Identifier
Values
[[1]] => 0
[[1,2]] => 0
[[1],[2]] => 0
[[1,2,3]] => 0
[[1,3],[2]] => 0
[[1,2],[3]] => 0
[[1],[2],[3]] => 0
[[1,2,3,4]] => 0
[[1,3,4],[2]] => 0
[[1,2,4],[3]] => 0
[[1,2,3],[4]] => 0
[[1,3],[2,4]] => 1
[[1,2],[3,4]] => 1
[[1,4],[2],[3]] => 0
[[1,3],[2],[4]] => 0
[[1,2],[3],[4]] => 0
[[1],[2],[3],[4]] => 0
[[1,2,3,4,5]] => 0
[[1,3,4,5],[2]] => 0
[[1,2,4,5],[3]] => 0
[[1,2,3,5],[4]] => 0
[[1,2,3,4],[5]] => 0
[[1,3,5],[2,4]] => 1
[[1,2,5],[3,4]] => 1
[[1,3,4],[2,5]] => 1
[[1,2,4],[3,5]] => 1
[[1,2,3],[4,5]] => 1
[[1,4,5],[2],[3]] => 0
[[1,3,5],[2],[4]] => 0
[[1,2,5],[3],[4]] => 0
[[1,3,4],[2],[5]] => 0
[[1,2,4],[3],[5]] => 0
[[1,2,3],[4],[5]] => 0
[[1,4],[2,5],[3]] => 1
[[1,3],[2,5],[4]] => 1
[[1,2],[3,5],[4]] => 1
[[1,3],[2,4],[5]] => 1
[[1,2],[3,4],[5]] => 1
[[1,5],[2],[3],[4]] => 0
[[1,4],[2],[3],[5]] => 0
[[1,3],[2],[4],[5]] => 0
[[1,2],[3],[4],[5]] => 0
[[1],[2],[3],[4],[5]] => 0
[[1,2,3,4,5,6]] => 0
[[1,3,4,5,6],[2]] => 0
[[1,2,4,5,6],[3]] => 0
[[1,2,3,5,6],[4]] => 0
[[1,2,3,4,6],[5]] => 0
[[1,2,3,4,5],[6]] => 0
[[1,3,5,6],[2,4]] => 1
[[1,2,5,6],[3,4]] => 1
[[1,3,4,6],[2,5]] => 1
[[1,2,4,6],[3,5]] => 1
[[1,2,3,6],[4,5]] => 1
[[1,3,4,5],[2,6]] => 1
[[1,2,4,5],[3,6]] => 1
[[1,2,3,5],[4,6]] => 1
[[1,2,3,4],[5,6]] => 1
[[1,4,5,6],[2],[3]] => 0
[[1,3,5,6],[2],[4]] => 0
[[1,2,5,6],[3],[4]] => 0
[[1,3,4,6],[2],[5]] => 0
[[1,2,4,6],[3],[5]] => 0
[[1,2,3,6],[4],[5]] => 0
[[1,3,4,5],[2],[6]] => 0
[[1,2,4,5],[3],[6]] => 0
[[1,2,3,5],[4],[6]] => 0
[[1,2,3,4],[5],[6]] => 0
[[1,3,5],[2,4,6]] => 3
[[1,2,5],[3,4,6]] => 3
[[1,3,4],[2,5,6]] => 3
[[1,2,4],[3,5,6]] => 3
[[1,2,3],[4,5,6]] => 3
[[1,4,6],[2,5],[3]] => 1
[[1,3,6],[2,5],[4]] => 1
[[1,2,6],[3,5],[4]] => 1
[[1,3,6],[2,4],[5]] => 1
[[1,2,6],[3,4],[5]] => 1
[[1,4,5],[2,6],[3]] => 1
[[1,3,5],[2,6],[4]] => 1
[[1,2,5],[3,6],[4]] => 1
[[1,3,4],[2,6],[5]] => 1
[[1,2,4],[3,6],[5]] => 1
[[1,2,3],[4,6],[5]] => 1
[[1,3,5],[2,4],[6]] => 1
[[1,2,5],[3,4],[6]] => 1
[[1,3,4],[2,5],[6]] => 1
[[1,2,4],[3,5],[6]] => 1
[[1,2,3],[4,5],[6]] => 1
[[1,5,6],[2],[3],[4]] => 0
[[1,4,6],[2],[3],[5]] => 0
[[1,3,6],[2],[4],[5]] => 0
[[1,2,6],[3],[4],[5]] => 0
[[1,4,5],[2],[3],[6]] => 0
[[1,3,5],[2],[4],[6]] => 0
[[1,2,5],[3],[4],[6]] => 0
[[1,3,4],[2],[5],[6]] => 0
[[1,2,4],[3],[5],[6]] => 0
[[1,2,3],[4],[5],[6]] => 0
[[1,4],[2,5],[3,6]] => 2
[[1,3],[2,5],[4,6]] => 2
>>> Load all 1115 entries. <<<[[1,2],[3,5],[4,6]] => 2
[[1,3],[2,4],[5,6]] => 2
[[1,2],[3,4],[5,6]] => 2
[[1,5],[2,6],[3],[4]] => 1
[[1,4],[2,6],[3],[5]] => 1
[[1,3],[2,6],[4],[5]] => 1
[[1,2],[3,6],[4],[5]] => 1
[[1,4],[2,5],[3],[6]] => 1
[[1,3],[2,5],[4],[6]] => 1
[[1,2],[3,5],[4],[6]] => 1
[[1,3],[2,4],[5],[6]] => 1
[[1,2],[3,4],[5],[6]] => 1
[[1,6],[2],[3],[4],[5]] => 0
[[1,5],[2],[3],[4],[6]] => 0
[[1,4],[2],[3],[5],[6]] => 0
[[1,3],[2],[4],[5],[6]] => 0
[[1,2],[3],[4],[5],[6]] => 0
[[1],[2],[3],[4],[5],[6]] => 0
[[1,2,3,4,5,6,7]] => 0
[[1,3,4,5,6,7],[2]] => 0
[[1,2,4,5,6,7],[3]] => 0
[[1,2,3,5,6,7],[4]] => 0
[[1,2,3,4,6,7],[5]] => 0
[[1,2,3,4,5,7],[6]] => 0
[[1,2,3,4,5,6],[7]] => 0
[[1,3,5,6,7],[2,4]] => 1
[[1,2,5,6,7],[3,4]] => 1
[[1,3,4,6,7],[2,5]] => 1
[[1,2,4,6,7],[3,5]] => 1
[[1,2,3,6,7],[4,5]] => 1
[[1,3,4,5,7],[2,6]] => 1
[[1,2,4,5,7],[3,6]] => 1
[[1,2,3,5,7],[4,6]] => 1
[[1,2,3,4,7],[5,6]] => 1
[[1,3,4,5,6],[2,7]] => 1
[[1,2,4,5,6],[3,7]] => 1
[[1,2,3,5,6],[4,7]] => 1
[[1,2,3,4,6],[5,7]] => 1
[[1,2,3,4,5],[6,7]] => 1
[[1,4,5,6,7],[2],[3]] => 0
[[1,3,5,6,7],[2],[4]] => 0
[[1,2,5,6,7],[3],[4]] => 0
[[1,3,4,6,7],[2],[5]] => 0
[[1,2,4,6,7],[3],[5]] => 0
[[1,2,3,6,7],[4],[5]] => 0
[[1,3,4,5,7],[2],[6]] => 0
[[1,2,4,5,7],[3],[6]] => 0
[[1,2,3,5,7],[4],[6]] => 0
[[1,2,3,4,7],[5],[6]] => 0
[[1,3,4,5,6],[2],[7]] => 0
[[1,2,4,5,6],[3],[7]] => 0
[[1,2,3,5,6],[4],[7]] => 0
[[1,2,3,4,6],[5],[7]] => 0
[[1,2,3,4,5],[6],[7]] => 0
[[1,3,5,7],[2,4,6]] => 3
[[1,2,5,7],[3,4,6]] => 3
[[1,3,4,7],[2,5,6]] => 3
[[1,2,4,7],[3,5,6]] => 3
[[1,2,3,7],[4,5,6]] => 3
[[1,3,5,6],[2,4,7]] => 3
[[1,2,5,6],[3,4,7]] => 3
[[1,3,4,6],[2,5,7]] => 3
[[1,2,4,6],[3,5,7]] => 3
[[1,2,3,6],[4,5,7]] => 3
[[1,3,4,5],[2,6,7]] => 3
[[1,2,4,5],[3,6,7]] => 3
[[1,2,3,5],[4,6,7]] => 3
[[1,2,3,4],[5,6,7]] => 3
[[1,4,6,7],[2,5],[3]] => 1
[[1,3,6,7],[2,5],[4]] => 1
[[1,2,6,7],[3,5],[4]] => 1
