Identifier
Identifier
Values
[[1,2]] => 0
[[1],[2]] => 1
[[1,2,3]] => 0
[[1,3],[2]] => 1
[[1,2],[3]] => 2
[[1],[2],[3]] => 0
[[1,2,3,4]] => 0
[[1,3,4],[2]] => 1
[[1,2,4],[3]] => 2
[[1,2,3],[4]] => 3
[[1,3],[2,4]] => 0
[[1,2],[3,4]] => 2
[[1,4],[2],[3]] => 3
[[1,3],[2],[4]] => 0
[[1,2],[3],[4]] => 1
[[1],[2],[3],[4]] => 2
[[1,2,3,4,5]] => 0
[[1,3,4,5],[2]] => 1
[[1,2,4,5],[3]] => 2
[[1,2,3,5],[4]] => 3
[[1,2,3,4],[5]] => 4
[[1,3,5],[2,4]] => 4
[[1,2,5],[3,4]] => 2
[[1,3,4],[2,5]] => 0
[[1,2,4],[3,5]] => 1
[[1,2,3],[4,5]] => 3
[[1,4,5],[2],[3]] => 3
[[1,3,5],[2],[4]] => 4
[[1,2,5],[3],[4]] => 0
[[1,3,4],[2],[5]] => 0
[[1,2,4],[3],[5]] => 1
[[1,2,3],[4],[5]] => 2
[[1,4],[2,5],[3]] => 2
[[1,3],[2,5],[4]] => 4
[[1,2],[3,5],[4]] => 0
[[1,3],[2,4],[5]] => 3
[[1,2],[3,4],[5]] => 1
[[1,5],[2],[3],[4]] => 1
[[1,4],[2],[3],[5]] => 2
[[1,3],[2],[4],[5]] => 3
[[1,2],[3],[4],[5]] => 4
[[1],[2],[3],[4],[5]] => 0
[[1,2,3,4,5,6]] => 0
[[1,3,4,5,6],[2]] => 1
[[1,2,4,5,6],[3]] => 2
[[1,2,3,5,6],[4]] => 3
[[1,2,3,4,6],[5]] => 4
[[1,2,3,4,5],[6]] => 5
[[1,3,5,6],[2,4]] => 4
[[1,2,5,6],[3,4]] => 2
[[1,3,4,6],[2,5]] => 5
[[1,2,4,6],[3,5]] => 0
[[1,2,3,6],[4,5]] => 3
[[1,3,4,5],[2,6]] => 0
[[1,2,4,5],[3,6]] => 1
[[1,2,3,5],[4,6]] => 2
[[1,2,3,4],[5,6]] => 4
[[1,4,5,6],[2],[3]] => 3
[[1,3,5,6],[2],[4]] => 4
[[1,2,5,6],[3],[4]] => 5
[[1,3,4,6],[2],[5]] => 5
[[1,2,4,6],[3],[5]] => 0
[[1,2,3,6],[4],[5]] => 1
[[1,3,4,5],[2],[6]] => 0
[[1,2,4,5],[3],[6]] => 1
[[1,2,3,5],[4],[6]] => 2
[[1,2,3,4],[5],[6]] => 3
[[1,3,5],[2,4,6]] => 3
[[1,2,5],[3,4,6]] => 1
[[1,3,4],[2,5,6]] => 5
[[1,2,4],[3,5,6]] => 0
[[1,2,3],[4,5,6]] => 3
[[1,4,6],[2,5],[3]] => 1
[[1,3,6],[2,5],[4]] => 4
[[1,2,6],[3,5],[4]] => 5
[[1,3,6],[2,4],[5]] => 2
[[1,2,6],[3,4],[5]] => 0
[[1,4,5],[2,6],[3]] => 2
[[1,3,5],[2,6],[4]] => 3
[[1,2,5],[3,6],[4]] => 4
[[1,3,4],[2,6],[5]] => 5
[[1,2,4],[3,6],[5]] => 0
[[1,2,3],[4,6],[5]] => 1
[[1,3,5],[2,4],[6]] => 3
[[1,2,5],[3,4],[6]] => 1
[[1,3,4],[2,5],[6]] => 4
[[1,2,4],[3,5],[6]] => 5
[[1,2,3],[4,5],[6]] => 2
[[1,5,6],[2],[3],[4]] => 0
[[1,4,6],[2],[3],[5]] => 1
[[1,3,6],[2],[4],[5]] => 2
[[1,2,6],[3],[4],[5]] => 3
[[1,4,5],[2],[3],[6]] => 2
[[1,3,5],[2],[4],[6]] => 3
[[1,2,5],[3],[4],[6]] => 4
[[1,3,4],[2],[5],[6]] => 4
[[1,2,4],[3],[5],[6]] => 5
[[1,2,3],[4],[5],[6]] => 0
[[1,4],[2,5],[3,6]] => 0
[[1,3],[2,5],[4,6]] => 3
[[1,2],[3,5],[4,6]] => 4
[[1,3],[2,4],[5,6]] => 2
[[1,2],[3,4],[5,6]] => 0
[[1,5],[2,6],[3],[4]] => 5
[[1,4],[2,6],[3],[5]] => 1
[[1,3],[2,6],[4],[5]] => 2
[[1,2],[3,6],[4],[5]] => 3
[[1,4],[2,5],[3],[6]] => 0
[[1,3],[2,5],[4],[6]] => 3
[[1,2],[3,5],[4],[6]] => 4
[[1,3],[2,4],[5],[6]] => 1
[[1,2],[3,4],[5],[6]] => 5
[[1,6],[2],[3],[4],[5]] => 4
[[1,5],[2],[3],[4],[6]] => 5
[[1,4],[2],[3],[5],[6]] => 0
[[1,3],[2],[4],[5],[6]] => 1
[[1,2],[3],[4],[5],[6]] => 2
[[1],[2],[3],[4],[5],[6]] => 3
[[1,2,3,4,5,6,7]] => 0
[[1,3,4,5,6,7],[2]] => 1
[[1,2,4,5,6,7],[3]] => 2
[[1,2,3,5,6,7],[4]] => 3
[[1,2,3,4,6,7],[5]] => 4
[[1,2,3,4,5,7],[6]] => 5
[[1,2,3,4,5,6],[7]] => 6
[[1,3,5,6,7],[2,4]] => 4
[[1,2,5,6,7],[3,4]] => 2
[[1,3,4,6,7],[2,5]] => 5
[[1,2,4,6,7],[3,5]] => 6
[[1,2,3,6,7],[4,5]] => 3
[[1,3,4,5,7],[2,6]] => 6
[[1,2,4,5,7],[3,6]] => 0
[[1,2,3,5,7],[4,6]] => 1
[[1,2,3,4,7],[5,6]] => 4
[[1,3,4,5,6],[2,7]] => 0
[[1,2,4,5,6],[3,7]] => 1
[[1,2,3,5,6],[4,7]] => 2
[[1,2,3,4,6],[5,7]] => 3
[[1,2,3,4,5],[6,7]] => 5
[[1,4,5,6,7],[2],[3]] => 3
[[1,3,5,6,7],[2],[4]] => 4
[[1,2,5,6,7],[3],[4]] => 5
[[1,3,4,6,7],[2],[5]] => 5
[[1,2,4,6,7],[3],[5]] => 6
[[1,2,3,6,7],[4],[5]] => 0
[[1,3,4,5,7],[2],[6]] => 6
[[1,2,4,5,7],[3],[6]] => 0
[[1,2,3,5,7],[4],[6]] => 1
[[1,2,3,4,7],[5],[6]] => 2
[[1,3,4,5,6],[2],[7]] => 0
[[1,2,4,5,6],[3],[7]] => 1
[[1,2,3,5,6],[4],[7]] => 2
[[1,2,3,4,6],[5],[7]] => 3
[[1,2,3,4,5],[6],[7]] => 4
[[1,3,5,7],[2,4,6]] => 2
[[1,2,5,7],[3,4,6]] => 0
[[1,3,4,7],[2,5,6]] => 5
[[1,2,4,7],[3,5,6]] => 6
[[1,2,3,7],[4,5,6]] => 3
[[1,3,5,6],[2,4,7]] => 3
[[1,2,5,6],[3,4,7]] => 1
[[1,3,4,6],[2,5,7]] => 4
[[1,2,4,6],[3,5,7]] => 5
[[1,2,3,6],[4,5,7]] => 2
[[1,3,4,5],[2,6,7]] => 6
[[1,2,4,5],[3,6,7]] => 0
[[1,2,3,5],[4,6,7]] => 1
[[1,2,3,4],[5,6,7]] => 4
[[1,4,6,7],[2,5],[3]] => 0
[[1,3,6,7],[2,5],[4]] => 4
[[1,2,6,7],[3,5],[4]] => 5
[[1,3,6,7],[2,4],[5]] => 1
[[1,2,6,7],[3,4],[5]] => 6
[[1,4,5,7],[2,6],[3]] => 1
[[1,3,5,7],[2,6],[4]] => 2
[[1,2,5,7],[3,6],[4]] => 3
[[1,3,4,7],[2,6],[5]] => 5
[[1,2,4,7],[3,6],[5]] => 6
[[1,2,3,7],[4,6],[5]] => 0
[[1,3,5,7],[2,4],[6]] => 2
