Identifier
Values
[1,0] => [2,1] => [[1],[2]] => 2
[1,0,1,0] => [3,1,2] => [[1,2],[3]] => 1
[1,1,0,0] => [2,3,1] => [[1,3],[2]] => 2
[1,0,1,0,1,0] => [4,1,2,3] => [[1,2,3],[4]] => 1
[1,0,1,1,0,0] => [3,1,4,2] => [[1,2],[3,4]] => 1
[1,1,0,0,1,0] => [2,4,1,3] => [[1,3],[2,4]] => 2
[1,1,0,1,0,0] => [4,3,1,2] => [[1,2],[3],[4]] => 1
[1,1,1,0,0,0] => [2,3,4,1] => [[1,3,4],[2]] => 2
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [[1,2,3,4],[5]] => 1
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [[1,2,3],[4,5]] => 1
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [[1,2,4],[3,5]] => 1
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [[1,2,3],[4],[5]] => 1
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [[1,2,5],[3,4]] => 1
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [[1,3,4],[2,5]] => 2
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [[1,3,5],[2,4]] => 2
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [[1,2,4],[3],[5]] => 1
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [[1,2,3],[4],[5]] => 1
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [[1,2],[3,5],[4]] => 1
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [[1,3,4],[2,5]] => 2
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [[1,3],[2,4],[5]] => 2
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [[1,2],[3,4],[5]] => 1
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[1,3,4,5],[2]] => 2
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [[1,2,3,4,5],[6]] => 1
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [[1,2,3,4],[5,6]] => 1
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [[1,2,3,5],[4,6]] => 1
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [[1,2,3,4],[5],[6]] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [[1,2,3,6],[4,5]] => 1
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [[1,2,4,5],[3,6]] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [[1,2,4],[3,5,6]] => 1
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [[1,2,3,5],[4],[6]] => 1
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [[1,2,3,4],[5],[6]] => 1
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [[1,2,3],[4,6],[5]] => 1
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [[1,2,5],[3,4,6]] => 1
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [[1,2,4],[3,5],[6]] => 1
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [[1,2,3],[4,5],[6]] => 1
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [[1,2,5,6],[3,4]] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [[1,3,4,5],[2,6]] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [[1,3,4],[2,5,6]] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [[1,3,5],[2,4,6]] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [[1,3,4],[2,5],[6]] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [[1,3,5,6],[2,4]] => 2
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [[1,2,4,5],[3],[6]] => 1
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [[1,2,4],[3,6],[5]] => 1
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[1,2,3,5],[4],[6]] => 1
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [[1,2,3,4],[5,6]] => 1
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [[1,2,3],[4,6],[5]] => 1
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [[1,2,5],[3,6],[4]] => 1
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [[1,2,4],[3,5],[6]] => 1
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [[1,2,3],[4,5],[6]] => 1
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [[1,2,6],[3,5],[4]] => 1
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [[1,3,4,5],[2,6]] => 2
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [[1,3,4,6],[2,5]] => 2
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [[1,3,5],[2,4],[6]] => 2
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [[1,3,4],[2,5],[6]] => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [[1,3,6],[2,4],[5]] => 2
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[1,2,5],[3,4],[6]] => 1
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [[1,2,4],[3,5],[6]] => 1
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [[1,2,3],[4],[5],[6]] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [[1,2,6],[3,4],[5]] => 1
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [[1,3,4,5],[2,6]] => 2
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [[1,3,4],[2,5],[6]] => 2
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [[1,3,5],[2,4],[6]] => 2
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [[1,2,5],[3,4],[6]] => 1
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[1,3,4,5,6],[2]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [[1,2,3,4,6],[5,7]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [[1,2,3,4,5],[6],[7]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [[1,2,3,4,7],[5,6]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [[1,2,3,5,6],[4,7]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [[1,2,3,5],[4,6,7]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [[1,2,3,4,6],[5],[7]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [[1,2,3,4,5],[6],[7]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [[1,2,3,4],[5,7],[6]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [[1,2,3,6],[4,5,7]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [[1,2,3,5],[4,6],[7]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [[1,2,3,4],[5,6],[7]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [[1,2,3,6,7],[4,5]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [[1,2,4,5,6],[3,7]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [[1,2,4,5],[3,6,7]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [[1,2,4,6],[3,5,7]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [[1,2,4,5],[3,6],[7]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [[1,2,4,7],[3,5,6]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [[1,2,3,5,6],[4],[7]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [[1,2,3,5],[4,7],[6]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [[1,2,3,4,6],[5],[7]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [[1,2,3,4,5],[6,7]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [[1,2,3,4],[5,7],[6]] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [[1,2,3,6],[4,7],[5]] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [[1,2,3,5],[4,6],[7]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [[1,2,3,4],[5,6],[7]] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [[1,2,3,7],[4,6],[5]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [[1,2,5,6],[3,4,7]] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [[1,2,5,7],[3,4,6]] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [[1,2,4,6],[3,5],[7]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [[1,2,4,5],[3,6],[7]] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [[1,2,4],[3,5,7],[6]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [[1,2,3,6],[4,5],[7]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [[1,2,3,5],[4,6],[7]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [[1,2,3,4],[5],[6],[7]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [[1,2,3,7],[4,5],[6]] => 1
