Identifier
Values
[[1]] => [1] => [1,0] => 0
[[1,2]] => [2] => [1,1,0,0] => 0
[[1],[2]] => [2] => [1,1,0,0] => 0
[[1,2,3]] => [3] => [1,1,1,0,0,0] => 0
[[1,3],[2]] => [2,1] => [1,1,0,0,1,0] => 1
[[1,2],[3]] => [3] => [1,1,1,0,0,0] => 0
[[1],[2],[3]] => [3] => [1,1,1,0,0,0] => 0
[[1,2,3,4]] => [4] => [1,1,1,1,0,0,0,0] => 0
[[1,3,4],[2]] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[[1,2,4],[3]] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[[1,2,3],[4]] => [4] => [1,1,1,1,0,0,0,0] => 0
[[1,3],[2,4]] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[[1,2],[3,4]] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[[1,4],[2],[3]] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[[1,3],[2],[4]] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[[1,2],[3],[4]] => [4] => [1,1,1,1,0,0,0,0] => 0
[[1],[2],[3],[4]] => [4] => [1,1,1,1,0,0,0,0] => 0
[[1,2,3,4,5]] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,4,5],[2]] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,2,4,5],[3]] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,3,5],[4]] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3,4],[5]] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,5],[2,4]] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,2,5],[3,4]] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,3,4],[2,5]] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,2,4],[3,5]] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,3],[4,5]] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,5],[2],[3]] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,3,5],[2],[4]] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,2,5],[3],[4]] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4],[2],[5]] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,2,4],[3],[5]] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,3],[4],[5]] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,4],[2,5],[3]] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,3],[2,5],[4]] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,2],[3,5],[4]] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3],[2,4],[5]] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,2],[3,4],[5]] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,5],[2],[3],[4]] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4],[2],[3],[5]] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,3],[2],[4],[5]] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,2],[3],[4],[5]] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1],[2],[3],[4],[5]] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,3,4,5,6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,4,5,6],[2]] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,4,5,6],[3]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,5,6],[4]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,6],[5]] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5],[6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,5,6],[2,4]] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5,6],[3,4]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3,4,6],[2,5]] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,4,6],[3,5]] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3,6],[4,5]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5],[2,6]] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,4,5],[3,6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,5],[4,6]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4],[5,6]] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,4,5,6],[2],[3]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3,5,6],[2],[4]] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5,6],[3],[4]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,3,4,6],[2],[5]] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,4,6],[3],[5]] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3,6],[4],[5]] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,4,5],[2],[6]] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,4,5],[3],[6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,5],[4],[6]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4],[5],[6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,5],[2,4,6]] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5],[3,4,6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3,4],[2,5,6]] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,4],[3,5,6]] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3],[4,5,6]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,4,6],[2,5],[3]] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,3,6],[2,5],[4]] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,6],[3,5],[4]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,3,6],[2,4],[5]] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,6],[3,4],[5]] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,4,5],[2,6],[3]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3,5],[2,6],[4]] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5],[3,6],[4]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,3,4],[2,6],[5]] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,4],[3,6],[5]] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3],[4,6],[5]] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,5],[2,4],[6]] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5],[3,4],[6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3,4],[2,5],[6]] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,4],[3,5],[6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3],[4,5],[6]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,5,6],[2],[3],[4]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,4,6],[2],[3],[5]] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,3,6],[2],[4],[5]] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,6],[3],[4],[5]] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,4,5],[2],[3],[6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3,5],[2],[4],[6]] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5],[3],[4],[6]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,3,4],[2],[5],[6]] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,4],[3],[5],[6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3],[4],[5],[6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,4],[2,5],[3,6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3],[2,5],[4,6]] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
>>> Load all 671 entries. <<<