[[1,2,5,7],[3,4],[6]] => 0
[[1,3,4,7],[2,5],[6]] => 3
[[1,2,4,7],[3,5],[6]] => 4
[[1,2,3,7],[4,5],[6]] => 1
[[1,4,5,6],[2,7],[3]] => 2
[[1,3,5,6],[2,7],[4]] => 3
[[1,2,5,6],[3,7],[4]] => 4
[[1,3,4,6],[2,7],[5]] => 4
[[1,2,4,6],[3,7],[5]] => 5
[[1,2,3,6],[4,7],[5]] => 6
[[1,3,4,5],[2,7],[6]] => 6
[[1,2,4,5],[3,7],[6]] => 0
[[1,2,3,5],[4,7],[6]] => 1
[[1,2,3,4],[5,7],[6]] => 2
[[1,3,5,6],[2,4],[7]] => 3
[[1,2,5,6],[3,4],[7]] => 1
[[1,3,4,6],[2,5],[7]] => 4
[[1,2,4,6],[3,5],[7]] => 5
[[1,2,3,6],[4,5],[7]] => 2
[[1,3,4,5],[2,6],[7]] => 5
[[1,2,4,5],[3,6],[7]] => 6
[[1,2,3,5],[4,6],[7]] => 0
[[1,2,3,4],[5,6],[7]] => 3
[[1,5,6,7],[2],[3],[4]] => 6
[[1,4,6,7],[2],[3],[5]] => 0
[[1,3,6,7],[2],[4],[5]] => 1
[[1,2,6,7],[3],[4],[5]] => 2
[[1,4,5,7],[2],[3],[6]] => 1
[[1,3,5,7],[2],[4],[6]] => 2
[[1,2,5,7],[3],[4],[6]] => 3
[[1,3,4,7],[2],[5],[6]] => 3
[[1,2,4,7],[3],[5],[6]] => 4
[[1,2,3,7],[4],[5],[6]] => 5
[[1,4,5,6],[2],[3],[7]] => 2
[[1,3,5,6],[2],[4],[7]] => 3
[[1,2,5,6],[3],[4],[7]] => 4
[[1,3,4,6],[2],[5],[7]] => 4
[[1,2,4,6],[3],[5],[7]] => 5
[[1,2,3,6],[4],[5],[7]] => 6
[[1,3,4,5],[2],[6],[7]] => 5
[[1,2,4,5],[3],[6],[7]] => 6
[[1,2,3,5],[4],[6],[7]] => 0
[[1,2,3,4],[5],[6],[7]] => 1
[[1,4,6],[2,5,7],[3]] => 6
[[1,3,6],[2,5,7],[4]] => 3
[[1,2,6],[3,5,7],[4]] => 4
[[1,3,6],[2,4,7],[5]] => 0
[[1,2,6],[3,4,7],[5]] => 5
[[1,4,5],[2,6,7],[3]] => 1
[[1,3,5],[2,6,7],[4]] => 2
[[1,2,5],[3,6,7],[4]] => 3
[[1,3,4],[2,6,7],[5]] => 5
[[1,2,4],[3,6,7],[5]] => 6
[[1,2,3],[4,6,7],[5]] => 0
[[1,3,5],[2,4,7],[6]] => 2
[[1,2,5],[3,4,7],[6]] => 0
[[1,3,4],[2,5,7],[6]] => 3
[[1,2,4],[3,5,7],[6]] => 4
[[1,2,3],[4,5,7],[6]] => 1
[[1,3,5],[2,4,6],[7]] => 1
[[1,2,5],[3,4,6],[7]] => 6
[[1,3,4],[2,5,6],[7]] => 4
[[1,2,4],[3,5,6],[7]] => 5
[[1,2,3],[4,5,6],[7]] => 2
[[1,4,7],[2,5],[3,6]] => 5
[[1,3,7],[2,5],[4,6]] => 2
[[1,2,7],[3,5],[4,6]] => 3
[[1,3,7],[2,4],[5,6]] => 1
[[1,2,7],[3,4],[5,6]] => 6
[[1,4,6],[2,5],[3,7]] => 6
[[1,3,6],[2,5],[4,7]] => 3
[[1,2,6],[3,5],[4,7]] => 4
[[1,3,6],[2,4],[5,7]] => 0
[[1,2,6],[3,4],[5,7]] => 5
[[1,4,5],[2,6],[3,7]] => 0
[[1,3,5],[2,6],[4,7]] => 1
[[1,2,5],[3,6],[4,7]] => 2
[[1,3,4],[2,6],[5,7]] => 4
[[1,2,4],[3,6],[5,7]] => 5
[[1,2,3],[4,6],[5,7]] => 6
[[1,3,5],[2,4],[6,7]] => 2
[[1,2,5],[3,4],[6,7]] => 0
[[1,3,4],[2,5],[6,7]] => 3
[[1,2,4],[3,5],[6,7]] => 4
[[1,2,3],[4,5],[6,7]] => 1
[[1,5,7],[2,6],[3],[4]] => 4
[[1,4,7],[2,6],[3],[5]] => 0
[[1,3,7],[2,6],[4],[5]] => 1
[[1,2,7],[3,6],[4],[5]] => 2
[[1,4,7],[2,5],[3],[6]] => 5
[[1,3,7],[2,5],[4],[6]] => 2
[[1,2,7],[3,5],[4],[6]] => 3
[[1,3,7],[2,4],[5],[6]] => 6
[[1,2,7],[3,4],[5],[6]] => 4
[[1,5,6],[2,7],[3],[4]] => 5
[[1,4,6],[2,7],[3],[5]] => 6
[[1,3,6],[2,7],[4],[5]] => 0
[[1,2,6],[3,7],[4],[5]] => 1
[[1,4,5],[2,7],[3],[6]] => 1
[[1,3,5],[2,7],[4],[6]] => 2
[[1,2,5],[3,7],[4],[6]] => 3
[[1,3,4],[2,7],[5],[6]] => 3
[[1,2,4],[3,7],[5],[6]] => 4
[[1,2,3],[4,7],[5],[6]] => 5
[[1,4,6],[2,5],[3],[7]] => 6
[[1,3,6],[2,5],[4],[7]] => 3
[[1,2,6],[3,5],[4],[7]] => 4
[[1,3,6],[2,4],[5],[7]] => 0
[[1,2,6],[3,4],[5],[7]] => 5
[[1,4,5],[2,6],[3],[7]] => 0
[[1,3,5],[2,6],[4],[7]] => 1
[[1,2,5],[3,6],[4],[7]] => 2
[[1,3,4],[2,6],[5],[7]] => 4
[[1,2,4],[3,6],[5],[7]] => 5
[[1,2,3],[4,6],[5],[7]] => 6
[[1,3,5],[2,4],[6],[7]] => 1
[[1,2,5],[3,4],[6],[7]] => 6
[[1,3,4],[2,5],[6],[7]] => 2
[[1,2,4],[3,5],[6],[7]] => 3
[[1,2,3],[4,5],[6],[7]] => 0
[[1,6,7],[2],[3],[4],[5]] => 3
[[1,5,7],[2],[3],[4],[6]] => 4
[[1,4,7],[2],[3],[5],[6]] => 5
[[1,3,7],[2],[4],[5],[6]] => 6
[[1,2,7],[3],[4],[5],[6]] => 0
[[1,5,6],[2],[3],[4],[7]] => 5
[[1,4,6],[2],[3],[5],[7]] => 6
[[1,3,6],[2],[4],[5],[7]] => 0
[[1,2,6],[3],[4],[5],[7]] => 1
[[1,4,5],[2],[3],[6],[7]] => 0
[[1,3,5],[2],[4],[6],[7]] => 1
[[1,2,5],[3],[4],[6],[7]] => 2
[[1,3,4],[2],[5],[6],[7]] => 2
[[1,2,4],[3],[5],[6],[7]] => 3
[[1,2,3],[4],[5],[6],[7]] => 4
[[1,5],[2,6],[3,7],[4]] => 3
[[1,4],[2,6],[3,7],[5]] => 6
[[1,3],[2,6],[4,7],[5]] => 0
[[1,2],[3,6],[4,7],[5]] => 1
[[1,4],[2,5],[3,7],[6]] => 5
[[1,3],[2,5],[4,7],[6]] => 2
[[1,2],[3,5],[4,7],[6]] => 3
[[1,3],[2,4],[5,7],[6]] => 6
[[1,2],[3,4],[5,7],[6]] => 4
[[1,4],[2,5],[3,6],[7]] => 4
[[1,3],[2,5],[4,6],[7]] => 1
[[1,2],[3,5],[4,6],[7]] => 2
[[1,3],[2,4],[5,6],[7]] => 0
[[1,2],[3,4],[5,6],[7]] => 5
[[1,6],[2,7],[3],[4],[5]] => 2
[[1,5],[2,7],[3],[4],[6]] => 4
[[1,4],[2,7],[3],[5],[6]] => 5
[[1,3],[2,7],[4],[5],[6]] => 6
[[1,2],[3,7],[4],[5],[6]] => 0
[[1,5],[2,6],[3],[4],[7]] => 3