>>> Load all 723 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [[1,2,5,6],[3,4,7]] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [[1,2,5],[3,4,6],[7]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [[1,2,4],[3,5,6],[7]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [[1,2,3,6],[4,5],[7]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [[1,3,4,5,6],[2,7]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [[1,3,4,5],[2,6,7]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [[1,3,4,6],[2,5,7]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [[1,3,4,5],[2,6],[7]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [[1,3,4,7],[2,5,6]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [[1,3,5,6],[2,4,7]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [[1,3,5,7],[2,4,6]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [[1,3,4,6],[2,5],[7]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [[1,3,4,5],[2,6],[7]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [[1,3,4],[2,5,7],[6]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [[1,3,5,6],[2,4,7]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [[1,3,5],[2,4,6],[7]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [[1,3,4],[2,5,6],[7]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [[1,3,5,6,7],[2,4]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [[1,2,4,5,6],[3],[7]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [[1,2,4,5],[3,7],[6]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [[1,2,4,6],[3,7],[5]] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [[1,2,4,5],[3,6],[7]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [[1,2,4,7],[3,6],[5]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [[1,2,3,5,6],[4],[7]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [[1,2,3,5],[4,7],[6]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [[1,2,3,4,6],[5,7]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [[1,2,3,4,5],[6],[7]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [[1,2,3,4],[5,6,7]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [[1,2,3,6],[4,7],[5]] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [[1,2,3,5],[4,6],[7]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [[1,2,3,4],[5,6],[7]] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [[1,2,3,7],[4,6],[5]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [[1,2,5,6],[3,7],[4]] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [[1,2,5],[3,6,7],[4]] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [[1,2,4,6],[3,5],[7]] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [[1,2,4,5],[3,6],[7]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [[1,2,4],[3,5,7],[6]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [[1,2,3,6],[4,5],[7]] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [[1,2,3,5],[4,6],[7]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [[1,2,3],[4,5,7],[6]] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [[1,2,6],[3,5,7],[4]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [[1,2,5],[3,6],[4,7]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [[1,2,4],[3,5,6],[7]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [[1,2,3],[4,5,6],[7]] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [[1,2,6,7],[3,5],[4]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [[1,3,4,5,6],[2,7]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [[1,3,4,5],[2,6,7]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [[1,3,4,6],[2,5,7]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [[1,3,4,5],[2,6],[7]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [[1,3,4,6,7],[2,5]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [[1,3,5,6],[2,4],[7]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [[1,3,5],[2,4,7],[6]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [[1,3,4,6],[2,5],[7]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [[1,3,4,5],[2,6,7]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [[1,3,4],[2,5,7],[6]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [[1,3,6],[2,4,7],[5]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [[1,3,5],[2,4,6],[7]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [[1,3,4],[2,5,6],[7]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [[1,3,6,7],[2,4],[5]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [[1,2,5,6],[3,4],[7]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [[1,2,5],[3,4,7],[6]] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [[1,2,4,6],[3,5],[7]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [[1,2,4,5],[3,7],[6]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [[1,2,4],[3,5,7],[6]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [[1,2,3,6],[4],[5],[7]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [[1,2,3,5],[4,7],[6]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [[1,2,6],[3,4,7],[5]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [[1,2,5],[3,4,6],[7]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [[1,2,4],[3,5,6],[7]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [[1,2,3],[4,6],[5],[7]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [[1,2,6,7],[3,4],[5]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [[1,3,4,5,6],[2,7]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [[1,3,4,5,7],[2,6]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [[1,3,4,6],[2,5],[7]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [[1,3,4,5],[2,6],[7]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [[1,3,4,7],[2,5],[6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [[1,3,5,6],[2,4],[7]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [[1,3,5],[2,4,6],[7]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [[1,3,4],[2,5],[6],[7]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [[1,3,5,7],[2,4],[6]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[1,2,5,6],[3,4],[7]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [[1,2,5],[3,4,6],[7]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [[1,2,4],[3,5],[6],[7]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [[1,2,3],[4,5],[6],[7]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [[1,2,5,7],[3,4],[6]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [[1,3,4,5,6],[2,7]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [[1,3,4,5],[2,6],[7]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [[1,3,4,6],[2,5],