[[1,3,6,7],[2,4],[5]] => 1
[[1,2,6,7],[3,4],[5]] => 1
[[1,4,5,7],[2,6],[3]] => 1
[[1,3,5,7],[2,6],[4]] => 1
[[1,2,5,7],[3,6],[4]] => 1
[[1,3,4,7],[2,6],[5]] => 1
[[1,2,4,7],[3,6],[5]] => 1
[[1,2,3,7],[4,6],[5]] => 1
[[1,3,5,7],[2,4],[6]] => 1
[[1,2,5,7],[3,4],[6]] => 1
[[1,3,4,7],[2,5],[6]] => 1
[[1,2,4,7],[3,5],[6]] => 1
[[1,2,3,7],[4,5],[6]] => 1
[[1,4,5,6],[2,7],[3]] => 1
[[1,3,5,6],[2,7],[4]] => 1
[[1,2,5,6],[3,7],[4]] => 1
[[1,3,4,6],[2,7],[5]] => 1
[[1,2,4,6],[3,7],[5]] => 1
[[1,2,3,6],[4,7],[5]] => 1
[[1,3,4,5],[2,7],[6]] => 1
[[1,2,4,5],[3,7],[6]] => 1
[[1,2,3,5],[4,7],[6]] => 1
[[1,2,3,4],[5,7],[6]] => 1
[[1,3,5,6],[2,4],[7]] => 1
[[1,2,5,6],[3,4],[7]] => 1
[[1,3,4,6],[2,5],[7]] => 1
[[1,2,4,6],[3,5],[7]] => 1
[[1,2,3,6],[4,5],[7]] => 1
[[1,3,4,5],[2,6],[7]] => 1
[[1,2,4,5],[3,6],[7]] => 1
[[1,2,3,5],[4,6],[7]] => 1
[[1,2,3,4],[5,6],[7]] => 1
[[1,5,6,7],[2],[3],[4]] => 0
[[1,4,6,7],[2],[3],[5]] => 0
[[1,3,6,7],[2],[4],[5]] => 0
[[1,2,6,7],[3],[4],[5]] => 0
[[1,4,5,7],[2],[3],[6]] => 0
[[1,3,5,7],[2],[4],[6]] => 0
[[1,2,5,7],[3],[4],[6]] => 0
[[1,3,4,7],[2],[5],[6]] => 0
[[1,2,4,7],[3],[5],[6]] => 0
[[1,2,3,7],[4],[5],[6]] => 0
[[1,4,5,6],[2],[3],[7]] => 0
[[1,3,5,6],[2],[4],[7]] => 0
[[1,2,5,6],[3],[4],[7]] => 0
[[1,3,4,6],[2],[5],[7]] => 0
[[1,2,4,6],[3],[5],[7]] => 0
[[1,2,3,6],[4],[5],[7]] => 0
[[1,3,4,5],[2],[6],[7]] => 0
[[1,2,4,5],[3],[6],[7]] => 0
[[1,2,3,5],[4],[6],[7]] => 0
[[1,2,3,4],[5],[6],[7]] => 0
[[1,4,6],[2,5,7],[3]] => 3
[[1,3,6],[2,5,7],[4]] => 3
[[1,2,6],[3,5,7],[4]] => 3
[[1,3,6],[2,4,7],[5]] => 3
[[1,2,6],[3,4,7],[5]] => 3
[[1,4,5],[2,6,7],[3]] => 3
[[1,3,5],[2,6,7],[4]] => 3
[[1,2,5],[3,6,7],[4]] => 3
[[1,3,4],[2,6,7],[5]] => 3
[[1,2,4],[3,6,7],[5]] => 3
[[1,2,3],[4,6,7],[5]] => 3
[[1,3,5],[2,4,7],[6]] => 3
[[1,2,5],[3,4,7],[6]] => 3
[[1,3,4],[2,5,7],[6]] => 3
[[1,2,4],[3,5,7],[6]] => 3
[[1,2,3],[4,5,7],[6]] => 3
[[1,3,5],[2,4,6],[7]] => 3
[[1,2,5],[3,4,6],[7]] => 3
[[1,3,4],[2,5,6],[7]] => 3
[[1,2,4],[3,5,6],[7]] => 3
[[1,2,3],[4,5,6],[7]] => 3
[[1,4,7],[2,5],[3,6]] => 2
[[1,3,7],[2,5],[4,6]] => 2
[[1,2,7],[3,5],[4,6]] => 2
[[1,3,7],[2,4],[5,6]] => 2
[[1,2,7],[3,4],[5,6]] => 2
[[1,4,6],[2,5],[3,7]] => 2
[[1,3,6],[2,5],[4,7]] => 2
[[1,2,6],[3,5],[4,7]] => 2
[[1,3,6],[2,4],[5,7]] => 2
[[1,2,6],[3,4],[5,7]] => 2
[[1,4,5],[2,6],[3,7]] => 2
[[1,3,5],[2,6],[4,7]] => 2
[[1,2,5],[3,6],[4,7]] => 2
[[1,3,4],[2,6],[5,7]] => 2
[[1,2,4],[3,6],[5,7]] => 2
[[1,2,3],[4,6],[5,7]] => 2
[[1,3,5],[2,4],[6,7]] => 2
[[1,2,5],[3,4],[6,7]] => 2
[[1,3,4],[2,5],[6,7]] => 2
[[1,2,4],[3,5],[6,7]] => 2
[[1,2,3],[4,5],[6,7]] => 2
[[1,5,7],[2,6],[3],[4]] => 1
[[1,4,7],[2,6],[3],[5]] => 1
[[1,3,7],[2,6],[4],[5]] => 1
[[1,2,7],[3,6],[4],[5]] => 1
[[1,4,7],[2,5],[3],[6]] => 1
[[1,3,7],[2,5],[4],[6]] => 1
[[1,2,7],[3,5],[4],[6]] => 1
[[1,3,7],[2,4],[5],[6]] => 1
[[1,2,7],[3,4],[5],[6]] => 1
[[1,5,6],[2,7],[3],[4]] => 1
[[1,4,6],[2,7],[3],[5]] => 1
[[1,3,6],[2,7],[4],[5]] => 1
[[1,2,6],[3,7],[4],[5]] => 1
[[1,4,5],[2,7],[3],[6]] => 1
[[1,3,5],[2,7],[4],[6]] => 1
[[1,2,5],[3,7],[4],[6]] => 1
[[1,3,4],[2,7],[5],[6]] => 1
[[1,2,4],[3,7],[5],[6]] => 1
[[1,2,3],[4,7],[5],[6]] => 1
[[1,4,6],[2,5],[3],[7]] => 1
[[1,3,6],[2,5],[4],[7]] => 1
[[1,2,6],[3,5],[4],[7]] => 1
[[1,3,6],[2,4],[5],[7]] => 1
[[1,2,6],[3,4],[5],[7]] => 1
[[1,4,5],[2,6],[3],[7]] => 1
[[1,3,5],[2,6],[4],[7]] => 1
[[1,2,5],[3,6],[4],[7]] => 1
[[1,3,4],[2,6],[5],[7]] => 1
[[1,2,4],[3,6],[5],[7]] => 1
[[1,2,3],[4,6],[5],[7]] => 1
[[1,3,5],[2,4],[6],[7]] => 1
[[1,2,5],[3,4],[6],[7]] => 1
[[1,3,4],[2,5],[6],[7]] => 1
[[1,2,4],[3,5],[6],[7]] => 1
[[1,2,3],[4,5],[6],[7]] => 1
[[1,6,7],[2],[3],[4],[5]] => 0
[[1,5,7],[2],[3],[4],[6]] => 0
[[1,4,7],[2],[3],[5],[6]] => 0
[[1,3,7],[2],[4],[5],[6]] => 0
[[1,2,7],[3],[4],[5],[6]] => 0
[[1,5,6],[2],[3],[4],[7]] => 0
[[1,4,6],[2],[3],[5],[7]] => 0
[[1,3,6],[2],[4],[5],[7]] => 0
[[1,2,6],[3],[4],[5],[7]] => 0
[[1,4,5],[2],[3],[6],[7]] => 0
[[1,3,5],[2],[4],[6],[7]] => 0
[[1,2,5],[3],[4],[6],[7]] => 0
[[1,3,4],[2],[5],[6],[7]] => 0
[[1,2,4],[3],[5],[6],[7]] => 0
[[1,2,3],[4],[5],[6],[7]] => 0
[[1,5],[2,6],[3,7],[4]] => 2
[[1,4],[2,6],[3,7],[5]] => 2
[[1,3],[2,6],[4,7],[5]] => 2
[[1,2],[3,6],[4,7],[5]] => 2
[[1,4],[2,5],[3,7],[6]] => 2
[[1,3],[2,5],[4,7],[6]] => 2