[[1,4],[2,6],[3],[5],[7]] => 6
[[1,3],[2,6],[4],[5],[7]] => 0
[[1,2],[3,6],[4],[5],[7]] => 1
[[1,4],[2,5],[3],[6],[7]] => 4
[[1,3],[2,5],[4],[6],[7]] => 1
[[1,2],[3,5],[4],[6],[7]] => 2
[[1,3],[2,4],[5],[6],[7]] => 5
[[1,2],[3,4],[5],[6],[7]] => 3
[[1,7],[2],[3],[4],[5],[6]] => 1
[[1,6],[2],[3],[4],[5],[7]] => 2
[[1,5],[2],[3],[4],[6],[7]] => 3
[[1,4],[2],[3],[5],[6],[7]] => 4
[[1,3],[2],[4],[5],[6],[7]] => 5
[[1,2],[3],[4],[5],[6],[7]] => 6
[[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]] => 1
[[1,2,4,5,6,7,8],[3]] => 2
[[1,2,3,5,6,7,8],[4]] => 3
[[1,2,3,4,6,7,8],[5]] => 4
[[1,2,3,4,5,7,8],[6]] => 5
[[1,2,3,4,5,6,8],[7]] => 6
[[1,2,3,4,5,6,7],[8]] => 7
[[1,3,5,6,7,8],[2,4]] => 4
[[1,2,5,6,7,8],[3,4]] => 2
[[1,3,4,6,7,8],[2,5]] => 5
[[1,2,4,6,7,8],[3,5]] => 6
[[1,2,3,6,7,8],[4,5]] => 3
[[1,3,4,5,7,8],[2,6]] => 6
[[1,2,4,5,7,8],[3,6]] => 7
[[1,2,3,5,7,8],[4,6]] => 0
[[1,2,3,4,7,8],[5,6]] => 4
[[1,3,4,5,6,8],[2,7]] => 7
[[1,2,4,5,6,8],[3,7]] => 0
[[1,2,3,5,6,8],[4,7]] => 1
[[1,2,3,4,6,8],[5,7]] => 2
[[1,2,3,4,5,8],[6,7]] => 5
[[1,3,4,5,6,7],[2,8]] => 0
[[1,2,4,5,6,7],[3,8]] => 1
[[1,2,3,5,6,7],[4,8]] => 2
[[1,2,3,4,6,7],[5,8]] => 3
[[1,2,3,4,5,7],[6,8]] => 4
[[1,2,3,4,5,6],[7,8]] => 6
[[1,4,5,6,7,8],[2],[3]] => 3
[[1,3,5,6,7,8],[2],[4]] => 4
[[1,2,5,6,7,8],[3],[4]] => 5
[[1,3,4,6,7,8],[2],[5]] => 5
[[1,2,4,6,7,8],[3],[5]] => 6
[[1,2,3,6,7,8],[4],[5]] => 7
[[1,3,4,5,7,8],[2],[6]] => 6
[[1,2,4,5,7,8],[3],[6]] => 7
[[1,2,3,5,7,8],[4],[6]] => 0
[[1,2,3,4,7,8],[5],[6]] => 1
[[1,3,4,5,6,8],[2],[7]] => 7
[[1,2,4,5,6,8],[3],[7]] => 0
[[1,2,3,5,6,8],[4],[7]] => 1
[[1,2,3,4,6,8],[5],[7]] => 2
[[1,2,3,4,5,8],[6],[7]] => 3
[[1,3,4,5,6,7],[2],[8]] => 0
[[1,2,4,5,6,7],[3],[8]] => 1
[[1,2,3,5,6,7],[4],[8]] => 2
[[1,2,3,4,6,7],[5],[8]] => 3
[[1,2,3,4,5,7],[6],[8]] => 4
[[1,2,3,4,5,6],[7],[8]] => 5
[[1,3,5,7,8],[2,4,6]] => 1
[[1,2,5,7,8],[3,4,6]] => 7
[[1,3,4,7,8],[2,5,6]] => 5
[[1,2,4,7,8],[3,5,6]] => 6
[[1,2,3,7,8],[4,5,6]] => 3
[[1,3,5,6,8],[2,4,7]] => 2
[[1,2,5,6,8],[3,4,7]] => 0
[[1,3,4,6,8],[2,5,7]] => 3
[[1,2,4,6,8],[3,5,7]] => 4
[[1,2,3,6,8],[4,5,7]] => 1
[[1,3,4,5,8],[2,6,7]] => 6
[[1,2,4,5,8],[3,6,7]] => 7
[[1,2,3,5,8],[4,6,7]] => 0
[[1,2,3,4,8],[5,6,7]] => 4
[[1,3,5,6,7],[2,4,8]] => 3
[[1,2,5,6,7],[3,4,8]] => 1
[[1,3,4,6,7],[2,5,8]] => 4
[[1,2,4,6,7],[3,5,8]] => 5
[[1,2,3,6,7],[4,5,8]] => 2
[[1,3,4,5,7],[2,6,8]] => 5
[[1,2,4,5,7],[3,6,8]] => 6
[[1,2,3,5,7],[4,6,8]] => 7
[[1,2,3,4,7],[5,6,8]] => 3
[[1,3,4,5,6],[2,7,8]] => 7
[[1,2,4,5,6],[3,7,8]] => 0
[[1,2,3,5,6],[4,7,8]] => 1
[[1,2,3,4,6],[5,7,8]] => 2
[[1,2,3,4,5],[6,7,8]] => 5
[[1,4,6,7,8],[2,5],[3]] => 7
[[1,3,6,7,8],[2,5],[4]] => 4
[[1,2,6,7,8],[3,5],[4]] => 5
[[1,3,6,7,8],[2,4],[5]] => 0
[[1,2,6,7,8],[3,4],[5]] => 6
[[1,4,5,7,8],[2,6],[3]] => 0
[[1,3,5,7,8],[2,6],[4]] => 1
[[1,2,5,7,8],[3,6],[4]] => 2
[[1,3,4,7,8],[2,6],[5]] => 5
[[1,2,4,7,8],[3,6],[5]] => 6
[[1,2,3,7,8],[4,6],[5]] => 7
[[1,3,5,7,8],[2,4],[6]] => 1
[[1,2,5,7,8],[3,4],[6]] => 7
[[1,3,4,7,8],[2,5],[6]] => 2
[[1,2,4,7,8],[3,5],[6]] => 3
[[1,2,3,7,8],[4,5],[6]] => 0
[[1,4,5,6,8],[2,7],[3]] => 1
[[1,3,5,6,8],[2,7],[4]] => 2
[[1,2,5,6,8],[3,7],[4]] => 3
[[1,3,4,6,8],[2,7],[5]] => 3
[[1,2,4,6,8],[3,7],[5]] => 4
[[1,2,3,6,8],[4,7],[5]] => 5
[[1,3,4,5,8],[2,7],[6]] => 6
[[1,2,4,5,8],[3,7],[6]] => 7
[[1,2,3,5,8],[4,7],[6]] => 0
[[1,2,3,4,8],[5,7],[6]] => 1
[[1,3,5,6,8],[2,4],[7]] => 2
[[1,2,5,6,8],[3,4],[7]] => 0
[[1,3,4,6,8],[2,5],[7]] => 3
[[1,2,4,6,8],[3,5],[7]] => 4
[[1,2,3,6,8],[4,5],[7]] => 1
[[1,3,4,5,8],[2,6],[7]] => 4
[[1,2,4,5,8],[3,6],[7]] => 5
[[1,2,3,5,8],[4,6],[7]] => 6
[[1,2,3,4,8],[5,6],[7]] => 2
[[1,4,5,6,7],[2,8],[3]] => 2
[[1,3,5,6,7],[2,8],[4]] => 3
[[1,2,5,6,7],[3,8],[4]] => 4
[[1,3,4,6,7],[2,8],[5]] => 4
[[1,2,4,6,7],[3,8],[5]] => 5
[[1,2,3,6,7],[4,8],[5]] => 6
[[1,3,4,5,7],[2,8],[6]] => 5
[[1,2,4,5,7],[3,8],[6]] => 6
[[1,2,3,5,7],[4,8],[6]] => 7
[[1,2,3,4,7],[5,8],[6]] => 0
[[1,3,4,5,6],[2,8],[7]] => 7
[[1,2,4,5,6],[3,8],[7]] => 0
[[1,2,3,5,6],[4,8],[7]] => 1
[[1,2,3,4,6],[5,8],[7]] => 2
[[1,2,3,4,5],[6,8],[7]] => 3
[[1,3,5,6,7],[2,4],[8]] => 3
[[1,2,5,6,7],[3,4],[8]] => 1
[[1,3,4,6,7],[2,5],[8]] => 4
[[1,2,4,6,7],[3,5],[8]] => 5
[[1,2,3,6,7],[4,5],[8]] => 2
[[1,3,4,5,7],[2,6],[8]] => 5
[[1,2,4,5,7],[3,6],[8]] => 6
[[1,2,3,5,7],[4,6],[8]] => 7
[[1,2,3,4,7],[5,6],[8]] => 3
[[1,3,4,5,6],[2,7],[8]] => 6
[[1,2,4,5,6],[3,7],[8]] => 7
[[1,2,3,5,6],[4,7],[8]] => 0
[[1,2,3,4,6],[5,7],[8]] => 1
[[1,2,3,4,5],[6,7],[8]] => 4