[[1,2],[3,5],[4,6]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,3],[2,4],[5,6]] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2],[3,4],[5,6]] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,5],[2,6],[3],[4]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,4],[2,6],[3],[5]] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,3],[2,6],[4],[5]] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2],[3,6],[4],[5]] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,4],[2,5],[3],[6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3],[2,5],[4],[6]] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2],[3,5],[4],[6]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,3],[2,4],[5],[6]] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2],[3,4],[5],[6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,6],[2],[3],[4],[5]] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,5],[2],[3],[4],[6]] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,4],[2],[3],[5],[6]] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3],[2],[4],[5],[6]] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2],[3],[4],[5],[6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1],[2],[3],[4],[5],[6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,3,4,5,6,7],[2]] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2,4,5,6,7],[3]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,5,6,7],[4]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,4,6,7],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,7],[6]] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,6],[7]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,5,6,7],[3,4]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,6,7],[4,5]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,3,4,5,7],[2,6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4,5,7],[3,6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3,5,7],[4,6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3,4,7],[5,6]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5,6],[2,7]] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2,4,5,6],[3,7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,5,6],[4,7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,4,6],[5,7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5],[6,7]] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,4,5,6,7],[2],[3]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,5,6,7],[3],[4]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,6,7],[4],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5,7],[2],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4,5,7],[3],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3,5,7],[4],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3,4,7],[5],[6]] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,3,4,5,6],[2],[7]] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2,4,5,6],[3],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,5,6],[4],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,4,6],[5],[7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5],[6],[7]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,5,7],[3,4,6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3,7],[4,5,6]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,5,6],[3,4,7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,6],[4,5,7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,3,4,5],[2,6,7]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4,5],[3,6,7]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3,5],[4,6,7]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3,4],[5,6,7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,6,7],[3,5],[4]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,4,5,7],[2,6],[3]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,5,7],[3,6],[4]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3,7],[4,6],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,5,7],[3,4],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,3,4,7],[2,5],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4,7],[3,5],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3,7],[4,5],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,4,5,6],[2,7],[3]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,5,6],[3,7],[4]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,6],[4,7],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5],[2,7],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4,5],[3,7],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3,5],[4,7],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3,4],[5,7],[6]] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,5,6],[3,4],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,6],[4,5],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,3,4,5],[2,6],[7]] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2,4,5],[3,6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,5],[4,6],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,4],[5,6],[7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,5,6,7],[2],[3],[4]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,6,7],[3],[4],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5,7],[2],[3],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,5,7],[3],[4],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,3,4,7],[2],[5],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4,7],[3],[5],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3,7],[4],[5],[6]] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,4,5,6],[2],[3],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,5,6],[3],[4],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,6],[4],[5],[7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5],[2],[6],[7]] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2,4,5],[3],[6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,5],[4],[6],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,4],[5],[6],[7]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,6],[3,5,7],[4]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,4,5],[2,6,7],[3]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,5],[3,6,7],[4]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3],[4,6,7],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,5],[3,4,7],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,3,4],[2,5,7],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4],[3,5,7],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3],[4,5,7],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,2,5],[3,4,6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3],[4,5,6],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,4,7],[2,5],[3,6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,7],[3,5],[4,6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,2,6],[3,5],[4,7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,4,5],[2,6],[3,7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,5],[3,6],[4,7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3],[4,6],[5,7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,5],[3,4],[6,7]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,3,4],[2,5],[6,7]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4],[3,5],[6,7]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3],[4,5],[6,7]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,5,7],[2,6],[3],[4]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,2,7],[3,6],[4],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,4,7],[2,5],[3],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,7],[3,5],[4],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,3,7],[2,4],[5],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,7],[3,4],[5],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,5,6],[2,7],[3],[4]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,6],[3,7],[4],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5],[2,7],[3],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,5],[3,7],[4],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,3,4],[2,7],[5],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4],[3,7],[5],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3],[4,7],[5],[6]] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,6],[3,5],[4],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,4,5],[2,6],[3],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,5],[3,6],[4],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3],[4,6],[5],[7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,5],[3,4],[