[[1,2],[3,5],[4,7],[6]] => 2
[[1,3],[2,4],[5,7],[6]] => 2
[[1,2],[3,4],[5,7],[6]] => 2
[[1,4],[2,5],[3,6],[7]] => 2
[[1,3],[2,5],[4,6],[7]] => 2
[[1,2],[3,5],[4,6],[7]] => 2
[[1,3],[2,4],[5,6],[7]] => 2
[[1,2],[3,4],[5,6],[7]] => 2
[[1,6],[2,7],[3],[4],[5]] => 1
[[1,5],[2,7],[3],[4],[6]] => 1
[[1,4],[2,7],[3],[5],[6]] => 1
[[1,3],[2,7],[4],[5],[6]] => 1
[[1,2],[3,7],[4],[5],[6]] => 1
[[1,5],[2,6],[3],[4],[7]] => 1
[[1,4],[2,6],[3],[5],[7]] => 1
[[1,3],[2,6],[4],[5],[7]] => 1
[[1,2],[3,6],[4],[5],[7]] => 1
[[1,4],[2,5],[3],[6],[7]] => 1
[[1,3],[2,5],[4],[6],[7]] => 1
[[1,2],[3,5],[4],[6],[7]] => 1
[[1,3],[2,4],[5],[6],[7]] => 1
[[1,2],[3,4],[5],[6],[7]] => 1
[[1,7],[2],[3],[4],[5],[6]] => 0
[[1,6],[2],[3],[4],[5],[7]] => 0
[[1,5],[2],[3],[4],[6],[7]] => 0
[[1,4],[2],[3],[5],[6],[7]] => 0
[[1,3],[2],[4],[5],[6],[7]] => 0
[[1,2],[3],[4],[5],[6],[7]] => 0
[[1],[2],[3],[4],[5],[6],[7]] => 0
[[1,2,3,4,5,6,7,8]] => 0
[[1,3,4,5,6,7,8],[2]] => 0
[[1,2,4,5,6,7,8],[3]] => 0
[[1,2,3,5,6,7,8],[4]] => 0
[[1,2,3,4,6,7,8],[5]] => 0
[[1,2,3,4,5,7,8],[6]] => 0
[[1,2,3,4,5,6,8],[7]] => 0
[[1,2,3,4,5,6,7],[8]] => 0
[[1,3,5,6,7,8],[2,4]] => 1
[[1,2,5,6,7,8],[3,4]] => 1
[[1,3,4,6,7,8],[2,5]] => 1
[[1,2,4,6,7,8],[3,5]] => 1
[[1,2,3,6,7,8],[4,5]] => 1
[[1,3,4,5,7,8],[2,6]] => 1
[[1,2,4,5,7,8],[3,6]] => 1
[[1,2,3,5,7,8],[4,6]] => 1
[[1,2,3,4,7,8],[5,6]] => 1
[[1,3,4,5,6,8],[2,7]] => 1
[[1,2,4,5,6,8],[3,7]] => 1
[[1,2,3,5,6,8],[4,7]] => 1
[[1,2,3,4,6,8],[5,7]] => 1
[[1,2,3,4,5,8],[6,7]] => 1
[[1,3,4,5,6,7],[2,8]] => 1
[[1,2,4,5,6,7],[3,8]] => 1
[[1,2,3,5,6,7],[4,8]] => 1
[[1,2,3,4,6,7],[5,8]] => 1
[[1,2,3,4,5,7],[6,8]] => 1
[[1,2,3,4,5,6],[7,8]] => 1
[[1,4,5,6,7,8],[2],[3]] => 0
[[1,3,5,6,7,8],[2],[4]] => 0
[[1,2,5,6,7,8],[3],[4]] => 0
[[1,3,4,6,7,8],[2],[5]] => 0
[[1,2,4,6,7,8],[3],[5]] => 0
[[1,2,3,6,7,8],[4],[5]] => 0
[[1,3,4,5,7,8],[2],[6]] => 0
[[1,2,4,5,7,8],[3],[6]] => 0
[[1,2,3,5,7,8],[4],[6]] => 0
[[1,2,3,4,7,8],[5],[6]] => 0
[[1,3,4,5,6,8],[2],[7]] => 0
[[1,2,4,5,6,8],[3],[7]] => 0
[[1,2,3,5,6,8],[4],[7]] => 0
[[1,2,3,4,6,8],[5],[7]] => 0
[[1,2,3,4,5,8],[6],[7]] => 0
[[1,3,4,5,6,7],[2],[8]] => 0
[[1,2,4,5,6,7],[3],[8]] => 0
[[1,2,3,5,6,7],[4],[8]] => 0
[[1,2,3,4,6,7],[5],[8]] => 0
[[1,2,3,4,5,7],[6],[8]] => 0
[[1,2,3,4,5,6],[7],[8]] => 0
[[1,3,5,7,8],[2,4,6]] => 3
[[1,2,5,7,8],[3,4,6]] => 3
[[1,3,4,7,8],[2,5,6]] => 3
[[1,2,4,7,8],[3,5,6]] => 3
[[1,2,3,7,8],[4,5,6]] => 3
[[1,3,5,6,8],[2,4,7]] => 3
[[1,2,5,6,8],[3,4,7]] => 3
[[1,3,4,6,8],[2,5,7]] => 3
[[1,2,4,6,8],[3,5,7]] => 3
[[1,2,3,6,8],[4,5,7]] => 3
[[1,3,4,5,8],[2,6,7]] => 3
[[1,2,4,5,8],[3,6,7]] => 3
[[1,2,3,5,8],[4,6,7]] => 3
[[1,2,3,4,8],[5,6,7]] => 3
[[1,3,5,6,7],[2,4,8]] => 3
[[1,2,5,6,7],[3,4,8]] => 3
[[1,3,4,6,7],[2,5,8]] => 3
[[1,2,4,6,7],[3,5,8]] => 3
[[1,2,3,6,7],[4,5,8]] => 3
[[1,3,4,5,7],[2,6,8]] => 3
[[1,2,4,5,7],[3,6,8]] => 3
[[1,2,3,5,7],[4,6,8]] => 3
[[1,2,3,4,7],[5,6,8]] => 3
[[1,3,4,5,6],[2,7,8]] => 3
[[1,2,4,5,6],[3,7,8]] => 3
[[1,2,3,5,6],[4,7,8]] => 3
[[1,2,3,4,6],[5,7,8]] => 3
[[1,2,3,4,5],[6,7,8]] => 3
[[1,4,6,7,8],[2,5],[3]] => 1
[[1,3,6,7,8],[2,5],[4]] => 1
[[1,2,6,7,8],[3,5],[4]] => 1
[[1,3,6,7,8],[2,4],[5]] => 1
[[1,2,6,7,8],[3,4],[5]] => 1
[[1,4,5,7,8],[2,6],[3]] => 1
[[1,3,5,7,8],[2,6],[4]] => 1
[[1,2,5,7,8],[3,6],[4]] => 1
[[1,3,4,7,8],[2,6],[5]] => 1
[[1,2,4,7,8],[3,6],[5]] => 1
[[1,2,3,7,8],[4,6],[5]] => 1
[[1,3,5,7,8],[2,4],[6]] => 1
[[1,2,5,7,8],[3,4],[6]] => 1
[[1,3,4,7,8],[2,5],[6]] => 1
[[1,2,4,7,8],[3,5],[6]] => 1
[[1,2,3,7,8],[4,5],[6]] => 1
[[1,4,5,6,8],[2,7],[3]] => 1
[[1,3,5,6,8],[2,7],[4]] => 1
[[1,2,5,6,8],[3,7],[4]] => 1
[[1,3,4,6,8],[2,7],[5]] => 1
[[1,2,4,6,8],[3,7],[5]] => 1
[[1,2,3,6,8],[4,7],[5]] => 1
[[1,3,4,5,8],[2,7],[6]] => 1
[[1,2,4,5,8],[3,7],[6]] => 1
[[1,2,3,5,8],[4,7],[6]] => 1
[[1,2,3,4,8],[5,7],[6]] => 1
[[1,3,5,6,8],[2,4],[7]] => 1
[[1,2,5,6,8],[3,4],[7]] => 1
[[1,3,4,6,8],[2,5],[7]] => 1
[[1,2,4,6,8],[3,5],[7]] => 1
[[1,2,3,6,8],[4,5],[7]] => 1
[[1,3,4,5,8],[2,6],[7]] => 1
[[1,2,4,5,8],[3,6],[7]] => 1
[[1,2,3,5,8],[4,6],[7]] => 1
[[1,2,3,4,8],[5,6],[7]] => 1
[[1,4,5,6,7],[2,8],[3]] => 1
[[1,3,5,6,7],[2,8],[4]] => 1
[[1,2,5,6,7],[3,8],[4]] => 1
[[1,3,4,6,7],[2,8],[5]] => 1
[[1,2,4,6,7],[3,8],[5]] => 1
[[1,2,3,6,7],[4,8],[5]] => 1
[[1,3,4,5,7],[2,8],[6]] => 1