[[1,5,6,7,8],[2],[3],[4]] => 6
[[1,4,6,7,8],[2],[3],[5]] => 7
[[1,3,6,7,8],[2],[4],[5]] => 0
[[1,2,6,7,8],[3],[4],[5]] => 1
[[1,4,5,7,8],[2],[3],[6]] => 0
[[1,3,5,7,8],[2],[4],[6]] => 1
[[1,2,5,7,8],[3],[4],[6]] => 2
[[1,3,4,7,8],[2],[5],[6]] => 2
[[1,2,4,7,8],[3],[5],[6]] => 3
[[1,2,3,7,8],[4],[5],[6]] => 4
[[1,4,5,6,8],[2],[3],[7]] => 1
[[1,3,5,6,8],[2],[4],[7]] => 2
[[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]] => 4
[[1,2,3,6,8],[4],[5],[7]] => 5
[[1,3,4,5,8],[2],[6],[7]] => 4
[[1,2,4,5,8],[3],[6],[7]] => 5
[[1,2,3,5,8],[4],[6],[7]] => 6
[[1,2,3,4,8],[5],[6],[7]] => 7
[[1,4,5,6,7],[2],[3],[8]] => 2
[[1,3,5,6,7],[2],[4],[8]] => 3
[[1,2,5,6,7],[3],[4],[8]] => 4
[[1,3,4,6,7],[2],[5],[8]] => 4
[[1,2,4,6,7],[3],[5],[8]] => 5
[[1,2,3,6,7],[4],[5],[8]] => 6
[[1,3,4,5,7],[2],[6],[8]] => 5
[[1,2,4,5,7],[3],[6],[8]] => 6
[[1,2,3,5,7],[4],[6],[8]] => 7
[[1,2,3,4,7],[5],[6],[8]] => 0
[[1,3,4,5,6],[2],[7],[8]] => 6
[[1,2,4,5,6],[3],[7],[8]] => 7
[[1,2,3,5,6],[4],[7],[8]] => 0
[[1,2,3,4,6],[5],[7],[8]] => 1
[[1,2,3,4,5],[6],[7],[8]] => 2
[[1,3,5,7],[2,4,6,8]] => 0
[[1,2,5,7],[3,4,6,8]] => 6
[[1,3,4,7],[2,5,6,8]] => 4
[[1,2,4,7],[3,5,6,8]] => 5
[[1,2,3,7],[4,5,6,8]] => 2
[[1,3,5,6],[2,4,7,8]] => 2
[[1,2,5,6],[3,4,7,8]] => 0
[[1,3,4,6],[2,5,7,8]] => 3
[[1,2,4,6],[3,5,7,8]] => 4
[[1,2,3,6],[4,5,7,8]] => 1
[[1,3,4,5],[2,6,7,8]] => 6
[[1,2,4,5],[3,6,7,8]] => 7
[[1,2,3,5],[4,6,7,8]] => 0
[[1,2,3,4],[5,6,7,8]] => 4
[[1,4,6,8],[2,5,7],[3]] => 5
[[1,3,6,8],[2,5,7],[4]] => 2
[[1,2,6,8],[3,5,7],[4]] => 3
[[1,3,6,8],[2,4,7],[5]] => 6
[[1,2,6,8],[3,4,7],[5]] => 4
[[1,4,5,8],[2,6,7],[3]] => 0
[[1,3,5,8],[2,6,7],[4]] => 1
[[1,2,5,8],[3,6,7],[4]] => 2
[[1,3,4,8],[2,6,7],[5]] => 5
[[1,2,4,8],[3,6,7],[5]] => 6
[[1,2,3,8],[4,6,7],[5]] => 7
[[1,3,5,8],[2,4,7],[6]] => 1
[[1,2,5,8],[3,4,7],[6]] => 7
[[1,3,4,8],[2,5,7],[6]] => 2
[[1,2,4,8],[3,5,7],[6]] => 3
[[1,2,3,8],[4,5,7],[6]] => 0
[[1,3,5,8],[2,4,6],[7]] => 7
[[1,2,5,8],[3,4,6],[7]] => 5
[[1,3,4,8],[2,5,6],[7]] => 3
[[1,2,4,8],[3,5,6],[7]] => 4
[[1,2,3,8],[4,5,6],[7]] => 1
[[1,4,6,7],[2,5,8],[3]] => 6
[[1,3,6,7],[2,5,8],[4]] => 3
[[1,2,6,7],[3,5,8],[4]] => 4
[[1,3,6,7],[2,4,8],[5]] => 7
[[1,2,6,7],[3,4,8],[5]] => 5
[[1,4,5,7],[2,6,8],[3]] => 7
[[1,3,5,7],[2,6,8],[4]] => 0
[[1,2,5,7],[3,6,8],[4]] => 1
[[1,3,4,7],[2,6,8],[5]] => 4
[[1,2,4,7],[3,6,8],[5]] => 5
[[1,2,3,7],[4,6,8],[5]] => 6
[[1,3,5,7],[2,4,8],[6]] => 0
[[1,2,5,7],[3,4,8],[6]] => 6
[[1,3,4,7],[2,5,8],[6]] => 1
[[1,2,4,7],[3,5,8],[6]] => 2
[[1,2,3,7],[4,5,8],[6]] => 7
[[1,4,5,6],[2,7,8],[3]] => 1
[[1,3,5,6],[2,7,8],[4]] => 2
[[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]] => 4
[[1,2,3,6],[4,7,8],[5]] => 5
[[1,3,4,5],[2,7,8],[6]] => 6
[[1,2,4,5],[3,7,8],[6]] => 7
[[1,2,3,5],[4,7,8],[6]] => 0
[[1,2,3,4],[5,7,8],[6]] => 1
[[1,3,5,6],[2,4,8],[7]] => 2
[[1,2,5,6],[3,4,8],[7]] => 0
[[1,3,4,6],[2,5,8],[7]] => 3
[[1,2,4,6],[3,5,8],[7]] => 4
[[1,2,3,6],[4,5,8],[7]] => 1
[[1,3,4,5],[2,6,8],[7]] => 4
[[1,2,4,5],[3,6,8],[7]] => 5
[[1,2,3,5],[4,6,8],[7]] => 6
[[1,2,3,4],[5,6,8],[7]] => 2
[[1,3,5,7],[2,4,6],[8]] => 0
[[1,2,5,7],[3,4,6],[8]] => 6
[[1,3,4,7],[2,5,6],[8]] => 4
[[1,2,4,7],[3,5,6],[8]] => 5
[[1,2,3,7],[4,5,6],[8]] => 2
[[1,3,5,6],[2,4,7],[8]] => 1
[[1,2,5,6],[3,4,7],[8]] => 7
[[1,3,4,6],[2,5,7],[8]] => 2
[[1,2,4,6],[3,5,7],[8]] => 3
[[1,2,3,6],[4,5,7],[8]] => 0
[[1,3,4,5],[2,6,7],[8]] => 5
[[1,2,4,5],[3,6,7],[8]] => 6
[[1,2,3,5],[4,6,7],[8]] => 7
[[1,2,3,4],[5,6,7],[8]] => 3
[[1,4,7,8],[2,5],[3,6]] => 4
[[1,3,7,8],[2,5],[4,6]] => 1
[[1,2,7,8],[3,5],[4,6]] => 2
[[1,3,7,8],[2,4],[5,6]] => 0
[[1,2,7,8],[3,4],[5,6]] => 6
[[1,4,6,8],[2,5],[3,7]] => 5
[[1,3,6,8],[2,5],[4,7]] => 2
[[1,2,6,8],[3,5],[4,7]] => 3
[[1,3,6,8],[2,4],[5,7]] => 6
[[1,2,6,8],[3,4],[5,7]] => 4
[[1,4,5,8],[2,6],[3,7]] => 6
[[1,3,5,8],[2,6],[4,7]] => 7
[[1,2,5,8],[3,6],[4,7]] => 0
[[1,3,4,8],[2,6],[5,7]] => 3
[[1,2,4,8],[3,6],[5,7]] => 4
[[1,2,3,8],[4,6],[5,7]] => 5
[[1,3,5,8],[2,4],[6,7]] => 1
[[1,2,5,8],[3,4],[6,7]] => 7
[[1,3,4,8],[2,5],[6,7]] => 2
[[1,2,4,8],[3,5],[6,7]] => 3
[[1,2,3,8],[4,5],[6,7]] => 0
[[1,4,6,7],[2,5],[3,8]] => 6
[[1,3,6,7],[2,5],[4,8]] => 3
[[1,2,6,7],[3,5],[4,8]] => 4
[[1,3,6,7],[2,4],[5,8]] => 7
[[1,2,6,7],[3,4],[5,8]] => 5
[[1,4,5,7],[2,6],[3,8]] => 7
[[1,3,5,7],[2,6],[4,8]] => 0
[[1,2,5,7],[3,6],[4,8]] => 1
[[1,3,4,7],[2,6],[5,8]] => 4
[[1,2,4,7],[3,6],[5,8]] => 5
[[1,2,3,7],[4,6],[5,8]] => 6
[[1,3,5,7],[2,4],[6,8]] => 0
[[1,2,5,7],[3,4],[6,8]] => 6