6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4],[2,5],[6],[7]] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2,4],[3,5],[6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3],[4,5],[6],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,6,7],[2],[3],[4],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,5,7],[2],[3],[4],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,4,7],[2],[3],[5],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,3,7],[2],[4],[5],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,7],[3],[4],[5],[6]] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,5,6],[2],[3],[4],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,6],[3],[4],[5],[7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5],[2],[3],[6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,5],[3],[4],[6],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,3,4],[2],[5],[6],[7]] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2,4],[3],[5],[6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3],[4],[5],[6],[7]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,5],[2,6],[3,7],[4]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2],[3,6],[4,7],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,4],[2,5],[3,7],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2],[3,5],[4,7],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,3],[2,4],[5,7],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2],[3,4],[5,7],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,4],[2,5],[3,6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2],[3,5],[4,6],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,6],[2,7],[3],[4],[5]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,5],[2,7],[3],[4],[6]] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[[1,4],[2,7],[3],[5],[6]] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[[1,3],[2,7],[4],[5],[6]] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2],[3,7],[4],[5],[6]] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,5],[2,6],[3],[4],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2],[3,6],[4],[5],[7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,4],[2,5],[3],[6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2],[3,5],[4],[6],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,3],[2,4],[5],[6],[7]] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2],[3,4],[5],[6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,7],[2],[3],[4],[5],[6]] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,6],[2],[3],[4],[5],[7]] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,5],[2],[3],[4],[6],[7]] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,4],[2],[3],[5],[6],[7]] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3],[2],[4],[5],[6],[7]] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2],[3],[4],[5],[6],[7]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1],[2],[3],[4],[5],[6],[7]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7,8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[[1,3,4,5,6,7,8],[2]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,3,5,6,7,8],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,4,5,7,8],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6,8],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,6,7],[8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[[1,3,5,6,7,8],[2,4]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,3,6,7,8],[4,5]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5,7,8],[2,6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5,7,8],[4,6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4,5,6,8],[2,7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,5,6,8],[3,7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,3,4,5,8],[6,7]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5,6,7],[2,8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,3,5,6,7],[4,8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,4,5,7],[6,8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6],[7,8]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,3,5,6,7,8],[2],[4]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,5,6,7,8],[3],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5,7,8],[2],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5,7,8],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3,4,7,8],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5,6,8],[2],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,5,6,8],[3],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,3,4,5,8],[6],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,3,4,5,6,7],[2],[8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,3,5,6,7],[4],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,4,5,7],[6],[8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6],[7],[8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[[1,3,5,7,8],[2,4,6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,3,7,8],[4,5,6]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,5,6,8],[3,4,7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5,8],[2,6,7]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5,8],[4,6,7]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5,6,7],[2,4,8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,3,6,7],[4,5,8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5,7],[2,6,8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5,7],[4,6,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4,5,6],[2,7,8]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,5,6],[3,7,8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,3,4,5],[6,7,8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,3,6,7,8],[2,5],[4]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,6,7,8],[3,5],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5,7,8],[2,6],[4]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5,7,8],[3,6],[4]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5,7,8],[2,4],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4,7,8],[2,5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,7,8],[4,5],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,4,5,6,8],[2,7],[3]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5,8],[2,7],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5,8],[4,7],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3,4,8],[5,7],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,5,6,8],[3,4],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5,8],[2,6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,5,8],[3,6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,5,6,7],[2,8],[4]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,5,6,7],[3,8],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5,7],[2,8],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5,7],[4,8],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3,4,7],[5,8],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5,6],[2,8],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,5,6],[3,8],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,3,4,5],[6,8],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,3,5,6,7],[2,4],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,3,6,7],[4,5],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5,7],[2,6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5,7],[4,6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4,5,6],[2,7],[8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,3,5,6],