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [[1,3,5,6],[2,4],[7]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [[1,2,3,4,5,6],[7,8]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [[1,2,3,4,5,7],[6,8]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [[1,2,3,4,5,6],[7],[8]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => [[1,2,3,4,5,8],[6,7]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [[1,2,3,4,6,7],[5,8]] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [[1,2,3,4,6],[5,7,8]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => [[1,2,3,4,5,7],[6],[8]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => [[1,2,3,4,5,6],[7],[8]] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [[1,2,3,4,7],[5,6,8]] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => [[1,2,3,4,6],[5,7],[8]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7],[8]] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => [[1,2,3,4,7,8],[5,6]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [4,1,2,7,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [[1,2,3,5,7],[4,6,8]] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [4,1,2,8,3,7,5,6] => [[1,2,3,5,6],[4,7],[8]] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,1,2,6,3,7,8,5] => [[1,2,3,5,8],[4,6,7]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => [[1,2,3,4,6,7],[5],[8]] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6] => [[1,2,3,4,6],[5,8],[7]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,1,2,6,3,4,5,7] => [[1,2,3,4,5,7],[6],[8]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [7,1,2,6,3,4,8,5] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,1,2,5,3,8,4,7] => [[1,2,3,4,7],[5,8],[6]] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [8,1,2,5,3,7,4,6] => [[1,2,3,4,6],[5,7],[8]] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => [[1,2,3,4,5],[6,7],[8]] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,1,2,5,3,7,8,4] => [[1,2,3,4,8],[5,7],[6]] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => [[1,2,3,6,7],[4,5,8]] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [4,1,2,5,7,3,8,6] => [[1,2,3,6,8],[4,5,7]] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [4,1,2,8,6,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [4,1,2,8,7,3,5,6] => [[1,2,3,5,6],[4,7],[8]] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6],[8]] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6] => [[1,2,3,4,6],[5,7],[8]] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => [[1,2,3,4,5],[6],[7],[8]] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4] => [[1,2,3,4,8],[5,6],[7]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [[1,2,3,6,7],[4,5,8]] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => [[1,2,3,6],[4,5,7],[8]] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,1,2,8,6,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [[1,2,3,4,7],[5,6],[8]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [[1,2,3,6,7,8],[4,5]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [[1,2,4,5,6],[3,7,8]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7] => [[1,2,4,5,7],[3,6,8]] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6] => [[1,2,4,5,6],[3,7],[8]] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,1,6,2,4,7,8,5] => [[1,2,4,5,8],[3,6,7]] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [[1,2,4,6,7],[3,5,8]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [[1,2,4,6],[3,5,7,8]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,8,2,6,4,5,7] => [[1,2,4,5,7],[3,6],[8]] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6] => [[1,2,4,5,6],[3,7],[8]] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,1,7,2,6,4,8,5] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [[1,2,4,7],[3,5,6,8]] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,5,2,8,7,4,6] => [[1,2,4,6],[3,5,7],[8]] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,8,2,6,7,4,5] => [[1,2,4,5],[3,6,7],[8]] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,1,5,2,6,7,8,4] => [[1,2,4,7,8],[3,5,6]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => [[1,2,3,5,6,7],[4],[8]] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => [[1,2,3,5,6],[4,8],[7]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,1,4,2,3,8,5,7] => [[1,2,3,5,7],[4,8],[6]] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [8,1,4,2,3,7,5,6] => [[1,2,3,5,6],[4,7],[8]] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,1,4,2,3,7,8,5] => [[1,2,3,5,8],[4,7],[6]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => [[1,2,3,4,6,7],[5],[8]] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,1,5,2,3,4,8,6] => [[1,2,3,4,6],[5,8],[7]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => [[1,2,3,4,5,6],[7],[8]] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => [[1,2,3,4,7],[5,8],[6]] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [8,1,5,2,3,7,4,6] => [[1,2,3,4,6],[5,7],[8]] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => [[1,2,3,4,5],[6,7],[8]] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,1,5,2,3,7,8,4] => [[1,2,3,4,8],[5,7],[6]] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [5,1,4,2,8,3,6,7] => [[1,2,3,6,7],[4,8],[5]] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => [[1,2,3,6],[4,7,8],[5]] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [8,1,4,2,7,3,5,6] => [[1,2,3,5,6],[4,7],[8]] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,1,5,2,6,3,4,7] => [[1,2,3,4,7],[5,6],[8]] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [8,1,5,2,7,3,4,6] => [[1,2,3,4,6],[5,7],[8]] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => [[1,2,3,4],[5,6,8],[7]] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,4,2,6,8,3,7] => [[1,2,3,7],[4,6,8],[5]] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,1,4,2,8,7,3,6] => [[1,2,3,6],[4,7],[5,8]] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [8,1,4,2,6,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4] => [[1,2,3,4],[5,6,7],[8]] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4,2,6,7,8,3] => [[1,2,3,7,8],[4,6],[5]] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,8,2,5,6,7] => [[1,2,5,6,7],[3,4,8]] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => [[1,2,5,6],[3,4,7,8]] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [[1,2,5,7],[3,4,6,8]] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,4,8,2,7,5,6] => [[1,2,5,6],[3,4,7],[8]] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => [[1,2,5,7,8],[3,4,6]] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,8,5,2,4,6,7] => [[1,2,4,6,7],[3,5],[8]] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,7,5,2,4,8,6] => [[1,2,4,6],[3,5,8],[7]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [[1,2,4,5,7],[3,6],[8]] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6] => [