[[1,3,4,7],[2,5],[6,8]] => 1
[[1,2,4,7],[3,5],[6,8]] => 2
[[1,2,3,7],[4,5],[6,8]] => 7
[[1,4,5,6],[2,7],[3,8]] => 0
[[1,3,5,6],[2,7],[4,8]] => 1
[[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]] => 3
[[1,2,3,6],[4,7],[5,8]] => 4
[[1,3,4,5],[2,7],[6,8]] => 5
[[1,2,4,5],[3,7],[6,8]] => 6
[[1,2,3,5],[4,7],[6,8]] => 7
[[1,2,3,4],[5,7],[6,8]] => 0
[[1,3,5,6],[2,4],[7,8]] => 2
[[1,2,5,6],[3,4],[7,8]] => 0
[[1,3,4,6],[2,5],[7,8]] => 3
[[1,2,4,6],[3,5],[7,8]] => 4
[[1,2,3,6],[4,5],[7,8]] => 1
[[1,3,4,5],[2,6],[7,8]] => 4
[[1,2,4,5],[3,6],[7,8]] => 5
[[1,2,3,5],[4,6],[7,8]] => 6
[[1,2,3,4],[5,6],[7,8]] => 2
[[1,5,7,8],[2,6],[3],[4]] => 3
[[1,4,7,8],[2,6],[3],[5]] => 7
[[1,3,7,8],[2,6],[4],[5]] => 0
[[1,2,7,8],[3,6],[4],[5]] => 1
[[1,4,7,8],[2,5],[3],[6]] => 4
[[1,3,7,8],[2,5],[4],[6]] => 1
[[1,2,7,8],[3,5],[4],[6]] => 2
[[1,3,7,8],[2,4],[5],[6]] => 5
[[1,2,7,8],[3,4],[5],[6]] => 3
[[1,5,6,8],[2,7],[3],[4]] => 4
[[1,4,6,8],[2,7],[3],[5]] => 5
[[1,3,6,8],[2,7],[4],[5]] => 6
[[1,2,6,8],[3,7],[4],[5]] => 7
[[1,4,5,8],[2,7],[3],[6]] => 0
[[1,3,5,8],[2,7],[4],[6]] => 1
[[1,2,5,8],[3,7],[4],[6]] => 2
[[1,3,4,8],[2,7],[5],[6]] => 2
[[1,2,4,8],[3,7],[5],[6]] => 3
[[1,2,3,8],[4,7],[5],[6]] => 4
[[1,4,6,8],[2,5],[3],[7]] => 5
[[1,3,6,8],[2,5],[4],[7]] => 2
[[1,2,6,8],[3,5],[4],[7]] => 3
[[1,3,6,8],[2,4],[5],[7]] => 6
[[1,2,6,8],[3,4],[5],[7]] => 4
[[1,4,5,8],[2,6],[3],[7]] => 6
[[1,3,5,8],[2,6],[4],[7]] => 7
[[1,2,5,8],[3,6],[4],[7]] => 0
[[1,3,4,8],[2,6],[5],[7]] => 3
[[1,2,4,8],[3,6],[5],[7]] => 4
[[1,2,3,8],[4,6],[5],[7]] => 5
[[1,3,5,8],[2,4],[6],[7]] => 7
[[1,2,5,8],[3,4],[6],[7]] => 5
[[1,3,4,8],[2,5],[6],[7]] => 0
[[1,2,4,8],[3,5],[6],[7]] => 1
[[1,2,3,8],[4,5],[6],[7]] => 6
[[1,5,6,7],[2,8],[3],[4]] => 5
[[1,4,6,7],[2,8],[3],[5]] => 6
[[1,3,6,7],[2,8],[4],[5]] => 7
[[1,2,6,7],[3,8],[4],[5]] => 0
[[1,4,5,7],[2,8],[3],[6]] => 7
[[1,3,5,7],[2,8],[4],[6]] => 0
[[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]] => 2
[[1,2,3,7],[4,8],[5],[6]] => 3
[[1,4,5,6],[2,8],[3],[7]] => 1
[[1,3,5,6],[2,8],[4],[7]] => 2
[[1,2,5,6],[3,8],[4],[7]] => 3
[[1,3,4,6],[2,8],[5],[7]] => 3
[[1,2,4,6],[3,8],[5],[7]] => 4
[[1,2,3,6],[4,8],[5],[7]] => 5
[[1,3,4,5],[2,8],[6],[7]] => 4
[[1,2,4,5],[3,8],[6],[7]] => 5
[[1,2,3,5],[4,8],[6],[7]] => 6
[[1,2,3,4],[5,8],[6],[7]] => 7
[[1,4,6,7],[2,5],[3],[8]] => 6
[[1,3,6,7],[2,5],[4],[8]] => 3
[[1,2,6,7],[3,5],[4],[8]] => 4
[[1,3,6,7],[2,4],[5],[8]] => 7
[[1,2,6,7],[3,4],[5],[8]] => 5
[[1,4,5,7],[2,6],[3],[8]] => 7
[[1,3,5,7],[2,6],[4],[8]] => 0
[[1,2,5,7],[3,6],[4],[8]] => 1
[[1,3,4,7],[2,6],[5],[8]] => 4
[[1,2,4,7],[3,6],[5],[8]] => 5
[[1,2,3,7],[4,6],[5],[8]] => 6
[[1,3,5,7],[2,4],[6],[8]] => 0
[[1,2,5,7],[3,4],[6],[8]] => 6
[[1,3,4,7],[2,5],[6],[8]] => 1
[[1,2,4,7],[3,5],[6],[8]] => 2
[[1,2,3,7],[4,5],[6],[8]] => 7
[[1,4,5,6],[2,7],[3],[8]] => 0
[[1,3,5,6],[2,7],[4],[8]] => 1
[[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]] => 3
[[1,2,3,6],[4,7],[5],[8]] => 4
[[1,3,4,5],[2,7],[6],[8]] => 5
[[1,2,4,5],[3,7],[6],[8]] => 6
[[1,2,3,5],[4,7],[6],[8]] => 7
[[1,2,3,4],[5,7],[6],[8]] => 0
[[1,3,5,6],[2,4],[7],[8]] => 1
[[1,2,5,6],[3,4],[7],[8]] => 7
[[1,3,4,6],[2,5],[7],[8]] => 2
[[1,2,4,6],[3,5],[7],[8]] => 3
[[1,2,3,6],[4,5],[7],[8]] => 0
[[1,3,4,5],[2,6],[7],[8]] => 3
[[1,2,4,5],[3,6],[7],[8]] => 4
[[1,2,3,5],[4,6],[7],[8]] => 5
[[1,2,3,4],[5,6],[7],[8]] => 1
[[1,6,7,8],[2],[3],[4],[5]] => 2
[[1,5,7,8],[2],[3],[4],[6]] => 3
[[1,4,7,8],[2],[3],[5],[6]] => 4
[[1,3,7,8],[2],[4],[5],[6]] => 5
[[1,2,7,8],[3],[4],[5],[6]] => 6
[[1,5,6,8],[2],[3],[4],[7]] => 4
[[1,4,6,8],[2],[3],[5],[7]] => 5
[[1,3,6,8],[2],[4],[5],[7]] => 6
[[1,2,6,8],[3],[4],[5],[7]] => 7
[[1,4,5,8],[2],[3],[6],[7]] => 6
[[1,3,5,8],[2],[4],[6],[7]] => 7
[[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]] => 1
[[1,2,3,8],[4],[5],[6],[7]] => 2
[[1,5,6,7],[2],[3],[4],[8]] => 5
[[1,4,6,7],[2],[3],[5],[8]] => 6
[[1,3,6,7],[2],[4],[5],[8]] => 7
[[1,2,6,7],[3],[4],[5],[8]] => 0
[[1,4,5,7],[2],[3],[6],[8]] => 7
[[1,3,5,7],[2],[4],[6],[8]] => 0
[[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]] => 2
[[1,2,3,7],[4],[5],[6],[8]] => 3
[[1,4,5,6],[2],[3],[7],[8]] => 0
[[1,3,5,6],[2],[4],[7],[8]] => 1
[[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]] => 3
[[1,2,3,6],[4],[5],[7],[8]] => 4
[[1,3,4,5],[2],[6],[7],[8]] => 3
[[1,2,4,5],[3],[6],[7],[8]] => 4
[[1,2,3,5],[4],[6],[7],[8]] => 5
[[1,2,3,4],[5],[6],[7],[8]] => 6
[[1,4,7],[2,5,8],[3,6]] => 3