[4,7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,4,5],[6,7],[8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,5,6,7,8],[2],[3],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5,7,8],[2],[4],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5,7,8],[3],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4,7,8],[2],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,7,8],[4],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5,6,8],[2],[3],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5,8],[2],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,5,8],[3],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,3,4,8],[5],[6],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,3,5,6,7],[2],[4],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,5,6,7],[3],[4],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5,7],[2],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5,7],[4],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3,4,7],[5],[6],[8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5,6],[2],[7],[8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,3,5,6],[4],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,4,5],[6],[7],[8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[[1,3,5,7],[2,4,6,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,3,7],[4,5,6,8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,5,6],[3,4,7,8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5],[2,6,7,8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5],[4,6,7,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5,8],[2,6,7],[4]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5,8],[3,6,7],[4]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5,8],[2,4,7],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4,8],[2,5,7],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,8],[4,5,7],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5,8],[3,4,6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,6,7],[2,5,8],[4]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,6,7],[3,5,8],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5,7],[2,6,8],[4]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5,7],[3,6,8],[4]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5,7],[2,4,8],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4,7],[2,5,8],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,7],[4,5,8],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,4,5,6],[2,7,8],[3]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5],[2,7,8],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5],[4,7,8],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3,4],[5,7,8],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,5,6],[3,4,8],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5],[2,6,8],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,5],[3,6,8],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,5,7],[2,4,6],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,3,7],[4,5,6],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5,6],[2,4,7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,3,6],[4,5,7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5],[2,6,7],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5],[4,6,7],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7,8],[2,5],[4,6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,7,8],[3,5],[4,6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,4,5,8],[2,6],[3,7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,5,8],[2,4],[6,7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4,8],[2,5],[6,7]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,8],[4,5],[6,7]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,6,7],[2,5],[4,8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,6,7],[3,5],[4,8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5,7],[2,6],[4,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5,7],[3,6],[4,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5,7],[2,4],[6,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4,7],[2,5],[6,8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,7],[4,5],[6,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5,6],[2,7],[4,8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,5,6],[3,7],[4,8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5],[2,7],[6,8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5],[4,7],[6,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3,4],[5,7],[6,8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,5,6],[3,4],[7,8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5],[2,6],[7,8]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,5],[3,6],[7,8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,5,7,8],[2,6],[3],[4]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7,8],[2,5],[4],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,7,8],[3,5],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7,8],[2,4],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5,8],[2,7],[4],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5,8],[3,7],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4,8],[2,7],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,8],[4,7],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5,8],[2,6],[3],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,5,8],[3,4],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,8],[2,5],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,8],[3,5],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,5,6,7],[2,8],[3],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5,7],[2,8],[4],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5,7],[3,8],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4,7],[2,8],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,7],[4,8],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5,6],[2,8],[3],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,5],[2,8],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,5],[3,8],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,3,4],[5,8],[6],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,3,6,7],[2,5],[4],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,6,7],[3,5],[4],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5,7],[2,6],[4],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5,7],[3,6],[4],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5,7],[2,4],[6],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4,7],[2,5],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,7],[4,5],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5,6],[2,7],[4],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,5,6],[3,7],[4],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5],[2,7],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,5],[4,7],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3,4],[5,7],[6],[8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,3,5,6],[2,4],[7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,3,6],[4,5],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5],[2,6],[7],[8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,3,5],[4,6],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,5,7,8],[2],[3],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7,8],[2],[4],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,7,8],[3],[4],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5,8],[2],[3],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4,8],[2],[5],