[1,2,4,5,6],[3,7,8]] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,7,6,2,4,8,5] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,6,5,2,8,4,7] => [[1,2,4,7],[3,5,8],[6]] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,8,5,2,7,4,6] => [[1,2,4,6],[3,5,7],[8]] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,8,6,2,7,4,5] => [[1,2,4,5],[3,6,7],[8]] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,5,2,7,8,4] => [[1,2,4,8],[3,5,7],[6]] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5],[8]] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,1,4,5,2,3,8,6] => [[1,2,3,6],[4,5,8],[7]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,1,4,6,2,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => [[1,2,3,5,6],[4,8],[7]] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [7,1,4,6,2,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,1,6,5,2,3,4,7] => [[1,2,3,4,7],[5],[6],[8]] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6] => [[1,2,3,4,6],[5,8],[7]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,1,4,5,2,8,3,7] => [[1,2,3,7],[4,5,8],[6]] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => [[1,2,3,6],[4,5,7],[8]] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [8,1,4,6,2,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4] => [[1,2,3,4],[5,7],[6],[8]] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [6,1,4,5,2,7,8,3] => [[1,2,3,7,8],[4,5],[6]] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => [[1,2,5,6,7],[3,4,8]] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => [[1,2,5,6,8],[3,4,7]] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,1,4,8,6,2,5,7] => [[1,2,5,7],[3,4,6],[8]] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6] => [[1,2,5,6],[3,4,7],[8]] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [3,1,4,7,6,2,8,5] => [[1,2,5,8],[3,4,6],[7]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,8,5,6,2,4,7] => [[1,2,4,7],[3,5,6],[8]] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => [[1,2,4,6],[3,5,7],[8]] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,1,8,7,6,2,4,5] => [[1,2,4,5],[3,6],[7],[8]] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,1,7,5,6,2,8,4] => [[1,2,4,8],[3,5,6],[7]] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,1,4,5,6,2,3,7] => [[1,2,3,6,7],[4,5],[8]] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => [[1,2,3,6],[4,5,7],[8]] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => [[1,2,3,5],[4,6],[7],[8]] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [8,1,7,5,6,2,3,4] => [[1,2,3,4],[5,6],[7],[8]] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3] => [[1,2,3,6,8],[4,5],[7]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => [[1,2,5,6,7],[3,4,8]] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6] => [[1,2,5,6],[3,4,7],[8]] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,1,4,8,6,7,2,5] => [[1,2,5,7],[3,4,6],[8]] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,8,5,6,7,2,4] => [[1,2,4,7],[3,5,6],[8]] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [8,1,4,5,6,7,2,3] => [[1,2,3,6,7],[4,5],[8]] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [[1,2,5,6,7,8],[3,4]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => [[1,3,4,5,6],[2,7,8]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => [[1,3,4,5,7],[2,6,8]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => [[1,3,4,5,6],[2,7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => [[1,3,4,5,8],[2,6,7]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => [[1,3,4,6,7],[2,5,8]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [[1,3,4,6],[2,5,7,8]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7] => [[1,3,4,5,7],[2,6],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,8,1,3,7,4,5,6] => [[1,3,4,5,6],[2,7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,7,1,3,6,4,8,5] => [[1,3,4,5],[2,6,8],[7]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,5,1,3,6,8,4,7] => [[1,3,4,7],[2,5,6,8]] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,3,8,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,8,1,3,6,7,4,5] => [[1,3,4,5],[2,6,7],[8]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,5,1,3,6,7,8,4] => [[1,3,4,7,8],[2,5,6]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [[1,3,5,6,7],[2,4,8]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,7,3,5,8,6] => [[1,3,5,6],[2,4,7,8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [[1,3,5,7],[2,4,6,8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,8,3,7,5,6] => [[1,3,5,6],[2,4,7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => [[1,3,5,7,8],[2,4,6]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7] => [[1,3,4,6,7],[2,5],[8]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,7,1,5,3,4,8,6] => [[1,3,4,6],[2,5,8],[7]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7] => [[1,3,4,5,7],[2,6],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [[1,3,4,5,6],[2,7,8]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,7,1,6,3,4,8,5] => [[1,3,4,5],[2,6,8],[7]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,6,1,5,3,8,4,7] => [[1,3,4,7],[2,5,8],[6]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,8,1,5,3,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,6,1,5,3,7,8,4] => [[1,3,4,8],[2,5,7],[6]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => [[1,3,5,6,7],[2,4,8]] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,5,7,3,8,6] => [[1,3,5,6,8],[2,4,7]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => [[1,3,5,7],[2,4,6],[8]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,8,7,3,5,6] => [[1,3,5,6],[2,4,7],[8]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,4,1,7,6,3,8,5] => [[1,3,5,8],[2,4,6],[7]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,8,1,5,6,3,4,7] => [[1,3,4,7],[2,5,6],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6] => [[1,3,4,6],[2,5,7],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => [[1,3,4,5],[2,6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,7,1,5,6,3,8,4] => [[1,3,4,8],[2,5,6],[7]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => [[1,3,5,6,7],[2,4,8]] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,8,7,3,6] => [[1,3,5,6],[2,4,7],[8]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1,8,6,7,3,5] => [[1,3,5,7],[2,4,6],[8]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,8,1,5,6,7,3,4] => [[1,3,4,7],[2,5,6],[8]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [[1,2,4,5,6,7],[3],[8]] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => [[1,2,4,5,6],[3,8],[7]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,3,1,2,4,8,5,7] => [[1,2,4,5,7],[3,8],[6]] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => [[1,2,4,5,6],[3,7],[8]] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,3,1,2,4,7,8,5] => [[1,2,4,5,8