[[1,3,7],[2,5,8],[4,6]] => 0
[[1,2,7],[3,5,8],[4,6]] => 1
[[1,3,7],[2,4,8],[5,6]] => 7
[[1,2,7],[3,4,8],[5,6]] => 5
[[1,4,6],[2,5,8],[3,7]] => 5
[[1,3,6],[2,5,8],[4,7]] => 2
[[1,2,6],[3,5,8],[4,7]] => 3
[[1,3,6],[2,4,8],[5,7]] => 6
[[1,2,6],[3,4,8],[5,7]] => 4
[[1,4,5],[2,6,8],[3,7]] => 6
[[1,3,5],[2,6,8],[4,7]] => 7
[[1,2,5],[3,6,8],[4,7]] => 0
[[1,3,4],[2,6,8],[5,7]] => 3
[[1,2,4],[3,6,8],[5,7]] => 4
[[1,2,3],[4,6,8],[5,7]] => 5
[[1,3,5],[2,4,8],[6,7]] => 1
[[1,2,5],[3,4,8],[6,7]] => 7
[[1,3,4],[2,5,8],[6,7]] => 2
[[1,2,4],[3,5,8],[6,7]] => 3
[[1,2,3],[4,5,8],[6,7]] => 0
[[1,4,6],[2,5,7],[3,8]] => 4
[[1,3,6],[2,5,7],[4,8]] => 1
[[1,2,6],[3,5,7],[4,8]] => 2
[[1,3,6],[2,4,7],[5,8]] => 5
[[1,2,6],[3,4,7],[5,8]] => 3
[[1,4,5],[2,6,7],[3,8]] => 7
[[1,3,5],[2,6,7],[4,8]] => 0
[[1,2,5],[3,6,7],[4,8]] => 1
[[1,3,4],[2,6,7],[5,8]] => 4
[[1,2,4],[3,6,7],[5,8]] => 5
[[1,2,3],[4,6,7],[5,8]] => 6
[[1,3,5],[2,4,7],[6,8]] => 0
[[1,2,5],[3,4,7],[6,8]] => 6
[[1,3,4],[2,5,7],[6,8]] => 1
[[1,2,4],[3,5,7],[6,8]] => 2
[[1,2,3],[4,5,7],[6,8]] => 7
[[1,3,5],[2,4,6],[7,8]] => 7
[[1,2,5],[3,4,6],[7,8]] => 5
[[1,3,4],[2,5,6],[7,8]] => 3
[[1,2,4],[3,5,6],[7,8]] => 4
[[1,2,3],[4,5,6],[7,8]] => 1
[[1,5,7],[2,6,8],[3],[4]] => 2
[[1,4,7],[2,6,8],[3],[5]] => 6
[[1,3,7],[2,6,8],[4],[5]] => 7
[[1,2,7],[3,6,8],[4],[5]] => 0
[[1,4,7],[2,5,8],[3],[6]] => 3
[[1,3,7],[2,5,8],[4],[6]] => 0
[[1,2,7],[3,5,8],[4],[6]] => 1
[[1,3,7],[2,4,8],[5],[6]] => 4
[[1,2,7],[3,4,8],[5],[6]] => 2
[[1,5,6],[2,7,8],[3],[4]] => 4
[[1,4,6],[2,7,8],[3],[5]] => 5
[[1,3,6],[2,7,8],[4],[5]] => 6
[[1,2,6],[3,7,8],[4],[5]] => 7
[[1,4,5],[2,7,8],[3],[6]] => 0
[[1,3,5],[2,7,8],[4],[6]] => 1
[[1,2,5],[3,7,8],[4],[6]] => 2
[[1,3,4],[2,7,8],[5],[6]] => 2
[[1,2,4],[3,7,8],[5],[6]] => 3
[[1,2,3],[4,7,8],[5],[6]] => 4
[[1,4,6],[2,5,8],[3],[7]] => 5
[[1,3,6],[2,5,8],[4],[7]] => 2
[[1,2,6],[3,5,8],[4],[7]] => 3
[[1,3,6],[2,4,8],[5],[7]] => 6
[[1,2,6],[3,4,8],[5],[7]] => 4
[[1,4,5],[2,6,8],[3],[7]] => 6
[[1,3,5],[2,6,8],[4],[7]] => 7
[[1,2,5],[3,6,8],[4],[7]] => 0
[[1,3,4],[2,6,8],[5],[7]] => 3
[[1,2,4],[3,6,8],[5],[7]] => 4
[[1,2,3],[4,6,8],[5],[7]] => 5
[[1,3,5],[2,4,8],[6],[7]] => 7
[[1,2,5],[3,4,8],[6],[7]] => 5
[[1,3,4],[2,5,8],[6],[7]] => 0
[[1,2,4],[3,5,8],[6],[7]] => 1
[[1,2,3],[4,5,8],[6],[7]] => 6
[[1,4,6],[2,5,7],[3],[8]] => 4
[[1,3,6],[2,5,7],[4],[8]] => 1
[[1,2,6],[3,5,7],[4],[8]] => 2
[[1,3,6],[2,4,7],[5],[8]] => 5
[[1,2,6],[3,4,7],[5],[8]] => 3
[[1,4,5],[2,6,7],[3],[8]] => 7
[[1,3,5],[2,6,7],[4],[8]] => 0
[[1,2,5],[3,6,7],[4],[8]] => 1
[[1,3,4],[2,6,7],[5],[8]] => 4
[[1,2,4],[3,6,7],[5],[8]] => 5
[[1,2,3],[4,6,7],[5],[8]] => 6
[[1,3,5],[2,4,7],[6],[8]] => 0
[[1,2,5],[3,4,7],[6],[8]] => 6
[[1,3,4],[2,5,7],[6],[8]] => 1
[[1,2,4],[3,5,7],[6],[8]] => 2
[[1,2,3],[4,5,7],[6],[8]] => 7
[[1,3,5],[2,4,6],[7],[8]] => 6
[[1,2,5],[3,4,6],[7],[8]] => 4
[[1,3,4],[2,5,6],[7],[8]] => 2
[[1,2,4],[3,5,6],[7],[8]] => 3
[[1,2,3],[4,5,6],[7],[8]] => 0
[[1,5,8],[2,6],[3,7],[4]] => 1
[[1,4,8],[2,6],[3,7],[5]] => 5
[[1,3,8],[2,6],[4,7],[5]] => 6
[[1,2,8],[3,6],[4,7],[5]] => 7
[[1,4,8],[2,5],[3,7],[6]] => 4
[[1,3,8],[2,5],[4,7],[6]] => 1
[[1,2,8],[3,5],[4,7],[6]] => 2
[[1,3,8],[2,4],[5,7],[6]] => 5
[[1,2,8],[3,4],[5,7],[6]] => 3
[[1,4,8],[2,5],[3,6],[7]] => 2
[[1,3,8],[2,5],[4,6],[7]] => 7
[[1,2,8],[3,5],[4,6],[7]] => 0
[[1,3,8],[2,4],[5,6],[7]] => 6
[[1,2,8],[3,4],[5,6],[7]] => 4
[[1,5,7],[2,6],[3,8],[4]] => 2
[[1,4,7],[2,6],[3,8],[5]] => 6
[[1,3,7],[2,6],[4,8],[5]] => 7
[[1,2,7],[3,6],[4,8],[5]] => 0
[[1,4,7],[2,5],[3,8],[6]] => 3
[[1,3,7],[2,5],[4,8],[6]] => 0
[[1,2,7],[3,5],[4,8],[6]] => 1
[[1,3,7],[2,4],[5,8],[6]] => 4
[[1,2,7],[3,4],[5,8],[6]] => 2
[[1,5,6],[2,7],[3,8],[4]] => 3
[[1,4,6],[2,7],[3,8],[5]] => 4
[[1,3,6],[2,7],[4,8],[5]] => 5
[[1,2,6],[3,7],[4,8],[5]] => 6
[[1,4,5],[2,7],[3,8],[6]] => 7
[[1,3,5],[2,7],[4,8],[6]] => 0
[[1,2,5],[3,7],[4,8],[6]] => 1
[[1,3,4],[2,7],[5,8],[6]] => 1
[[1,2,4],[3,7],[5,8],[6]] => 2
[[1,2,3],[4,7],[5,8],[6]] => 3
[[1,4,6],[2,5],[3,8],[7]] => 5
[[1,3,6],[2,5],[4,8],[7]] => 2
[[1,2,6],[3,5],[4,8],[7]] => 3
[[1,3,6],[2,4],[5,8],[7]] => 6
[[1,2,6],[3,4],[5,8],[7]] => 4
[[1,4,5],[2,6],[3,8],[7]] => 6
[[1,3,5],[2,6],[4,8],[7]] => 7
[[1,2,5],[3,6],[4,8],[7]] => 0
[[1,3,4],[2,6],[5,8],[7]] => 3
[[1,2,4],[3,6],[5,8],[7]] => 4
[[1,2,3],[4,6],[5,8],[7]] => 5
[[1,3,5],[2,4],[6,8],[7]] => 7
[[1,2,5],[3,4],[6,8],[7]] => 5
[[1,3,4],[2,5],[6,8],[7]] => 0
[[1,2,4],[3,5],[6,8],[7]] => 1
