[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => 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] => [[1,2,3,4,5,6,7],[8]] => {{1,2,3,4,5,6,7},{8}} => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,5,7] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,5,6,8] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,5,8,6] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,5,6,7] => [[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] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => [[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] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => 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] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 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] => [[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => 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] => [[1,2,3,4,5,6,7],[8]] => {{1,2,3,4,5,6,7},{8}} => 6
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,4,7] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,4,6,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,4,8,6] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,4,6] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,4,6,7] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,4,5,8,7] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5,8] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,4,7,8,5] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,4,8,5,7] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,4,5,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,4,8,5] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,4,5] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,4,5,7] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,4,5,8,6] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,4,8,5,6] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,4,5,6] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[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] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,6,7] => [[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] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 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] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,5,6,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,5,6,7] => [[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] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 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] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,6,7] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 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] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => 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] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 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] => [[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => 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] => [[1,2,3,4,5,6,7],[8]] => {{1,2,3,4,5,6,7},{8}} => 6
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,3,7] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,3,6,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,4,5,7,3,8,6] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,3,6] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,3,6,7] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,3,5,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,3,5] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,3,5,6,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,3,5,6,7] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,3,4,6,7,8] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,3,4,6,8,7] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,3,4,7,6,8] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,3,4,7,8,6] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,3,4,8,6,7] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,4,7,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,3,6,7,4,8] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,3,6,7,8,4] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,2,5,3,7,4,6,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,3,8,4,6,7] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,3,7,4,8] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,3,7,8,4] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,3,8,4] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,3,4] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,3,4,6,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,3,4,6,7] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,3,4,5,7,8] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,3,4,5,8,7] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,6,3,4,7,5,8] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,3,4,7,8,5] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,3,4,8,5,7] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,6,3,7,4,5,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,3,8,4,5,7] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,3,4,5,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,6,8,3,4,5,7] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,3,4,5,6,8] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,3,4,5,8,6] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,3,8,4,5,6] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,3,4,5,6] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[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] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => [[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] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,5,6,7] => [[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] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 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] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 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] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => [[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] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 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] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 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] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 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] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,6,7] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 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] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 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] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,5,6,7] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 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] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => 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] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 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] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,6,7] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 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] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => 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] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 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] => [[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => 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] => [[1,2,3,4,5,6,7],[8]] => {{1,2,3,4,5,6,7},{8}} => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,2,7] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,2,6,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,2,6] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,2,6,7] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,2,5,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,2,7,5,8] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,2,5,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,2,8,5] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,3,4,7,2,5,6,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,2,5,6,7] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,2,4,6,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,2,6,7,4,8] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,2,4,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,2,7,8,4] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,2,4,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,2,8,4] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,2,4] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,2,4,5,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,2,4,5,6,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,2,3,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,2,3,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,3,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,2,3,6,7,5,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,2,3,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,2,3,8,5,6,7] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,3,6,7,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,2,5,6,7,3,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,8,3] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,6,3,5,7,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,7,3,5,6,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,8,3,5,6,7] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,2,6,3,7,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,7,3,8] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,2,6,7,8,3] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,2,3,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,2,7,3,8] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,2,7,8,3] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,2,8,3] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,2,3] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,2,3,5,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,2,3,5,6,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,2,3,4,6,8,7] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,2,3,4,7,8,6] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,2,3,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,2,3,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,3,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,5,2,3,7,4,6,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,2,3,8,4,6,7] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,6,3,4,7,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,8,3,4,6,7] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,2,3,4,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2,3,4,5,8,7] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,2,3,4,7,5,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,3,4,7,8,5] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,2,3,4,8,5,7] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,2,3,7,4,5,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,2,3,8,4,5,7] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,7,3,4,5,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,8,3,4,5,7] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,2,3,4,5,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,2,3,4,8,5,6] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,2,3,8,4,5,6] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,8,3,4,5,6] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[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] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,6,7] => [[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] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,5,6,7] => [[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] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,4,5,7,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => [[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] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 