],[3,7],[6]] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,3,1,2,8,4,6,7] => [[1,2,4,6,7],[3,8],[5]] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,3,1,2,7,4,8,6] => [[1,2,4,6],[3,7,8],[5]] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,3,1,2,6,4,5,7] => [[1,2,4,5,7],[3,6],[8]] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [8,3,1,2,7,4,5,6] => [[1,2,4,5,6],[3,7],[8]] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1,2,6,8,4,7] => [[1,2,4,7],[3,6,8],[5]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,1,2,8,7,4,6] => [[1,2,4,6],[3,7],[5,8]] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [8,3,1,2,6,7,4,5] => [[1,2,4,5],[3,6,7],[8]] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,1,2,6,7,8,4] => [[1,2,4,7,8],[3,6],[5]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [[1,2,3,5,6,7],[4],[8]] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,4,1,2,3,5,8,6] => [[1,2,3,5,6],[4,8],[7]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,1,2,3,8,5,7] => [[1,2,3,5,7],[4,8],[6]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,4,1,2,3,7,5,6] => [[1,2,3,5,6],[4,7],[8]] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,4,1,2,3,7,8,5] => [[1,2,3,5,8],[4,7],[6]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [[1,2,3,4,5,7],[6],[8]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7],[8]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => [[1,2,3,4,7],[5,6,8]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [[1,2,3,4,6],[5,7],[8]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => [[1,2,3,4,5],[6,7],[8]] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => [[1,2,3,4,8],[5,6,7]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,2,8,3,6,7] => [[1,2,3,6,7],[4,8],[5]] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,4,1,2,7,3,8,6] => [[1,2,3,6],[4,7,8],[5]] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,4,1,2,6,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => [[1,2,3,5,6],[4,7],[8]] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7] => [[1,2,3,4,7],[5,6],[8]] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [[1,2,3,4,6],[5,7],[8]] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5] => [[1,2,3,4,5],[6],[7],[8]] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [[1,2,3,4],[5,6,8],[7]] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [5,4,1,2,6,8,3,7] => [[1,2,3,7],[4,6,8],[5]] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6] => [[1,2,3,6],[4,7],[5,8]] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [[1,2,3,4],[5,6,7],[8]] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,4,1,2,6,7,8,3] => [[1,2,3,7,8],[4,6],[5]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7] => [[1,2,5,6,7],[3,8],[4]] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,3,1,7,2,5,8,6] => [[1,2,5,6],[3,7,8],[4]] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7] => [[1,2,5,7],[3,6,8],[4]] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3,1,8,2,7,5,6] => [[1,2,5,6],[3,7],[4,8]] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3,1,6,2,7,8,5] => [[1,2,5,8],[3,6,7],[4]] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,3,1,5,2,4,6,7] => [[1,2,4,6,7],[3,5],[8]] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6] => [[1,2,4,6],[3,5,8],[7]] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,3,1,6,2,4,5,7] => [[1,2,4,5,7],[3,6],[8]] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [[1,2,4,5,6],[3,8],[7]] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,1,5,2,8,4,7] => [[1,2,4,7],[3,5,8],[6]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => [[1,2,4,6],[3,5,7],[8]] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8,3,1,6,2,7,4,5] => [[1,2,4,5],[3,6,7],[8]] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4] => [[1,2,4,8],[3,5,7],[6]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,4,1,5,2,3,6,7] => [[1,2,3,6,7],[4,5],[8]] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => [[1,2,3,6],[4,5,8],[7]] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,4,1,6,2,3,5,7] => [[1,2,3,5,7],[4,6],[8]] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [[1,2,3,5,6],[4,8],[7]] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7] => [[1,2,3,4,7],[5,8],[6]] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [[1,2,3,4,6],[5],[7],[8]] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [[1,2,3,4,5],[6],[7],[8]] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [[1,2,3,4],[5,7,8],[6]] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => [[1,2,3,7],[4,5,8],[6]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6] => [[1,2,3,6],[4,5,7],[8]] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => [[1,2,3,5],[4,6,7],[8]] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [[1,2,3,4],[5,7],[6,8]] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => [[1,2,3,8],[4,5,7],[6]] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,5,8,2,6,7] => [[1,2,6,7],[3,5,8],[4]] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [4,3,1,5,7,2,8,6] => [[1,2,6,8],[3,5,7],[4]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [4,3,1,8,6,2,5,7] => [[1,2,5,7],[3,6],[4,8]] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => [[1,2,5,6],[3,7],[4,8]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,1,7,6,2,8,5] => [[1,2,5],[3,6,8],[4,7]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => [[1,2,4,7],[3,5,6],[8]] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => [[1,2,4,6],[3,5,7],[8]] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => [[1,2,4,5],[3,6],[7],[8]] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => [[1,2,4,8],[3,5,6],[7]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => [[1,2,3,7],[4,5,6],[8]] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => [[1,2,3,6],[4,5,7],[8]] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => [[1,2,3,5],[4,6],[7],[8]] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [[1,2,3,4],[5,6],[7,8]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => [[1,2,3,8],[4,5,6],[7]] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => [[1,2,6,7],[3,5,8],[4]] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6] => [[1,2,6],[3,5,7],[4,8]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => [[1,2,5],[3,6,7],[4,8]] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8,3,1,5,6,7,2,4] => [[1,2,4,7],[3,5,6],[8]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [[1,2,3,7],[4,5,6],[8]] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [[1,2,6,7,8],[3,5],[4]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,3,7,1,4,5,8,6] => [[1,3,4,5,6],[2,7,8]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => [[1,3,4,5,7],[2,6,8]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,3,8,1,4,7,5,6] => [[1,3,4,5,6],[2,7],[8]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