[[1,2,4,5,7],[3,8],[6]] => 1
[[1,2,3,5,7],[4,8],[6]] => 1
[[1,2,3,4,7],[5,8],[6]] => 1
[[1,3,4,5,6],[2,8],[7]] => 1
[[1,2,4,5,6],[3,8],[7]] => 1
[[1,2,3,5,6],[4,8],[7]] => 1
[[1,2,3,4,6],[5,8],[7]] => 1
[[1,2,3,4,5],[6,8],[7]] => 1
[[1,3,5,6,7],[2,4],[8]] => 1
[[1,2,5,6,7],[3,4],[8]] => 1
[[1,3,4,6,7],[2,5],[8]] => 1
[[1,2,4,6,7],[3,5],[8]] => 1
[[1,2,3,6,7],[4,5],[8]] => 1
[[1,3,4,5,7],[2,6],[8]] => 1
[[1,2,4,5,7],[3,6],[8]] => 1
[[1,2,3,5,7],[4,6],[8]] => 1
[[1,2,3,4,7],[5,6],[8]] => 1
[[1,3,4,5,6],[2,7],[8]] => 1
[[1,2,4,5,6],[3,7],[8]] => 1
[[1,2,3,5,6],[4,7],[8]] => 1
[[1,2,3,4,6],[5,7],[8]] => 1
[[1,2,3,4,5],[6,7],[8]] => 1
[[1,5,6,7,8],[2],[3],[4]] => 0
[[1,4,6,7,8],[2],[3],[5]] => 0
[[1,3,6,7,8],[2],[4],[5]] => 0
[[1,2,6,7,8],[3],[4],[5]] => 0
[[1,4,5,7,8],[2],[3],[6]] => 0
[[1,3,5,7,8],[2],[4],[6]] => 0
[[1,2,5,7,8],[3],[4],[6]] => 0
[[1,3,4,7,8],[2],[5],[6]] => 0
[[1,2,4,7,8],[3],[5],[6]] => 0
[[1,2,3,7,8],[4],[5],[6]] => 0
[[1,4,5,6,8],[2],[3],[7]] => 0
[[1,3,5,6,8],[2],[4],[7]] => 0
[[1,2,5,6,8],[3],[4],[7]] => 0
[[1,3,4,6,8],[2],[5],[7]] => 0
[[1,2,4,6,8],[3],[5],[7]] => 0
[[1,2,3,6,8],[4],[5],[7]] => 0
[[1,3,4,5,8],[2],[6],[7]] => 0
[[1,2,4,5,8],[3],[6],[7]] => 0
[[1,2,3,5,8],[4],[6],[7]] => 0
[[1,2,3,4,8],[5],[6],[7]] => 0
[[1,4,5,6,7],[2],[3],[8]] => 0
[[1,3,5,6,7],[2],[4],[8]] => 0
[[1,2,5,6,7],[3],[4],[8]] => 0
[[1,3,4,6,7],[2],[5],[8]] => 0
[[1,2,4,6,7],[3],[5],[8]] => 0
[[1,2,3,6,7],[4],[5],[8]] => 0
[[1,3,4,5,7],[2],[6],[8]] => 0
[[1,2,4,5,7],[3],[6],[8]] => 0
[[1,2,3,5,7],[4],[6],[8]] => 0
[[1,2,3,4,7],[5],[6],[8]] => 0
[[1,3,4,5,6],[2],[7],[8]] => 0
[[1,2,4,5,6],[3],[7],[8]] => 0
[[1,2,3,5,6],[4],[7],[8]] => 0
[[1,2,3,4,6],[5],[7],[8]] => 0
[[1,2,3,4,5],[6],[7],[8]] => 0
[[1,3,5,7],[2,4,6,8]] => 6
[[1,2,5,7],[3,4,6,8]] => 6
[[1,3,4,7],[2,5,6,8]] => 6
[[1,2,4,7],[3,5,6,8]] => 6
[[1,2,3,7],[4,5,6,8]] => 6
[[1,3,5,6],[2,4,7,8]] => 6
[[1,2,5,6],[3,4,7,8]] => 6
[[1,3,4,6],[2,5,7,8]] => 6
[[1,2,4,6],[3,5,7,8]] => 6
[[1,2,3,6],[4,5,7,8]] => 6
[[1,3,4,5],[2,6,7,8]] => 6
[[1,2,4,5],[3,6,7,8]] => 6
[[1,2,3,5],[4,6,7,8]] => 6
[[1,2,3,4],[5,6,7,8]] => 6
[[1,4,6,8],[2,5,7],[3]] => 3
[[1,3,6,8],[2,5,7],[4]] => 3
[[1,2,6,8],[3,5,7],[4]] => 3
[[1,3,6,8],[2,4,7],[5]] => 3
[[1,2,6,8],[3,4,7],[5]] => 3
[[1,4,5,8],[2,6,7],[3]] => 3
[[1,3,5,8],[2,6,7],[4]] => 3
[[1,2,5,8],[3,6,7],[4]] => 3
[[1,3,4,8],[2,6,7],[5]] => 3
[[1,2,4,8],[3,6,7],[5]] => 3
[[1,2,3,8],[4,6,7],[5]] => 3
[[1,3,5,8],[2,4,7],[6]] => 3
[[1,2,5,8],[3,4,7],[6]] => 3
[[1,3,4,8],[2,5,7],[6]] => 3
[[1,2,4,8],[3,5,7],[6]] => 3
[[1,2,3,8],[4,5,7],[6]] => 3
[[1,3,5,8],[2,4,6],[7]] => 3
[[1,2,5,8],[3,4,6],[7]] => 3
[[1,3,4,8],[2,5,6],[7]] => 3
[[1,2,4,8],[3,5,6],[7]] => 3
[[1,2,3,8],[4,5,6],[7]] => 3
[[1,4,6,7],[2,5,8],[3]] => 3
[[1,3,6,7],[2,5,8],[4]] => 3
[[1,2,6,7],[3,5,8],[4]] => 3
[[1,3,6,7],[2,4,8],[5]] => 3
[[1,2,6,7],[3,4,8],[5]] => 3
[[1,4,5,7],[2,6,8],[3]] => 3
[[1,3,5,7],[2,6,8],[4]] => 3
[[1,2,5,7],[3,6,8],[4]] => 3
[[1,3,4,7],[2,6,8],[5]] => 3
[[1,2,4,7],[3,6,8],[5]] => 3
[[1,2,3,7],[4,6,8],[5]] => 3
[[1,3,5,7],[2,4,8],[6]] => 3
[[1,2,5,7],[3,4,8],[6]] => 3
[[1,3,4,7],[2,5,8],[6]] => 3
[[1,2,4,7],[3,5,8],[6]] => 3
[[1,2,3,7],[4,5,8],[6]] => 3
[[1,4,5,6],[2,7,8],[3]] => 3
[[1,3,5,6],[2,7,8],[4]] => 3
[[1,2,5,6],[3,7,8],[4]] => 3
[[1,3,4,6],[2,7,8],[5]] => 3
[[1,2,4,6],[3,7,8],[5]] => 3
[[1,2,3,6],[4,7,8],[5]] => 3
[[1,3,4,5],[2,7,8],[6]] => 3
[[1,2,4,5],[3,7,8],[6]] => 3
[[1,2,3,5],[4,7,8],[6]] => 3
[[1,2,3,4],[5,7,8],[6]] => 3
[[1,3,5,6],[2,4,8],[7]] => 3
[[1,2,5,6],[3,4,8],[7]] => 3
[[1,3,4,6],[2,5,8],[7]] => 3
[[1,2,4,6],[3,5,8],[7]] => 3
[[1,2,3,6],[4,5,8],[7]] => 3
[[1,3,4,5],[2,6,8],[7]] => 3
[[1,2,4,5],[3,6,8],[7]] => 3
[[1,2,3,5],[4,6,8],[7]] => 3
[[1,2,3,4],[5,6,8],[7]] => 3
[[1,3,5,7],[2,4,6],[8]] => 3
[[1,2,5,7],[3,4,6],[8]] => 3
[[1,3,4,7],[2,5,6],[8]] => 3
[[1,2,4,7],[3,5,6],[8]] => 3
[[1,2,3,7],[4,5,6],[8]] => 3
[[1,3,5,6],[2,4,7],[8]] => 3
[[1,2,5,6],[3,4,7],[8]] => 3
[[1,3,4,6],[2,5,7],[8]] => 3
[[1,2,4,6],[3,5,7],[8]] => 3
[[1,2,3,6],[4,5,7],[8]] => 3
[[1,3,4,5],[2,6,7],[8]] => 3
[[1,2,4,5],[3,6,7],[8]] => 3
[[1,2,3,5],[4,6,7],[8]] => 3
[[1,2,3,4],[5,6,7],[8]] => 3
[[1,4,7,8],[2,5],[3,6]] => 2
[[1,3,7,8],[2,5],[4,6]] => 2
[[1,2,7,8],[3,5],[4,6]] => 2