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4,8],[3],[5],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,3,8],[4],[5],[6],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,5,6,7],[2],[3],[4],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5,7],[2],[4],[6],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5,7],[3],[4],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4,7],[2],[5],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3,7],[4],[5],[6],[8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,3,5,6],[2],[4],[7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,5,6],[3],[4],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,5],[2],[6],[7],[8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,3,5],[4],[6],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,4],[5],[6],[7],[8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[[1,3,7],[2,5,8],[4,6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,7],[3,5,8],[4,6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,4,5],[2,6,8],[3,7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,5],[2,4,8],[6,7]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4],[2,5,8],[6,7]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3],[4,5,8],[6,7]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,6],[2,5,7],[4,8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,6],[3,5,7],[4,8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5],[2,6,7],[4,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5],[3,6,7],[4,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5],[2,4,7],[6,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4],[2,5,7],[6,8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3],[4,5,7],[6,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5],[3,4,6],[7,8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,5,7],[2,6,8],[3],[4]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7],[2,5,8],[4],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,7],[3,5,8],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7],[2,4,8],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3,5],[2,7,8],[4],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5],[3,7,8],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4],[2,7,8],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3],[4,7,8],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5],[2,6,8],[3],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,5],[3,4,8],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4],[2,5,8],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4],[3,5,8],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,6],[2,5,7],[4],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,6],[3,5,7],[4],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5],[2,6,7],[4],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5],[3,6,7],[4],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5],[2,4,7],[6],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4],[2,5,7],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3],[4,5,7],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,5],[2,4,6],[7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,3],[4,5,6],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,8],[2,5],[4,7],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,8],[3,5],[4,7],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,8],[2,4],[5,7],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,4,8],[2,5],[3,6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,5,7],[2,6],[3,8],[4]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7],[2,5],[4,8],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,7],[3,5],[4,8],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7],[2,4],[5,8],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,5,6],[2,7],[3,8],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5],[2,7],[4,8],[6]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5],[3,7],[4,8],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4],[2,7],[5,8],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3],[4,7],[5,8],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5],[2,6],[3,8],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,5],[3,4],[6,8],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4],[2,5],[6,8],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4],[3,5],[6,8],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,7],[2,5],[4,6],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,7],[3,5],[4,6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,6],[2,5],[4,7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,6],[3,5],[4,7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5],[2,6],[4,7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,5],[3,6],[4,7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5],[2,4],[6,7],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,3,4],[2,5],[6,7],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3],[4,5],[6,7],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,5,8],[2,7],[3],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,8],[2,7],[4],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,8],[3,7],[4],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4,8],[2,5],[3],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,8],[2,4],[5],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,8],[3,4],[5],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,5,7],[2,8],[3],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7],[2,8],[4],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,7],[3,8],[4],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4,5],[2,8],[3],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,4],[2,8],[5],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,4],[3,8],[5],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,3],[4,8],[5],[6],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,5,7],[2,6],[3],[4],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7],[2,5],[4],[6],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,7],[3,5],[4],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7],[2,4],[5],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,5,6],[2,7],[3],[4],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5],[2,7],[4],[6],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2,5],[3,7],[4],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,4],[2,7],[5],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,3],[4,7],[5],[6],[8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,3,6],[2,5],[4],[7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,6],[3,5],[4],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5],[2,6],[4],[7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,5],[3,6],[4],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5],[2,4],[6],[7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,3,4],[2,5],[6],[7],[8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,3],[4,5],[6],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,7,8],[2],[3],[4],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4,8],[2],[3],[5],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3,8],[2],[4],[5],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2,8],[3],[4],[5],[6],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,5,7],[2],[3],[4],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3,7],[2],[4],[5],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2,7],[3],[4],[5],[6],[8