,3,6,1,4,7,8,5] => [[1,3,4,5,8],[2,6,7]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => [[1,3,4,6,7],[2,5,8]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => [[1,3,4,6,8],[2,5,7]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,3,8,1,6,4,5,7] => [[1,3,4,5,7],[2,6],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => [[1,3,4,5,6],[2,7],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,3,7,1,6,4,8,5] => [[1,3,4,5],[2,6,8],[7]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => [[1,3,4,6,7],[2,5,8]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,3,5,1,8,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,3,8,1,6,7,4,5] => [[1,3,4,5],[2,6,7],[8]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => [[1,3,5,6,7],[2,4],[8]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,7,4,1,3,5,8,6] => [[1,3,5,6],[2,4,8],[7]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => [[1,3,5,7],[2,4,8],[6]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,8,4,1,3,7,5,6] => [[1,3,5,6],[2,4,7],[8]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,6,4,1,3,7,8,5] => [[1,3,5,8],[2,4,7],[6]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7] => [[1,3,4,6,7],[2,5],[8]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6] => [[1,3,4,6],[2,5,8],[7]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7] => [[1,3,4,5,7],[2,6,8]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [[1,3,4,5,6],[2,7],[8]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [[1,3,4,5],[2,6,7,8]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,6,5,1,3,8,4,7] => [[1,3,4,7],[2,5,8],[6]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => [[1,3,4,5],[2,6,7],[8]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,6,5,1,3,7,8,4] => [[1,3,4,8],[2,5,7],[6]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,5,4,1,8,3,6,7] => [[1,3,6,7],[2,4,8],[5]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,5,4,1,7,3,8,6] => [[1,3,6,8],[2,4,7],[5]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => [[1,3,5,7],[2,4,6],[8]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [[1,3,5,6],[2,4,7],[8]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,7,4,1,6,3,8,5] => [[1,3,5,8],[2,4,6],[7]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7] => [[1,3,4,7],[2,5,6],[8]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [[1,3,4,6],[2,5,7],[8]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => [[1,3,4,5],[2,6,8],[7]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4] => [[1,3,4,8],[2,5,6],[7]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,5,4,1,6,8,3,7] => [[1,3,6,7],[2,4,8],[5]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,5,4,1,8,7,3,6] => [[1,3,6],[2,4,7],[5,8]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => [[1,3,5,7],[2,4,6],[8]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => [[1,3,4,7],[2,5,6],[8]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,5,4,1,6,7,8,3] => [[1,3,6,7,8],[2,4],[5]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6] => [[1,2,5,6],[3,4,8],[7]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,3,4,1,2,8,5,7] => [[1,2,5,7],[3,4,8],[6]] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [8,3,4,1,2,7,5,6] => [[1,2,5,6],[3,4,7],[8]] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3,4,1,2,7,8,5] => [[1,2,5,8],[3,4,7],[6]] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,3,5,1,2,4,6,7] => [[1,2,4,6,7],[3,5],[8]] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6] => [[1,2,4,6],[3,5,8],[7]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,3,8,1,2,4,5,7] => [[1,2,4,5,7],[3,8],[6]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => [[1,2,4,5,6],[3,7],[8]] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => [[1,2,4,5],[3,7,8],[6]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => [[1,2,4,7],[3,5,8],[6]] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6] => [[1,2,4,6],[3,5,7],[8]] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => [[1,2,4,5],[3,7],[6,8]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [6,3,5,1,2,7,8,4] => [[1,2,4,8],[3,5,7],[6]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,5,4,1,2,3,6,7] => [[1,2,3,6,7],[4],[5],[8]] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => [[1,2,3,6],[4,8],[5],[7]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [[1,2,3,5,7],[4,8],[6]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => [[1,2,3,5,6],[4],[7],[8]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => [[1,2,3,5],[4,7,8],[6]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [[1,2,3,4,7],[5,8],[6]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [[1,2,3,4,6],[5],[7],[8]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => [[1,2,3,4],[5,7,8],[6]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,5,4,1,2,8,3,7] => [[1,2,3,7],[4,8],[5],[6]] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => [[1,2,3,6],[4,7],[5],[8]] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [[1,2,3,5],[4,7],[6,8]] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => [[1,2,3,4],[5,7],[6,8]] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => [[1,2,3,8],[4,7],[5],[6]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,3,4,1,8,2,6,7] => [[1,2,6,7],[3,4,8],[5]] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,3,4,1,7,2,8,6] => [[1,2,6,8],[3,4,7],[5]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,3,4,1,6,2,5,7] => [[1,2,5,7],[3,4,6],[8]] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => [[1,2,5,6],[3,4,7],[8]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7,3,4,1,6,2,8,5] => [[1,2,5,8],[3,4,6],[7]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,3,5,1,6,2,4,7] => [[1,2,4,7],[3,5,6],[8]] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => [[1,2,4,6],[3,5,7],[8]] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [[1,2,4,5],[3,6],[7,8]] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4] => [[1,2,4,8],[3,5,6],[7]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => [[1,2,3,7],[4,6],[5],[8]] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => [[1,2,3,6],[4,7],[5],[8]] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [[1,2,3,5],[4,6],[7,8]] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => [[1,2,3,4],[5,6],[7,8]] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => [[1,2,3],[4,6,8],[5],[7]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [5,3,4,1,6,8,2,7] => [[1,2,6,7],[3,4,8],[5]] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6] => [[1,2,6],[3,4,7],[5,8]] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => [[1,2,5,7],[3,4,6],[8]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => [[1,2,4,7],[3,5,6],[8]] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [[1,2,3],[4,6,7],[5],[8]] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => [[1,2,6,7,8],[3,4],[5]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,4,7,1,5,8,6] => [[1,3,4,5,6],[2,7,8]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,4,6,1,8,5,7] => [[1,3,4,5,7],[2,6,8]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,4,8,1,7,5,6] => [[1,3,4,5,6],[2,7],[8]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => [[1,3,4,5,7,8],[2,6]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,8,5,1,4,6,7] => [[1,3,4,6,7],[2,5],[8]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,7,5,1,4,8,6] => [[1,3,4,6],[2,5,8],[7]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,8,6,1,4,5,7] => [[1,3,4,5,7],[2,6],[8]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6] => [[1,3,4,5,6],[2,7,8]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => [[1,3,4,5],[2,6,8],[7]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,6,5,1,8,4,7] => [[1,3,4,7],[2,5,8],[6]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => [[1,3,4,6],[2,5,7],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5] => [[1,3,4,5],[2,6,7],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => [[1,3,4,7,8],[2,5],[6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => [[1,3,5,6,7],[2,4],[8]] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,7,4,5,1,3,8,6] => [[1,3,5,6],[2,4,8],[7]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => [[1,3,5,7],[2,4,6],[8]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [[1,3,5,6],[2,4,8],[7]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5] => [[1,3,5,8],[2,4,6],[7]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [[1,3,4,7],[2,5],[6],[8]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => [[1,3,4,6],[2,5,8],[7]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => [[1,3,4,5],[2,6,8],[7]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => [[1,3,4],[2,5,8],[6],[7]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,6,4,5,1,8,3,7] => [[1,3,5,7],[2,4,8],[6]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [[1,3,5,6],[2,4,7],[8]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [[1,3,5,7],[2,4,6],[8]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [[1,3,4],[2,5,7],[6],[8]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => [[1,3,5,7,8],[2,4],[6]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,3,4,5,1,2,6,7] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,3,4,5,1,2,8,6] => [[1,2,5,6],[3,4,8],[7]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,3,4,6,1,2,5,7] => [[1,2,5,7],[3,4,6],[8]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [[1,2,5,6],[3,4,8],[7]] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7,3,4,6,1,2,8,5] => [[1,2,5,8],[3,4,6],[7]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [[1,2,4,7],[3,5],[6],[8]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [[1,2,4,6],[3,5],[7,8]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [[1,2,4,5],[3,6],[7,8]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4] => [[1,2,4],[3,5,8],[6],[7]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => [[1,2,3,7],[4,5],[6],[8]] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [[1,2,3,6],[4,5],[7,8]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => [[1,2,3,5],[4,6],[7,8]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => [[1,2,3],[4,5,8],[6],[7]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,4,5,1,8,2,7] => [[1,2,5,7],[3,4,8],[6]] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8,3,4,5,1,7,2,6] => [[1,2,5,6],[3,4,7],[8]] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => [[1,2,5,7],[3,4,6],[8]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => [[1,2,4],[3,5,7],[6],[8]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => [[1,2,3],[4,5,7],[6],[8]] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => [[1,2,5,7,8],[3,4],[6]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,3,4,5,8,1,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => [[1,3,4,5,6,8],[2,7]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => [[1,3,4,5,7],[2,6],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => [[1,3,4,5,6],[2,7],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,4,7,6,1,8,5] => [[1,3,4,5,8],[2,6],[7]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7] => [[1,3,4,6,7],[2,5],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => [[1,3,4,6],[2,5,7],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => [[1,3,4,5],[2,6],[7],[8]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => [[1,3,4,6,8],[2,5],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => [[1,3,5,6,7],[2,4],[8]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => [[1,3,5,6],[2,4,7],[8]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [[1,3,5],[2,4,6],[7],[8]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [[1,3,4],[2,5,6],[7],[8]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3] => [[1,3,5,6,8],[2,4],[7]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => [[1,2,5,6],[3,4,7],[8]] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => [[1,2,5],[3,4,6],[7],[8]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => [[1,2,4],[3,5,6],[7],[8]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => [[1,2,3],[4,5,6],[7],[8]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => [[1,2,5,6,8],[3,4],[7]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => [[1,3,4,5,6,7],[2,8]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => [[1,3,4,5,6],[2,7],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => [[1,3,4,5,7],[2,6],[8]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => [[1,3,4,6,7],[2,5],[8]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => [[1,3,5,6,7],[2,4],[8]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => [[1,2,5,6,7],[3,4],[8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [[1,2,3,4,5,6,7],[8,9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [[1,2,3,4,5,6,8],[7,9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,7],[8],[9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => [[1,2,3,4,5,6,9],[7,8]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8] => [[1,2,3,4,5,7,8],[6,9]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [9,1,2,3,4,7,5,6,8] => [[1,2,3,4,5,6,8],[7],[9]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,1,2,3,4,8,5,6,7] => [[1,2,3,4,5,6,7],[8],[9]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,1,2,3,4,9,8,5,7] => [[1,2,3,4,5,7],[6,8],[9]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [9,1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8],[9]] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => [[1,2,3,4,5,8,9],[6,7]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [5,1,2,3,9,4,6,7,8] => [[1,2,3,4,6,7,8],[5,9]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