[[1,3,7,8],[2,4],[5,6]] => 2
[[1,2,7,8],[3,4],[5,6]] => 2
[[1,4,6,8],[2,5],[3,7]] => 2
[[1,3,6,8],[2,5],[4,7]] => 2
[[1,2,6,8],[3,5],[4,7]] => 2
[[1,3,6,8],[2,4],[5,7]] => 2
[[1,2,6,8],[3,4],[5,7]] => 2
[[1,4,5,8],[2,6],[3,7]] => 2
[[1,3,5,8],[2,6],[4,7]] => 2
[[1,2,5,8],[3,6],[4,7]] => 2
[[1,3,4,8],[2,6],[5,7]] => 2
[[1,2,4,8],[3,6],[5,7]] => 2
[[1,2,3,8],[4,6],[5,7]] => 2
[[1,3,5,8],[2,4],[6,7]] => 2
[[1,2,5,8],[3,4],[6,7]] => 2
[[1,3,4,8],[2,5],[6,7]] => 2
[[1,2,4,8],[3,5],[6,7]] => 2
[[1,2,3,8],[4,5],[6,7]] => 2
[[1,4,6,7],[2,5],[3,8]] => 2
[[1,3,6,7],[2,5],[4,8]] => 2
[[1,2,6,7],[3,5],[4,8]] => 2
[[1,3,6,7],[2,4],[5,8]] => 2
[[1,2,6,7],[3,4],[5,8]] => 2
[[1,4,5,7],[2,6],[3,8]] => 2
[[1,3,5,7],[2,6],[4,8]] => 2
[[1,2,5,7],[3,6],[4,8]] => 2
[[1,3,4,7],[2,6],[5,8]] => 2
[[1,2,4,7],[3,6],[5,8]] => 2
[[1,2,3,7],[4,6],[5,8]] => 2
[[1,3,5,7],[2,4],[6,8]] => 2
[[1,2,5,7],[3,4],[6,8]] => 2
[[1,3,4,7],[2,5],[6,8]] => 2
[[1,2,4,7],[3,5],[6,8]] => 2
[[1,2,3,7],[4,5],[6,8]] => 2
[[1,4,5,6],[2,7],[3,8]] => 2
[[1,3,5,6],[2,7],[4,8]] => 2
[[1,2,5,6],[3,7],[4,8]] => 2
[[1,3,4,6],[2,7],[5,8]] => 2
[[1,2,4,6],[3,7],[5,8]] => 2
[[1,2,3,6],[4,7],[5,8]] => 2
[[1,3,4,5],[2,7],[6,8]] => 2
[[1,2,4,5],[3,7],[6,8]] => 2
[[1,2,3,5],[4,7],[6,8]] => 2
[[1,2,3,4],[5,7],[6,8]] => 2
[[1,3,5,6],[2,4],[7,8]] => 2
[[1,2,5,6],[3,4],[7,8]] => 2
[[1,3,4,6],[2,5],[7,8]] => 2
[[1,2,4,6],[3,5],[7,8]] => 2
[[1,2,3,6],[4,5],[7,8]] => 2
[[1,3,4,5],[2,6],[7,8]] => 2
[[1,2,4,5],[3,6],[7,8]] => 2
[[1,2,3,5],[4,6],[7,8]] => 2
[[1,2,3,4],[5,6],[7,8]] => 2
[[1,5,7,8],[2,6],[3],[4]] => 1
[[1,4,7,8],[2,6],[3],[5]] => 1
[[1,3,7,8],[2,6],[4],[5]] => 1
[[1,2,7,8],[3,6],[4],[5]] => 1
[[1,4,7,8],[2,5],[3],[6]] => 1
[[1,3,7,8],[2,5],[4],[6]] => 1
[[1,2,7,8],[3,5],[4],[6]] => 1
[[1,3,7,8],[2,4],[5],[6]] => 1
[[1,2,7,8],[3,4],[5],[6]] => 1
[[1,5,6,8],[2,7],[3],[4]] => 1
[[1,4,6,8],[2,7],[3],[5]] => 1
[[1,3,6,8],[2,7],[4],[5]] => 1
[[1,2,6,8],[3,7],[4],[5]] => 1
[[1,4,5,8],[2,7],[3],[6]] => 1
[[1,3,5,8],[2,7],[4],[6]] => 1
[[1,2,5,8],[3,7],[4],[6]] => 1
[[1,3,4,8],[2,7],[5],[6]] => 1
[[1,2,4,8],[3,7],[5],[6]] => 1
[[1,2,3,8],[4,7],[5],[6]] => 1
[[1,4,6,8],[2,5],[3],[7]] => 1
[[1,3,6,8],[2,5],[4],[7]] => 1
[[1,2,6,8],[3,5],[4],[7]] => 1
[[1,3,6,8],[2,4],[5],[7]] => 1
[[1,2,6,8],[3,4],[5],[7]] => 1
[[1,4,5,8],[2,6],[3],[7]] => 1
[[1,3,5,8],[2,6],[4],[7]] => 1
[[1,2,5,8],[3,6],[4],[7]] => 1
[[1,3,4,8],[2,6],[5],[7]] => 1
[[1,2,4,8],[3,6],[5],[7]] => 1
[[1,2,3,8],[4,6],[5],[7]] => 1
[[1,3,5,8],[2,4],[6],[7]] => 1
[[1,2,5,8],[3,4],[6],[7]] => 1
[[1,3,4,8],[2,5],[6],[7]] => 1
[[1,2,4,8],[3,5],[6],[7]] => 1
[[1,2,3,8],[4,5],[6],[7]] => 1
[[1,5,6,7],[2,8],[3],[4]] => 1
[[1,4,6,7],[2,8],[3],[5]] => 1
[[1,3,6,7],[2,8],[4],[5]] => 1
[[1,2,6,7],[3,8],[4],[5]] => 1
[[1,4,5,7],[2,8],[3],[6]] => 1
[[1,3,5,7],[2,8],[4],[6]] => 1
[[1,2,5,7],[3,8],[4],[6]] => 1
[[1,3,4,7],[2,8],[5],[6]] => 1
[[1,2,4,7],[3,8],[5],[6]] => 1
[[1,2,3,7],[4,8],[5],[6]] => 1
[[1,4,5,6],[2,8],[3],[7]] => 1
[[1,3,5,6],[2,8],[4],[7]] => 1
[[1,2,5,6],[3,8],[4],[7]] => 1
[[1,3,4,6],[2,8],[5],[7]] => 1
[[1,2,4,6],[3,8],[5],[7]] => 1
[[1,2,3,6],[4,8],[5],[7]] => 1
[[1,3,4,5],[2,8],[6],[7]] => 1
[[1,2,4,5],[3,8],[6],[7]] => 1
[[1,2,3,5],[4,8],[6],[7]] => 1
[[1,2,3,4],[5,8],[6],[7]] => 1
[[1,4,6,7],[2,5],[3],[8]] => 1
[[1,3,6,7],[2,5],[4],[8]] => 1
[[1,2,6,7],[3,5],[4],[8]] => 1
[[1,3,6,7],[2,4],[5],[8]] => 1
[[1,2,6,7],[3,4],[5],[8]] => 1
[[1,4,5,7],[2,6],[3],[8]] => 1
[[1,3,5,7],[2,6],[4],[8]] => 1
[[1,2,5,7],[3,6],[4],[8]] => 1
[[1,3,4,7],[2,6],[5],[8]] => 1
[[1,2,4,7],[3,6],[5],[8]] => 1
[[1,2,3,7],[4,6],[5],[8]] => 1
[[1,3,5,7],[2,4],[6],[8]] => 1
[[1,2,5,7],[3,4],[6],[8]] => 1
[[1,3,4,7],[2,5],[6],[8]] => 1
[[1,2,4,7],[3,5],[6],[8]] => 1
[[1,2,3,7],[4,5],[6],[8]] => 1
[[1,4,5,6],[2,7],[3],[8]] => 1
[[1,3,5,6],[2,7],[4],[8]] => 1
[[1,2,5,6],[3,7],[4],[8]] => 1
[[1,3,4,6],[2,7],[5],[8]] => 1
[[1,2,4,6],[3,7],[5],[8]] => 1
[[1,2,3,6],[4,7],[5],[8]] => 1
[[1,3,4,5],[2,7],[6],[8]] => 1
[[1,2,4,5],[3,7],[6],[8]] => 1
[[1,2,3,5],[4,7],[6],[8]] => 1
[[1,2,3,4],[5,7],[6],[8]] => 1
[[1,3,5,6],[2,4],[7],[8]] => 1
[[1,2,5,6],[3,4],[7],[8]] => 1
[[1,3,4,6],[2,5],[7],[8]] => 1
[[1,2,4,6],[3,5],[7],[8]] => 1
[[1,2,3,6],[4,5],[7],[8]] => 1
[[1,3,4,5],[2,6],[7],[8]] => 1