[[1,2,3],[4,5],[6,8],[7]] => 6
[[1,4,7],[2,5],[3,6],[8]] => 3
[[1,3,7],[2,5],[4,6],[8]] => 0
[[1,2,7],[3,5],[4,6],[8]] => 1
[[1,3,7],[2,4],[5,6],[8]] => 7
[[1,2,7],[3,4],[5,6],[8]] => 5
[[1,4,6],[2,5],[3,7],[8]] => 4
[[1,3,6],[2,5],[4,7],[8]] => 1
[[1,2,6],[3,5],[4,7],[8]] => 2
[[1,3,6],[2,4],[5,7],[8]] => 5
[[1,2,6],[3,4],[5,7],[8]] => 3
[[1,4,5],[2,6],[3,7],[8]] => 5
[[1,3,5],[2,6],[4,7],[8]] => 6
[[1,2,5],[3,6],[4,7],[8]] => 7
[[1,3,4],[2,6],[5,7],[8]] => 2
[[1,2,4],[3,6],[5,7],[8]] => 3
[[1,2,3],[4,6],[5,7],[8]] => 4
[[1,3,5],[2,4],[6,7],[8]] => 0
[[1,2,5],[3,4],[6,7],[8]] => 6
[[1,3,4],[2,5],[6,7],[8]] => 1
[[1,2,4],[3,5],[6,7],[8]] => 2
[[1,2,3],[4,5],[6,7],[8]] => 7
[[1,6,8],[2,7],[3],[4],[5]] => 0
[[1,5,8],[2,7],[3],[4],[6]] => 3
[[1,4,8],[2,7],[3],[5],[6]] => 4
[[1,3,8],[2,7],[4],[5],[6]] => 5
[[1,2,8],[3,7],[4],[5],[6]] => 6
[[1,5,8],[2,6],[3],[4],[7]] => 1
[[1,4,8],[2,6],[3],[5],[7]] => 5
[[1,3,8],[2,6],[4],[5],[7]] => 6
[[1,2,8],[3,6],[4],[5],[7]] => 7
[[1,4,8],[2,5],[3],[6],[7]] => 2
[[1,3,8],[2,5],[4],[6],[7]] => 7
[[1,2,8],[3,5],[4],[6],[7]] => 0
[[1,3,8],[2,4],[5],[6],[7]] => 3
[[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]] => 2
[[1,4,7],[2,8],[3],[5],[6]] => 3
[[1,3,7],[2,8],[4],[5],[6]] => 4
[[1,2,7],[3,8],[4],[5],[6]] => 5
[[1,5,6],[2,8],[3],[4],[7]] => 4
[[1,4,6],[2,8],[3],[5],[7]] => 5
[[1,3,6],[2,8],[4],[5],[7]] => 6
[[1,2,6],[3,8],[4],[5],[7]] => 7
[[1,4,5],[2,8],[3],[6],[7]] => 6
[[1,3,5],[2,8],[4],[6],[7]] => 7
[[1,2,5],[3,8],[4],[6],[7]] => 0
[[1,3,4],[2,8],[5],[6],[7]] => 0
[[1,2,4],[3,8],[5],[6],[7]] => 1
[[1,2,3],[4,8],[5],[6],[7]] => 2
[[1,5,7],[2,6],[3],[4],[8]] => 2
[[1,4,7],[2,6],[3],[5],[8]] => 6
[[1,3,7],[2,6],[4],[5],[8]] => 7
[[1,2,7],[3,6],[4],[5],[8]] => 0
[[1,4,7],[2,5],[3],[6],[8]] => 3
[[1,3,7],[2,5],[4],[6],[8]] => 0
[[1,2,7],[3,5],[4],[6],[8]] => 1
[[1,3,7],[2,4],[5],[6],[8]] => 4
[[1,2,7],[3,4],[5],[6],[8]] => 2
[[1,5,6],[2,7],[3],[4],[8]] => 3
[[1,4,6],[2,7],[3],[5],[8]] => 4
[[1,3,6],[2,7],[4],[5],[8]] => 5
[[1,2,6],[3,7],[4],[5],[8]] => 6
[[1,4,5],[2,7],[3],[6],[8]] => 7
[[1,3,5],[2,7],[4],[6],[8]] => 0
[[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]] => 2
[[1,2,3],[4,7],[5],[6],[8]] => 3
[[1,4,6],[2,5],[3],[7],[8]] => 4
[[1,3,6],[2,5],[4],[7],[8]] => 1
[[1,2,6],[3,5],[4],[7],[8]] => 2
[[1,3,6],[2,4],[5],[7],[8]] => 5
[[1,2,6],[3,4],[5],[7],[8]] => 3
[[1,4,5],[2,6],[3],[7],[8]] => 5
[[1,3,5],[2,6],[4],[7],[8]] => 6
[[1,2,5],[3,6],[4],[7],[8]] => 7
[[1,3,4],[2,6],[5],[7],[8]] => 2
[[1,2,4],[3,6],[5],[7],[8]] => 3
[[1,2,3],[4,6],[5],[7],[8]] => 4
[[1,3,5],[2,4],[6],[7],[8]] => 6
[[1,2,5],[3,4],[6],[7],[8]] => 4
[[1,3,4],[2,5],[6],[7],[8]] => 7
[[1,2,4],[3,5],[6],[7],[8]] => 0
[[1,2,3],[4,5],[6],[7],[8]] => 5
[[1,7,8],[2],[3],[4],[5],[6]] => 7
[[1,6,8],[2],[3],[4],[5],[7]] => 0
[[1,5,8],[2],[3],[4],[6],[7]] => 1
[[1,4,8],[2],[3],[5],[6],[7]] => 2
[[1,3,8],[2],[4],[5],[6],[7]] => 3
[[1,2,8],[3],[4],[5],[6],[7]] => 4
[[1,6,7],[2],[3],[4],[5],[8]] => 1
[[1,5,7],[2],[3],[4],[6],[8]] => 2
[[1,4,7],[2],[3],[5],[6],[8]] => 3
[[1,3,7],[2],[4],[5],[6],[8]] => 4
[[1,2,7],[3],[4],[5],[6],[8]] => 5
[[1,5,6],[2],[3],[4],[7],[8]] => 3
[[1,4,6],[2],[3],[5],[7],[8]] => 4
[[1,3,6],[2],[4],[5],[7],[8]] => 5
[[1,2,6],[3],[4],[5],[7],[8]] => 6
[[1,4,5],[2],[3],[6],[7],[8]] => 5
[[1,3,5],[2],[4],[6],[7],[8]] => 6
[[1,2,5],[3],[4],[6],[7],[8]] => 7
[[1,3,4],[2],[5],[6],[7],[8]] => 7
[[1,2,4],[3],[5],[6],[7],[8]] => 0
[[1,2,3],[4],[5],[6],[7],[8]] => 1
[[1,5],[2,6],[3,7],[4,8]] => 0
[[1,4],[2,6],[3,7],[5,8]] => 4
[[1,3],[2,6],[4,7],[5,8]] => 5
[[1,2],[3,6],[4,7],[5,8]] => 6
[[1,4],[2,5],[3,7],[6,8]] => 3
[[1,3],[2,5],[4,7],[6,8]] => 0
[[1,2],[3,5],[4,7],[6,8]] => 1
[[1,3],[2,4],[5,7],[6,8]] => 4
[[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]] => 7
[[1,2],[3,5],[4,6],[7,8]] => 0
[[1,3],[2,4],[5,6],[7,8]] => 6
[[1,2],[3,4],[5,6],[7,8]] => 4
[[1,6],[2,7],[3,8],[4],[5]] => 7
[[1,5],[2,7],[3,8],[4],[6]] => 2
[[1,4],[2,7],[3,8],[5],[6]] => 3
[[1,3],[2,7],[4,8],[5],[6]] => 4
[[1,2],[3,7],[4,8],[5],[6]] => 5
[[1,5],[2,6],[3,8],[4],[7]] => 1
[[1,4],[2,6],[3,8],[5],[7]] => 5
[[1,3],[2,6],[4,8],[5],[7]] => 6
[[1,2],[3,6],[4,8],[5],[7]] => 7
[[1,4],[2,5],[3,8],[6],[7]] => 2
[[1,3],[2,5],[4,8],[6],[7]] => 7
[[1,2],[3,5],[4,8],[6],[7]] => 0
[[1,3],[2,4],[5,8],[6],[7]] => 3
[[1,2],[3,4],[5,8],[6],[7]] => 1
[[1,5],[2,6],[3,7],[4],[8]] => 0
[[1,4],[2,6],[3,7],[5],[8]] => 4
[[1,3],[2,6],[4,7],[5],[8]] => 5