,1,2,3,9,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [9,1,2,3,6,8,4,5,7] => [[1,2,3,4,5,7],[6,8],[9]] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => [[1,2,3,4,7,8,9],[5,6]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,1,2,5,3,4,6,7,8] => [[1,2,3,4,6,7,8],[5],[9]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,1,2,8,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8],[9]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [7,1,2,8,3,4,5,9,6] => [[1,2,3,4,5,6],[7,8,9]] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [9,1,2,8,6,7,3,4,5] => [[1,2,3,4,5],[6,7],[8],[9]] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [9,1,2,5,6,7,8,3,4] => [[1,2,3,4,7,8],[5,6],[9]] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3] => [[1,2,3,6,7,8,9],[4,5]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3,9]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,8,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8],[9]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,1,8,9,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,8,2,9,7] => [[1,2,5,6,7,9],[3,4,8]] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [9,1,8,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7],[8],[9]] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,5,1,3,6,7,8,9,4] => [[1,3,4,7,8,9],[2,5,6]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => [[1,3,5,7,9],[2,4,6,8]] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => [[1,3,5,6,7,8,9],[2,4]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3],[9]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [8,3,1,2,4,5,6,9,7] => [[1,2,4,5,6,7],[3,9],[8]] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [6,3,1,2,4,7,8,9,5] => [[1,2,4,5,8,9],[3,7],[6]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,4,1,2,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4],[9]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,9,1,2,3,4,6,7,8] => [[1,2,3,4,6,7,8],[5,9]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,6,1,2,3,4,5,7,8] => [[1,2,3,4,5,7,8],[6],[9]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7],[9]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [9,6,1,2,3,4,8,5,7] => [[1,2,3,4,5,7],[6,8],[9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,7,1,2,3,4,8,5,6] => [[1,2,3,4,5,6],[7,8],[9]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,8,1,2,3,7,4,5,6] => [[1,2,3,4,5,6],[7],[8],[9]] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [9,6,1,2,3,7,8,4,5] => [[1,2,3,4,5],[6,7,8],[9]] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,6,1,2,3,7,8,9,4] => [[1,2,3,4,8,9],[5,6,7]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,9,1,2,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6],[9]] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [9,8,1,2,6,7,3,4,5] => [[1,2,3,4,5],[6,7],[8],[9]] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [9,8,1,6,2,7,3,4,5] => [[1,2,3,4,5],[6,7],[8],[9]] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,7,6,2,3,4,5] => [[1,2,3,4,5],[6],[7],[8],[9]] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,9,1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7],[8,9]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,9,1,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => [[1,3,4,6,7,8,9],[2,5]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,9,4,1,6,3,8,5,7] => [[1,3,5,7],[2,4,6,8],[9]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,9,8,1,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8],[9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,7,8,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8],[9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,8,1,2,3,4,9,5] => [[1,2,3,4,5],[6,7,8,9]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,9,1,5,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,6,1,7,8,9,5] => [[1,3,4,5,7,8,9],[2,6]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,9,1,6,7,8] => [[1,3,4,5,6,7,8],[2,9]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => [[1,3,4,5,6,8,9],[2,7]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,9,1,7,8] => [[1,3,4,5,6,7,8],[2,9]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => [[1,3,4,5,6,7,9],[2,8]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => [[1,3,4,5,6,7,8],[2,9]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => [[1,3,5,6,7,8,9,10],[2,4]] => 2
[] => [1] => [[1]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,10,7] => [[1,2,3,4,5,6,7],[8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [10,7,1,2,3,4,5,9,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,10,1,2,3,4,5,9,6,7] => [[1,2,3,4,5,6,7],[8,9],[10]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [10,7,1,2,3,4,9,5,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,6,1,2,3,4,10,9,5,8] => [[1,2,3,4,5,8],[6,9],[7,10]] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [10,7,1,2,3,4,8,9,5,6] => [[1,2,3,4,5,6],[7,8,9],[10]] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [10,9,1,2,3,7,8,4,5,6] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [10,9,1,2,8,7,3,4,5,6] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,8,1,9,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9],[10]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,7,9,1,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,9,8,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [2,7,8,9,1,3,4,5,10,6] => [[1,3,4,5,6],[2,7,8,9,10]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,1,2,3,4,5,6,9,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [10,1,2,3,4,5,9,6,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,1,2,3,4,10,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,3,9,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,9,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,10,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,1,2,3,4,5,10,9,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,1,2,3,4,5,8,9,10,6] => [[1,2,3,4,5,6,9,10],[7,8]] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,5] => [[1,2,3,4,5,8,9,10],[6,7]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,1,10,9,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,1,8,9,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9],[10]] => 1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,4] => [[1,2,3,4,7,8,9,10],[5,6]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3],[10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,10,1,2,3,4,5,6,7,9] => [[1,2,3,4,5,6,7,9],[8,10]] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,7,1,2,3,4,8,9,10,6] => [[1,2,3,4,6,9,10],[5,7,8]] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The index of the last row whose first entry is the row number in a standard Young tableau.
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.