[[1,2,4,5],[3,6],[7],[8]] => 1
[[1,2,3,5],[4,6],[7],[8]] => 1
[[1,2,3,4],[5,6],[7],[8]] => 1
[[1,6,7,8],[2],[3],[4],[5]] => 0
[[1,5,7,8],[2],[3],[4],[6]] => 0
[[1,4,7,8],[2],[3],[5],[6]] => 0
[[1,3,7,8],[2],[4],[5],[6]] => 0
[[1,2,7,8],[3],[4],[5],[6]] => 0
[[1,5,6,8],[2],[3],[4],[7]] => 0
[[1,4,6,8],[2],[3],[5],[7]] => 0
[[1,3,6,8],[2],[4],[5],[7]] => 0
[[1,2,6,8],[3],[4],[5],[7]] => 0
[[1,4,5,8],[2],[3],[6],[7]] => 0
[[1,3,5,8],[2],[4],[6],[7]] => 0
[[1,2,5,8],[3],[4],[6],[7]] => 0
[[1,3,4,8],[2],[5],[6],[7]] => 0
[[1,2,4,8],[3],[5],[6],[7]] => 0
[[1,2,3,8],[4],[5],[6],[7]] => 0
[[1,5,6,7],[2],[3],[4],[8]] => 0
[[1,4,6,7],[2],[3],[5],[8]] => 0
[[1,3,6,7],[2],[4],[5],[8]] => 0
[[1,2,6,7],[3],[4],[5],[8]] => 0
[[1,4,5,7],[2],[3],[6],[8]] => 0
[[1,3,5,7],[2],[4],[6],[8]] => 0
[[1,2,5,7],[3],[4],[6],[8]] => 0
[[1,3,4,7],[2],[5],[6],[8]] => 0
[[1,2,4,7],[3],[5],[6],[8]] => 0
[[1,2,3,7],[4],[5],[6],[8]] => 0
[[1,4,5,6],[2],[3],[7],[8]] => 0
[[1,3,5,6],[2],[4],[7],[8]] => 0
[[1,2,5,6],[3],[4],[7],[8]] => 0
[[1,3,4,6],[2],[5],[7],[8]] => 0
[[1,2,4,6],[3],[5],[7],[8]] => 0
[[1,2,3,6],[4],[5],[7],[8]] => 0
[[1,3,4,5],[2],[6],[7],[8]] => 0
[[1,2,4,5],[3],[6],[7],[8]] => 0
[[1,2,3,5],[4],[6],[7],[8]] => 0
[[1,2,3,4],[5],[6],[7],[8]] => 0
[[1,4,7],[2,5,8],[3,6]] => 4
[[1,3,7],[2,5,8],[4,6]] => 4
[[1,2,7],[3,5,8],[4,6]] => 4
[[1,3,7],[2,4,8],[5,6]] => 4
[[1,2,7],[3,4,8],[5,6]] => 4
[[1,4,6],[2,5,8],[3,7]] => 4
[[1,3,6],[2,5,8],[4,7]] => 4
[[1,2,6],[3,5,8],[4,7]] => 4
[[1,3,6],[2,4,8],[5,7]] => 4
[[1,2,6],[3,4,8],[5,7]] => 4
[[1,4,5],[2,6,8],[3,7]] => 4
[[1,3,5],[2,6,8],[4,7]] => 4
[[1,2,5],[3,6,8],[4,7]] => 4
[[1,3,4],[2,6,8],[5,7]] => 4
[[1,2,4],[3,6,8],[5,7]] => 4
[[1,2,3],[4,6,8],[5,7]] => 4
[[1,3,5],[2,4,8],[6,7]] => 4
[[1,2,5],[3,4,8],[6,7]] => 4
[[1,3,4],[2,5,8],[6,7]] => 4
[[1,2,4],[3,5,8],[6,7]] => 4
[[1,2,3],[4,5,8],[6,7]] => 4
[[1,4,6],[2,5,7],[3,8]] => 4
[[1,3,6],[2,5,7],[4,8]] => 4
[[1,2,6],[3,5,7],[4,8]] => 4
[[1,3,6],[2,4,7],[5,8]] => 4
[[1,2,6],[3,4,7],[5,8]] => 4
[[1,4,5],[2,6,7],[3,8]] => 4
[[1,3,5],[2,6,7],[4,8]] => 4
[[1,2,5],[3,6,7],[4,8]] => 4
[[1,3,4],[2,6,7],[5,8]] => 4
[[1,2,4],[3,6,7],[5,8]] => 4
[[1,2,3],[4,6,7],[5,8]] => 4
[[1,3,5],[2,4,7],[6,8]] => 4
[[1,2,5],[3,4,7],[6,8]] => 4
[[1,3,4],[2,5,7],[6,8]] => 4
[[1,2,4],[3,5,7],[6,8]] => 4
[[1,2,3],[4,5,7],[6,8]] => 4
[[1,3,5],[2,4,6],[7,8]] => 4
[[1,2,5],[3,4,6],[7,8]] => 4
[[1,3,4],[2,5,6],[7,8]] => 4
[[1,2,4],[3,5,6],[7,8]] => 4
[[1,2,3],[4,5,6],[7,8]] => 4
[[1,5,7],[2,6,8],[3],[4]] => 3
[[1,4,7],[2,6,8],[3],[5]] => 3
[[1,3,7],[2,6,8],[4],[5]] => 3
[[1,2,7],[3,6,8],[4],[5]] => 3
[[1,4,7],[2,5,8],[3],[6]] => 3
[[1,3,7],[2,5,8],[4],[6]] => 3
[[1,2,7],[3,5,8],[4],[6]] => 3
[[1,3,7],[2,4,8],[5],[6]] => 3
[[1,2,7],[3,4,8],[5],[6]] => 3
[[1,5,6],[2,7,8],[3],[4]] => 3
[[1,4,6],[2,7,8],[3],[5]] => 3
[[1,3,6],[2,7,8],[4],[5]] => 3
[[1,2,6],[3,7,8],[4],[5]] => 3
[[1,4,5],[2,7,8],[3],[6]] => 3
[[1,3,5],[2,7,8],[4],[6]] => 3
[[1,2,5],[3,7,8],[4],[6]] => 3
[[1,3,4],[2,7,8],[5],[6]] => 3
[[1,2,4],[3,7,8],[5],[6]] => 3
[[1,2,3],[4,7,8],[5],[6]] => 3
[[1,4,6],[2,5,8],[3],[7]] => 3
[[1,3,6],[2,5,8],[4],[7]] => 3
[[1,2,6],[3,5,8],[4],[7]] => 3
[[1,3,6],[2,4,8],[5],[7]] => 3
[[1,2,6],[3,4,8],[5],[7]] => 3
[[1,4,5],[2,6,8],[3],[7]] => 3
[[1,3,5],[2,6,8],[4],[7]] => 3
[[1,2,5],[3,6,8],[4],[7]] => 3
[[1,3,4],[2,6,8],[5],[7]] => 3
[[1,2,4],[3,6,8],[5],[7]] => 3
[[1,2,3],[4,6,8],[5],[7]] => 3
[[1,3,5],[2,4,8],[6],[7]] => 3
[[1,2,5],[3,4,8],[6],[7]] => 3
[[1,3,4],[2,5,8],[6],[7]] => 3
[[1,2,4],[3,5,8],[6],[7]] => 3
[[1,2,3],[4,5,8],[6],[7]] => 3
[[1,4,6],[2,5,7],[3],[8]] => 3
[[1,3,6],[2,5,7],[4],[8]] => 3
[[1,2,6],[3,5,7],[4],[8]] => 3
[[1,3,6],[2,4,7],[5],[8]] => 3
[[1,2,6],[3,4,7],[5],[8]] => 3
[[1,4,5],[2,6,7],[3],[8]] => 3
[[1,3,5],[2,6,7],[4],[8]] => 3
[[1,2,5],[3,6,7],[4],[8]] => 3
[[1,3,4],[2,6,7],[5],[8]] => 3
[[1,2,4],[3,6,7],[5],[8]] => 3
[[1,2,3],[4,6,7],[5],[8]] => 3
[[1,3,5],[2,4,7],[6],[8]] => 3
[[1,2,5],[3,4,7],[6],[8]] => 3
[[1,3,4],[2,5,7],[6],[8]] => 3
[[1,2,4],[3,5,7],[6],[8]] => 3
[[1,2,3],[4,5,7],[6],[8]] => 3
[[1,3,5],[2,4,6],[7],[8]] => 3
[[1,2,5],[3,4,6],[7],[8]] => 3
[[1,3,4],[2,5,6],[7],[8]] => 3
[[1,2,4],[3,5,6],[7],[8]] => 3
[[1,2,3],[4,5,6],[7],[8]] => 3
[[1,5,8],[2,6],[3,7],[4]] => 2