[[1,2],[3,6],[4,7],[5],[8]] => 6
[[1,4],[2,5],[3,7],[6],[8]] => 3
[[1,3],[2,5],[4,7],[6],[8]] => 0
[[1,2],[3,5],[4,7],[6],[8]] => 1
[[1,3],[2,4],[5,7],[6],[8]] => 4
[[1,2],[3,4],[5,7],[6],[8]] => 2
[[1,4],[2,5],[3,6],[7],[8]] => 1
[[1,3],[2,5],[4,6],[7],[8]] => 6
[[1,2],[3,5],[4,6],[7],[8]] => 7
[[1,3],[2,4],[5,6],[7],[8]] => 5
[[1,2],[3,4],[5,6],[7],[8]] => 3
[[1,7],[2,8],[3],[4],[5],[6]] => 6
[[1,6],[2,8],[3],[4],[5],[7]] => 0
[[1,5],[2,8],[3],[4],[6],[7]] => 1
[[1,4],[2,8],[3],[5],[6],[7]] => 2
[[1,3],[2,8],[4],[5],[6],[7]] => 3
[[1,2],[3,8],[4],[5],[6],[7]] => 4
[[1,6],[2,7],[3],[4],[5],[8]] => 7
[[1,5],[2,7],[3],[4],[6],[8]] => 2
[[1,4],[2,7],[3],[5],[6],[8]] => 3
[[1,3],[2,7],[4],[5],[6],[8]] => 4
[[1,2],[3,7],[4],[5],[6],[8]] => 5
[[1,5],[2,6],[3],[4],[7],[8]] => 0
[[1,4],[2,6],[3],[5],[7],[8]] => 4
[[1,3],[2,6],[4],[5],[7],[8]] => 5
[[1,2],[3,6],[4],[5],[7],[8]] => 6
[[1,4],[2,5],[3],[6],[7],[8]] => 1
[[1,3],[2,5],[4],[6],[7],[8]] => 6
[[1,2],[3,5],[4],[6],[7],[8]] => 7
[[1,3],[2,4],[5],[6],[7],[8]] => 2
[[1,2],[3,4],[5],[6],[7],[8]] => 0
[[1,8],[2],[3],[4],[5],[6],[7]] => 5
[[1,7],[2],[3],[4],[5],[6],[8]] => 6
[[1,6],[2],[3],[4],[5],[7],[8]] => 7
[[1,5],[2],[3],[4],[6],[7],[8]] => 0
[[1,4],[2],[3],[5],[6],[7],[8]] => 1
[[1,3],[2],[4],[5],[6],[7],[8]] => 2
[[1,2],[3],[4],[5],[6],[7],[8]] => 3
[[1],[2],[3],[4],[5],[6],[7],[8]] => 4
[[1,2,3,4,5,6,7,8,9]] => 0
[[1,3,4,5,6,7,8,9],[2]] => 1
[[1,2,4,5,6,7,8,9],[3]] => 2
[[1,2,3,5,6,7,8,9],[4]] => 3
[[1,2,3,4,6,7,8,9],[5]] => 4
[[1,2,3,4,5,7,8,9],[6]] => 5
[[1,2,3,4,5,6,8,9],[7]] => 6
[[1,2,3,4,5,6,7,9],[8]] => 7
[[1,2,3,4,5,6,7,8],[9]] => 8
[[1,3,5,6,7,8,9],[2,4]] => 4
[[1,2,5,6,7,8,9],[3,4]] => 2
[[1,3,4,6,7,8,9],[2,5]] => 5
[[1,2,4,6,7,8,9],[3,5]] => 6
[[1,2,3,6,7,8,9],[4,5]] => 3
[[1,3,4,5,7,8,9],[2,6]] => 6
[[1,2,4,5,7,8,9],[3,6]] => 7
[[1,2,3,5,7,8,9],[4,6]] => 8
[[1,2,3,4,7,8,9],[5,6]] => 4
[[1,3,4,5,6,8,9],[2,7]] => 7
[[1,2,4,5,6,8,9],[3,7]] => 8
[[1,2,3,5,6,8,9],[4,7]] => 0
[[1,2,3,4,6,8,9],[5,7]] => 1
[[1,2,3,4,5,8,9],[6,7]] => 5
[[1,3,4,5,6,7,9],[2,8]] => 8
[[1,2,4,5,6,7,9],[3,8]] => 0
[[1,2,3,5,6,7,9],[4,8]] => 1
[[1,2,3,4,6,7,9],[5,8]] => 2
[[1,2,3,4,5,7,9],[6,8]] => 3
[[1,2,3,4,5,6,9],[7,8]] => 6
[[1,3,4,5,6,7,8],[2,9]] => 0
[[1,2,4,5,6,7,8],[3,9]] => 1
[[1,2,3,5,6,7,8],[4,9]] => 2
[[1,2,3,4,6,7,8],[5,9]] => 3
[[1,2,3,4,5,7,8],[6,9]] => 4
[[1,2,3,4,5,6,8],[7,9]] => 5
[[1,2,3,4,5,6,7],[8,9]] => 7
[[1,4,5,6,7,8,9],[2],[3]] => 3
[[1,3,5,6,7,8,9],[2],[4]] => 4
[[1,2,5,6,7,8,9],[3],[4]] => 5
[[1,3,4,6,7,8,9],[2],[5]] => 5
[[1,2,4,6,7,8,9],[3],[5]] => 6
[[1,2,3,6,7,8,9],[4],[5]] => 7
[[1,3,4,5,7,8,9],[2],[6]] => 6
[[1,2,4,5,7,8,9],[3],[6]] => 7
[[1,2,3,5,7,8,9],[4],[6]] => 8
[[1,2,3,4,7,8,9],[5],[6]] => 0
[[1,3,4,5,6,8,9],[2],[7]] => 7
[[1,2,4,5,6,8,9],[3],[7]] => 8
[[1,2,3,5,6,8,9],[4],[7]] => 0
[[1,2,3,4,6,8,9],[5],[7]] => 1
[[1,2,3,4,5,8,9],[6],[7]] => 2
[[1,3,4,5,6,7,9],[2],[8]] => 8
[[1,2,4,5,6,7,9],[3],[8]] => 0
[[1,2,3,5,6,7,9],[4],[8]] => 1
[[1,2,3,4,6,7,9],[5],[8]] => 2
[[1,2,3,4,5,7,9],[6],[8]] => 3
[[1,2,3,4,5,6,9],[7],[8]] => 4
[[1,3,4,5,6,7,8],[2],[9]] => 0
[[1,2,4,5,6,7,8],[3],[9]] => 1
[[1,2,3,5,6,7,8],[4],[9]] => 2
[[1,2,3,4,6,7,8],[5],[9]] => 3
[[1,2,3,4,5,7,8],[6],[9]] => 4
[[1,2,3,4,5,6,8],[7],[9]] => 5
[[1,2,3,4,5,6,7],[8],[9]] => 6
[[1,3,5,7,8,9],[2,4,6]] => 0
[[1,2,5,7,8,9],[3,4,6]] => 7
[[1,3,4,7,8,9],[2,5,6]] => 5
[[1,2,4,7,8,9],[3,5,6]] => 6
[[1,2,3,7,8,9],[4,5,6]] => 3
[[1,3,5,6,8,9],[2,4,7]] => 1
[[1,2,5,6,8,9],[3,4,7]] => 8
[[1,3,4,6,8,9],[2,5,7]] => 2
[[1,2,4,6,8,9],[3,5,7]] => 3
[[1,2,3,6,8,9],[4,5,7]] => 0
[[1,3,4,5,8,9],[2,6,7]] => 6
[[1,2,4,5,8,9],[3,6,7]] => 7
[[1,2,3,5,8,9],[4,6,7]] => 8
[[1,2,3,4,8,9],[5,6,7]] => 4
[[1,3,5,6,7,9],[2,4,8]] => 2
[[1,2,5,6,7,9],[3,4,8]] => 0
[[1,3,4,6,7,9],[2,5,8]] => 3
[[1,2,4,6,7,9],[3,5,8]] => 4
[[1,2,3,6,7,9],[4,5,8]] => 1
[[1,3,4,5,7,9],[2,6,8]] => 4
[[1,2,4,5,7,9],[3,6,8]] => 5
[[1,2,3,5,7,9],[4,6,8]] => 6
Description
The modular (standard) major index of a standard tableau.
The modular major index is the usual major index St000330The (standard) major index of a standard tableau. modulo $n$, where $n$ is the number of boxes in the standard tableau.
References
[1] Swanson, J. P. On the Existence of Tableaux with Given Modular Major Index arXiv:1701.04963
Code
def statistic(T):
n = sum(T.shape())
return T.standard_major_index() % n


Created
Feb 02, 2017 at 20:00 by Christian Stump
Updated
Feb 02, 2017 at 20:00 by Christian Stump