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] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 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] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,3,4,6,7,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,3,4,5,6,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [[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] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => 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] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 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] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 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] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,6,7] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 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] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 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] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,7,5,6,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,5,6,7] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 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] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 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] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 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] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 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] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,4,5,7,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,4,5,6,7] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 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] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => 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] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 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] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 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] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,6,7] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 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] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 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] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 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] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,5,6,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,5,6,7] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 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] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => 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] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 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] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 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] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,6,7] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 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] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => 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] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 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] => [[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => 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] => [[1,2,3,4,5,6,7],[8]] => {{1,2,3,4,5,6,7},{8}} => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,1,6,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,1,8,6] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,1,6,7] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,1,5,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,1,7,5,8] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,1,7,8,5] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,1,5,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,1,5] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,1,5,6,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,1,5,6,7] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,1,4,6,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,1,6,4,7,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,1,6,7,8,4] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,1,4,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,1,7,8,4] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,1,4,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,1,8,4] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,1,4] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,1,4,5,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,1,4,5,6,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,3,6,7,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3,7,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,1,5,6,7,3,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,8,3] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,1,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,4,5,1,6,3,7,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,1,6,7,8,3] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,1,3,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,1,7,3,8] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,1,7,8,3] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,1,3,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,1,3] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => 6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,1,3,4,6,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,2,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,2,4,5,7,8,6] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,4,6,7,5,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,4,6,7,8,5] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,2,4,8,5,6,7] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,6,7,4,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,5,6,7,8,4] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,2,7,4,5,6,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,2,8,4,5,6,7] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,2,6,7,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,4,5,6,7,2,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,8,2] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,7,2,4,5,6,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,2,6,7,8] => [[1,2,4,6,7,8],[3,5]] => {{1,2,4,6,7,8},{3,5}} => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2,7,8] => [[1,2,4,5,7,8],[3,6]] => {{1,2,4,5,7,8},{3,6}} => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,1,5,6,7,2,8] => [[1,2,4,5,6,8],[3,7]] => {{1,2,4,5,6,8},{3,7}} => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,8,2] => [[1,2,4,5,6,7],[3,8]] => {{1,2,4,5,6,7},{3,8}} => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,1,2,6,7,8] => [[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => 6
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,1,6,2,7,8] => [[1,2,3,5,7,8],[4,6]] => {{1,2,3,5,7,8},{4,6}} => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,1,6,7,2,8] => [[1,2,3,5,6,8],[4,7]] => {{1,2,3,5,6,8},{4,7}} => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,1,6,7,8,2] => [[1,2,3,5,6,7],[4,8]] => {{1,2,3,5,6,7},{4,8}} => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,1,2,7,8] => [[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,1,7,2,8] => [[1,2,3,4,6,8],[5,7]] => {{1,2,3,4,6,8},{5,7}} => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,1,7,8,2] => [[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,1,2,8] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,1,8,2] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,1,2,4,6,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,1,2,4,5,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,1,2,4,5,6,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,3,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,3,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,3,5,7,8,6] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,3,5,8,6,7] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,3,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,3,6,7,5,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,3,6,7,8,5] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,2,5,3,6,7,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,2,5,6,3,7,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,6,7,3,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,5,6,7,8,3] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,7,3,5,6,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,2,8,3,5,6,7] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,3,6,7,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,1,7,2,3,5,6,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,1,2,3,6,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,6,1,2,3,5,7,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,1,2,3,5,6,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,4,7,8,6] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,4,8,6,7] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,2,3,6,4,7,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,2,3,6,7,4,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,2,3,6,7,8,4] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,2,3,8,4,6,7] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,2,6,3,4,7,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,1,2,7,3,4,6,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,1,2,8,3,4,6,7] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,1,7,2,3,4,6,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,1,2,3,4,6,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,7,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,2,3,4,7,5,8] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,2,3,4,7,8,5] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2,3,4,8,5,7] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,1,2,3,8,4,5,7] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,2,7,3,4,5,8] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2,8,3,4,5,7] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,7,2,3,4,5,8] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,8] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => [[1,3,4,5,6,7],[2,8]] => {{1,3,4,5,6,7},{2,8}} => 4
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,8,5,6] => [[1,3,4,5,6,8],[2,7]] => {{1,3,4,5,6,8},{2,7}} => 4
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1,2,3,8,4,5,6] => [[1,3,4,5,7,8],[2,6]] => {{1,3,4,5,7,8},{2,6}} => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1,2,8,3,4,5,6] => [[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => 4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [[1,3,5,6,7,8],[2,4]] => {{1,3,5,6,7,8},{2,4}} => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 6
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,0,1 4,0,1 2,0,11,0,1 15,0,26,0,1 5,0,69,0,57,0,1 56,0,252,0,120,0,1
F2=1+q2
F3=4 q+q3
F4=2+11 q2+q4
F5=15 q+26 q3+q5
F6=5+69 q2+57 q4+q6
F7=56 q+252 q3+120 q5+q7
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.
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
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.
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 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength n in an n×n square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength n in an n×n square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
rows
Description
The set partition whose blocks are the rows of the tableau.
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