[[1,4,8],[2,6],[3,7],[5]] => 2
[[1,3,8],[2,6],[4,7],[5]] => 2
[[1,2,8],[3,6],[4,7],[5]] => 2
[[1,4,8],[2,5],[3,7],[6]] => 2
[[1,3,8],[2,5],[4,7],[6]] => 2
[[1,2,8],[3,5],[4,7],[6]] => 2
[[1,3,8],[2,4],[5,7],[6]] => 2
[[1,2,8],[3,4],[5,7],[6]] => 2
[[1,4,8],[2,5],[3,6],[7]] => 2
[[1,3,8],[2,5],[4,6],[7]] => 2
[[1,2,8],[3,5],[4,6],[7]] => 2
[[1,3,8],[2,4],[5,6],[7]] => 2
[[1,2,8],[3,4],[5,6],[7]] => 2
[[1,5,7],[2,6],[3,8],[4]] => 2
[[1,4,7],[2,6],[3,8],[5]] => 2
[[1,3,7],[2,6],[4,8],[5]] => 2
[[1,2,7],[3,6],[4,8],[5]] => 2
[[1,4,7],[2,5],[3,8],[6]] => 2
[[1,3,7],[2,5],[4,8],[6]] => 2
[[1,2,7],[3,5],[4,8],[6]] => 2
[[1,3,7],[2,4],[5,8],[6]] => 2
[[1,2,7],[3,4],[5,8],[6]] => 2
[[1,5,6],[2,7],[3,8],[4]] => 2
[[1,4,6],[2,7],[3,8],[5]] => 2
[[1,3,6],[2,7],[4,8],[5]] => 2
[[1,2,6],[3,7],[4,8],[5]] => 2
[[1,4,5],[2,7],[3,8],[6]] => 2
[[1,3,5],[2,7],[4,8],[6]] => 2
[[1,2,5],[3,7],[4,8],[6]] => 2
[[1,3,4],[2,7],[5,8],[6]] => 2
[[1,2,4],[3,7],[5,8],[6]] => 2
[[1,2,3],[4,7],[5,8],[6]] => 2
[[1,4,6],[2,5],[3,8],[7]] => 2
[[1,3,6],[2,5],[4,8],[7]] => 2
[[1,2,6],[3,5],[4,8],[7]] => 2
[[1,3,6],[2,4],[5,8],[7]] => 2
[[1,2,6],[3,4],[5,8],[7]] => 2
[[1,4,5],[2,6],[3,8],[7]] => 2
[[1,3,5],[2,6],[4,8],[7]] => 2
[[1,2,5],[3,6],[4,8],[7]] => 2
[[1,3,4],[2,6],[5,8],[7]] => 2
[[1,2,4],[3,6],[5,8],[7]] => 2
[[1,2,3],[4,6],[5,8],[7]] => 2
[[1,3,5],[2,4],[6,8],[7]] => 2
[[1,2,5],[3,4],[6,8],[7]] => 2
[[1,3,4],[2,5],[6,8],[7]] => 2
[[1,2,4],[3,5],[6,8],[7]] => 2
[[1,2,3],[4,5],[6,8],[7]] => 2
[[1,4,7],[2,5],[3,6],[8]] => 2
[[1,3,7],[2,5],[4,6],[8]] => 2
[[1,2,7],[3,5],[4,6],[8]] => 2
[[1,3,7],[2,4],[5,6],[8]] => 2
[[1,2,7],[3,4],[5,6],[8]] => 2
[[1,4,6],[2,5],[3,7],[8]] => 2
[[1,3,6],[2,5],[4,7],[8]] => 2
[[1,2,6],[3,5],[4,7],[8]] => 2
[[1,3,6],[2,4],[5,7],[8]] => 2
[[1,2,6],[3,4],[5,7],[8]] => 2
[[1,4,5],[2,6],[3,7],[8]] => 2
[[1,3,5],[2,6],[4,7],[8]] => 2
[[1,2,5],[3,6],[4,7],[8]] => 2
[[1,3,4],[2,6],[5,7],[8]] => 2
[[1,2,4],[3,6],[5,7],[8]] => 2
[[1,2,3],[4,6],[5,7],[8]] => 2
[[1,3,5],[2,4],[6,7],[8]] => 2
[[1,2,5],[3,4],[6,7],[8]] => 2
[[1,3,4],[2,5],[6,7],[8]] => 2
[[1,2,4],[3,5],[6,7],[8]] => 2
[[1,2,3],[4,5],[6,7],[8]] => 2
[[1,6,8],[2,7],[3],[4],[5]] => 1
[[1,5,8],[2,7],[3],[4],[6]] => 1
[[1,4,8],[2,7],[3],[5],[6]] => 1
[[1,3,8],[2,7],[4],[5],[6]] => 1
[[1,2,8],[3,7],[4],[5],[6]] => 1
[[1,5,8],[2,6],[3],[4],[7]] => 1
[[1,4,8],[2,6],[3],[5],[7]] => 1
[[1,3,8],[2,6],[4],[5],[7]] => 1
[[1,2,8],[3,6],[4],[5],[7]] => 1
[[1,4,8],[2,5],[3],[6],[7]] => 1
[[1,3,8],[2,5],[4],[6],[7]] => 1
[[1,2,8],[3,5],[4],[6],[7]] => 1
[[1,3,8],[2,4],[5],[6],[7]] => 1
[[1,2,8],[3,4],[5],[6],[7]] => 1
[[1,6,7],[2,8],[3],[4],[5]] => 1
[[1,5,7],[2,8],[3],[4],[6]] => 1
[[1,4,7],[2,8],[3],[5],[6]] => 1
[[1,3,7],[2,8],[4],[5],[6]] => 1
[[1,2,7],[3,8],[4],[5],[6]] => 1
[[1,5,6],[2,8],[3],[4],[7]] => 1
[[1,4,6],[2,8],[3],[5],[7]] => 1
[[1,3,6],[2,8],[4],[5],[7]] => 1
[[1,2,6],[3,8],[4],[5],[7]] => 1
[[1,4,5],[2,8],[3],[6],[7]] => 1
[[1,3,5],[2,8],[4],[6],[7]] => 1
[[1,2,5],[3,8],[4],[6],[7]] => 1
[[1,3,4],[2,8],[5],[6],[7]] => 1
[[1,2,4],[3,8],[5],[6],[7]] => 1
[[1,2,3],[4,8],[5],[6],[7]] => 1
[[1,5,7],[2,6],[3],[4],[8]] => 1
[[1,4,7],[2,6],[3],[5],[8]] => 1
[[1,3,7],[2,6],[4],[5],[8]] => 1
[[1,2,7],[3,6],[4],[5],[8]] => 1
[[1,4,7],[2,5],[3],[6],[8]] => 1
[[1,3,7],[2,5],[4],[6],[8]] => 1
[[1,2,7],[3,5],[4],[6],[8]] => 1
[[1,3,7],[2,4],[5],[6],[8]] => 1
[[1,2,7],[3,4],[5],[6],[8]] => 1
[[1,5,6],[2,7],[3],[4],[8]] => 1
[[1,4,6],[2,7],[3],[5],[8]] => 1
[[1,3,6],[2,7],[4],[5],[8]] => 1
[[1,2,6],[3,7],[4],[5],[8]] => 1
[[1,4,5],[2,7],[3],[6],[8]] => 1
[[1,3,5],[2,7],[4],[6],[8]] => 1
[[1,2,5],[3,7],[4],[6],[8]] => 1
[[1,3,4],[2,7],[5],[6],[8]] => 1
[[1,2,4],[3,7],[5],[6],[8]] => 1
[[1,2,3],[4,7],[5],[6],[8]] => 1
[[1,4,6],[2,5],[3],[7],[8]] => 1
[[1,3,6],[2,5],[4],[7],[8]] => 1
[[1,2,6],[3,5],[4],[7],[8]] => 1
[[1,3,6],[2,4],[5],[7],[8]] => 1
[[1,2,6],[3,4],[5],[7],[8]] => 1
[[1,4,5],[2,6],[3],[7],[8]] => 1
[[1,3,5],[2,6],[4],[7],[8]] => 1
[[1,2,5],[3,6],[4],[7],[8]] => 1
[[1,3,4],[2,6],[5],[7],[8]] => 1
[[1,2,4],[3,6],[5],[7],[8]] => 1
[[1,2,3],[4,6],[5],[7],[8]] => 1
[[1,3,5],[2,4],[6],[7],[8]] => 1
[[1,2,5],[3,4],[6],[7],[8]] => 1
[[1,3,4],[2,5],[6],[7],[8]] => 1
[[1,2,4],[3,5],[6],[7],[8]] => 1