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,5,6],[2],[3],[4],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,5],[2],[4],[6],[7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,5],[3],[4],[6],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4],[2],[5],[6],[7],[8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,3],[4],[5],[6],[7],[8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[[1,5],[2,6],[3,7],[4,8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3],[2,5],[4,7],[6,8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2],[3,5],[4,7],[6,8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3],[2,4],[5,7],[6,8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,4],[2,5],[3,6],[7,8]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,5],[2,7],[3,8],[4],[6]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3],[2,7],[4,8],[5],[6]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2],[3,7],[4,8],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4],[2,5],[3,8],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3],[2,4],[5,8],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2],[3,4],[5,8],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,5],[2,6],[3,7],[4],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3],[2,5],[4,7],[6],[8]] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[[1,2],[3,5],[4,7],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3],[2,4],[5,7],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,3],[2,5],[4,6],[7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2],[3,5],[4,6],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,7],[2,8],[3],[4],[5],[6]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,4],[2,8],[3],[5],[6],[7]] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,3],[2,8],[4],[5],[6],[7]] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[[1,2],[3,8],[4],[5],[6],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,5],[2,7],[3],[4],[6],[8]] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[[1,3],[2,7],[4],[5],[6],[8]] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[1,2],[3,7],[4],[5],[6],[8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,5],[2,6],[3],[4],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3],[2,5],[4],[6],[7],[8]] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2],[3,5],[4],[6],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3],[2,4],[5],[6],[7],[8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,8],[2],[3],[4],[5],[6],[7]] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[[1,7],[2],[3],[4],[5],[6],[8]] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[[1,5],[2],[3],[4],[6],[7],[8]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3],[2],[4],[5],[6],[7],[8]] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2],[3],[4],[5],[6],[7],[8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[[1],[2],[3],[4],[5],[6],[7],[8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7,8,9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7,8],[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7],[8,9]] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,6,7],[8],[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6],[7,8,9]] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6],[7,8],[9]] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6],[7],[8],[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5],[6],[7],[8],[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4],[5],[6],[7],[8],[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7,8,9,10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7,8,9],[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7,8],[9,10]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,6,7,8],[9],[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6,7],[8,9,10]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6,7],[8,9],[10]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6,7],[8],[9],[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[[1,3,4,5,6,7,8,9],[2]] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[[1,3,4,5,6,7,8,9,10],[2]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,6,7,9],[8]] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,6,9],[7,8]] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6,9],[7],[8]] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,9],[6],[7],[8]] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,9],[5],[6],[7],[8]] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,9],[4],[5],[6],[7],[8]] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[[1,3],[2,9],[4],[5],[6],[7],[8]] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[[1,2,3,4,5,6,7,8,10],[9]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,6,7,10],[8,9]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6,7,10],[8],[9]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,6,10],[7],[8],[9]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,5,10],[6],[7],[8],[9]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,4,10],[5],[6],[7],[8],[9]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,3,10],[4],[5],[6],[7],[8],[9]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,3,4,5,6,7,8],[2,9]] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[1,3,4,5,6,7,8],[2],[9]] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[1,3,4,5,6,7],[2,8,9]] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[[1,3,4,5,6,7],[2,9],[8]] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[[1,3,4,5,6,7],[2],[8],[9]] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[1,3,4,5,6],[2],[7],[8],[9]] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[1,3,4,5],[2],[6],[7],[8],[9]] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[1,3,4],[2],[5],[6],[7],[8],[9]] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[1,3],[2],[4],[5],[6],[7],[8],[9]] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[1,3,4,5,6,7,8,9],[2,10]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[[1,3,4,5,6,7,8,9],[2],[10]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[[1,3,4,5,6,7,8],[2],[9],[10]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[[1,3,4,5,6,7],[2],[8],[9],[10]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[[1,3,4,5,6],[2],[7],[8],[9],[10]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[[1,3,4,5],[2],[6],[7],[8],[9],[10]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[[1,3,4],[2],[5],[6],[7],[8],[9],[10]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[[1,2,3,4,5,6,7,9,10],[8]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,8,9],[3],[4],[5],[6],[7]] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2],[3,8],[4],[5],[6],[7],[9]] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2,9,10],[3],[4],[5],[6],[7],[8]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[[1,2],[3,9],[4],[5],[6],[7],[8],[10]] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
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Description
The bounce count of a Dyck path.
For a Dyck path $D$ of length $2n$, this is the number of points $(i,i)$ for $1 \leq i < n$ that are touching points of the bounce path of $D$.
Map
valley composition
Description
The composition corresponding to the valley set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a valley if $i-1$ is a descent and $i$ is an ascent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the valley set of $T$.
Map
bounce path
Description
The bounce path determined by an integer composition.