[[1,2,3],[4,5],[6],[7],[8]] => 1
[[1,7,8],[2],[3],[4],[5],[6]] => 0
[[1,6,8],[2],[3],[4],[5],[7]] => 0
[[1,5,8],[2],[3],[4],[6],[7]] => 0
[[1,4,8],[2],[3],[5],[6],[7]] => 0
[[1,3,8],[2],[4],[5],[6],[7]] => 0
[[1,2,8],[3],[4],[5],[6],[7]] => 0
[[1,6,7],[2],[3],[4],[5],[8]] => 0
[[1,5,7],[2],[3],[4],[6],[8]] => 0
[[1,4,7],[2],[3],[5],[6],[8]] => 0
[[1,3,7],[2],[4],[5],[6],[8]] => 0
[[1,2,7],[3],[4],[5],[6],[8]] => 0
[[1,5,6],[2],[3],[4],[7],[8]] => 0
[[1,4,6],[2],[3],[5],[7],[8]] => 0
[[1,3,6],[2],[4],[5],[7],[8]] => 0
[[1,2,6],[3],[4],[5],[7],[8]] => 0
[[1,4,5],[2],[3],[6],[7],[8]] => 0
[[1,3,5],[2],[4],[6],[7],[8]] => 0
[[1,2,5],[3],[4],[6],[7],[8]] => 0
[[1,3,4],[2],[5],[6],[7],[8]] => 0
[[1,2,4],[3],[5],[6],[7],[8]] => 0
[[1,2,3],[4],[5],[6],[7],[8]] => 0
[[1,5],[2,6],[3,7],[4,8]] => 3
[[1,4],[2,6],[3,7],[5,8]] => 3
[[1,3],[2,6],[4,7],[5,8]] => 3
[[1,2],[3,6],[4,7],[5,8]] => 3
[[1,4],[2,5],[3,7],[6,8]] => 3
[[1,3],[2,5],[4,7],[6,8]] => 3
[[1,2],[3,5],[4,7],[6,8]] => 3
[[1,3],[2,4],[5,7],[6,8]] => 3
[[1,2],[3,4],[5,7],[6,8]] => 3
[[1,4],[2,5],[3,6],[7,8]] => 3
[[1,3],[2,5],[4,6],[7,8]] => 3
[[1,2],[3,5],[4,6],[7,8]] => 3
[[1,3],[2,4],[5,6],[7,8]] => 3
[[1,2],[3,4],[5,6],[7,8]] => 3
[[1,6],[2,7],[3,8],[4],[5]] => 2
[[1,5],[2,7],[3,8],[4],[6]] => 2
[[1,4],[2,7],[3,8],[5],[6]] => 2
[[1,3],[2,7],[4,8],[5],[6]] => 2
[[1,2],[3,7],[4,8],[5],[6]] => 2
[[1,5],[2,6],[3,8],[4],[7]] => 2
[[1,4],[2,6],[3,8],[5],[7]] => 2
[[1,3],[2,6],[4,8],[5],[7]] => 2
[[1,2],[3,6],[4,8],[5],[7]] => 2
[[1,4],[2,5],[3,8],[6],[7]] => 2
[[1,3],[2,5],[4,8],[6],[7]] => 2
[[1,2],[3,5],[4,8],[6],[7]] => 2
[[1,3],[2,4],[5,8],[6],[7]] => 2
[[1,2],[3,4],[5,8],[6],[7]] => 2
[[1,5],[2,6],[3,7],[4],[8]] => 2
[[1,4],[2,6],[3,7],[5],[8]] => 2
[[1,3],[2,6],[4,7],[5],[8]] => 2
[[1,2],[3,6],[4,7],[5],[8]] => 2
[[1,4],[2,5],[3,7],[6],[8]] => 2
[[1,3],[2,5],[4,7],[6],[8]] => 2
[[1,2],[3,5],[4,7],[6],[8]] => 2
[[1,3],[2,4],[5,7],[6],[8]] => 2
[[1,2],[3,4],[5,7],[6],[8]] => 2
[[1,4],[2,5],[3,6],[7],[8]] => 2
[[1,3],[2,5],[4,6],[7],[8]] => 2
[[1,2],[3,5],[4,6],[7],[8]] => 2
[[1,3],[2,4],[5,6],[7],[8]] => 2
[[1,2],[3,4],[5,6],[7],[8]] => 2
[[1,7],[2,8],[3],[4],[5],[6]] => 1
[[1,6],[2,8],[3],[4],[5],[7]] => 1
[[1,5],[2,8],[3],[4],[6],[7]] => 1
[[1,4],[2,8],[3],[5],[6],[7]] => 1
[[1,3],[2,8],[4],[5],[6],[7]] => 1
[[1,2],[3,8],[4],[5],[6],[7]] => 1
[[1,6],[2,7],[3],[4],[5],[8]] => 1
[[1,5],[2,7],[3],[4],[6],[8]] => 1
[[1,4],[2,7],[3],[5],[6],[8]] => 1
[[1,3],[2,7],[4],[5],[6],[8]] => 1
[[1,2],[3,7],[4],[5],[6],[8]] => 1
[[1,5],[2,6],[3],[4],[7],[8]] => 1
[[1,4],[2,6],[3],[5],[7],[8]] => 1
[[1,3],[2,6],[4],[5],[7],[8]] => 1
[[1,2],[3,6],[4],[5],[7],[8]] => 1
[[1,4],[2,5],[3],[6],[7],[8]] => 1
[[1,3],[2,5],[4],[6],[7],[8]] => 1
[[1,2],[3,5],[4],[6],[7],[8]] => 1
[[1,3],[2,4],[5],[6],[7],[8]] => 1
[[1,2],[3,4],[5],[6],[7],[8]] => 1
[[1,8],[2],[3],[4],[5],[6],[7]] => 0
[[1,7],[2],[3],[4],[5],[6],[8]] => 0
[[1,6],[2],[3],[4],[5],[7],[8]] => 0
[[1,5],[2],[3],[4],[6],[7],[8]] => 0
[[1,4],[2],[3],[5],[6],[7],[8]] => 0
[[1,3],[2],[4],[5],[6],[7],[8]] => 0
[[1,2],[3],[4],[5],[6],[7],[8]] => 0
[[1],[2],[3],[4],[5],[6],[7],[8]] => 0
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
8,2 16,10 32,34,5,5 64,98,35,35 128,258,154,168,42,0,14
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4$
$F_{4} = 8 + 2\ q$
$F_{5} = 16 + 10\ q$
$F_{6} = 32 + 34\ q + 5\ q^{2} + 5\ q^{3}$
$F_{7} = 64 + 98\ q + 35\ q^{2} + 35\ q^{3}$
$F_{8} = 128 + 258\ q + 154\ q^{2} + 168\ q^{3} + 42\ q^{4} + 14\ q^{6}$
Description
The number of inversions of a standard tableau.
Let $T$ be a tableau. An inversion is an attacking pair $(c,d)$ of the shape of $T$ (see St000016The number of attacking pairs of a standard tableau. for a definition of this) such that the entry of $c$ in $T$ is greater than the entry of $d$.
Let $T$ be a tableau. An inversion is an attacking pair $(c,d)$ of the shape of $T$ (see St000016The number of attacking pairs of a standard tableau. for a definition of this) such that the entry of $c$ in $T$ is greater than the entry of $d$.
Code
def statistic(x):
return len(x.inversions())
Created
Sep 27, 2011 at 20:02 by Chris Berg
Updated
Oct 16, 2015 at 11:10 by Christian Stump
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