Identifier
Values
[[1,2]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[2,2]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[1],[2]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[1,3]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[2,3]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[3,3]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[1],[3]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[2],[3]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[1,1,2]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,2,2]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,2,2]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,2],[2]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,4]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[2,4]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[3,4]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[4,4]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[1],[4]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[2],[4]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[3],[4]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[1,1,3]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,2,3]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,3,3]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,2,3]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,3,3]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,3,3]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,3],[2]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,3],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,3],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,1,1,2]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,2,2]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,2,2]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,2,2]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,2],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,5]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[2,5]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[3,5]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[4,5]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[5,5]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[1],[5]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[2],[5]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[3],[5]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[4],[5]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[1,1,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,2,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,3,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,4,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,2,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,3,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,4,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,3,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,4,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4,4,4]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,4],[2]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,4],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,4],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,4],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,4],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,4],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,1,1,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,2,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,3,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,2,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,3,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,3,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,2,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,3,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,3,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,3,3]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,3],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,3,3],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,3,3],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,3,3],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,1,1,1,2]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,2,2]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,2,2]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,2,2]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,2,2]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,2],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,6]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[2,6]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[3,6]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[4,6]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[5,6]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[6,6]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[1],[6]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[2],[6]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[3],[6]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[4],[6]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[5],[6]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[1,1,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,2,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,3,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,4,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,5,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,2,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,3,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,4,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,5,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,3,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,4,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,5,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
>>> Load all 745 entries. <<<
[[4,4,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4,5,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[5,5,5]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,5],[2]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,5],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,5],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,5],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,5],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,5],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,5],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,5],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,5],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[4,5],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,1,1,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,2,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,3,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,2,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,3,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,3,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,4,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,2,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,3,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,3,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,4,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,3,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,4,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,4,4,4]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,4],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,3,4],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,4,4],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,3,4],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,4,4],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,4,4],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,3,4],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,4,4],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,4,4],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,4,4],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,1,1,1,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,2,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,2,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,3,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,2,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,3,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,3,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,2,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,3,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,3,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,3,3,3]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,3],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3,3],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3,3],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3,3],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,3,3],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,1,1,2]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,1,2,2]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,2,2,2]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,2,2,2]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,2,2],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,7]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[2,7]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[3,7]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[4,7]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[5,7]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[6,7]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[7,7]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[1],[7]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[2],[7]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[3],[7]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[4],[7]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[5],[7]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[6],[7]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[1,1,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,2,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,3,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,4,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,5,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,6,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,2,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,3,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,4,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,5,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,6,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,3,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,4,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,5,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,6,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4,4,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4,5,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4,6,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[5,5,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[5,6,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[6,6,6]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,6],[2]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,6],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,6],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,6],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,6],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,6],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,6],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,6],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,6],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,6],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,6],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,6],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[4,6],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[4,6],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[5,6],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,1,1,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,2,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,3,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,2,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,3,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,3,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,4,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,4,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,5,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,2,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,3,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,3,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,4,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,4,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,5,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,3,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,4,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,4,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,5,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,4,4,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,4,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,5,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[5,5,5,5]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,5],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,3,5],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,4,5],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,5,5],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,3,5],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,4,5],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,5,5],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,4,5],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,5,5],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,5,5],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,3,5],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,4,5],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,5,5],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,4,5],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,5,5],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,5,5],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,4,5],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,5,5],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,5,5],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[4,5,5],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,1,1,1,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,2,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,2,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,3,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,3,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,2,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,3,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,3,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,3,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,3,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,4,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,2,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,3,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,3,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,3,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,3,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,4,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,3,3,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,3,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,4,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[4,4,4,4,4]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,4],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3,4],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,4,4],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3,4],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4,4],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4,4],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3,4],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4,4],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4,4],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4,4],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,3,4],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,4,4],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,4,4,4],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,4,4,4],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,4,4,4],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,1,1,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,1,2,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,1,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,2,2,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,2,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,2,2,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,2,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,3,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[3,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,2,3],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,3,3],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,3,3],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3,3,3],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3,3,3],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,3,3,3,3],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,2,2,2,2],[2]] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,8]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[2,8]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[3,8]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[4,8]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[5,8]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[6,8]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[7,8]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[8,8]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[1],[8]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[2],[8]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[3],[8]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[4],[8]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[5],[8]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[6],[8]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[7],[8]] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1
[[1,1,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,2,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,3,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,4,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,5,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,6,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,7,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,2,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,3,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,4,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,5,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,6,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[2,7,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,3,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,4,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,5,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,6,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[3,7,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4,4,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4,5,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4,6,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4,7,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[5,5,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[5,6,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[5,7,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[6,6,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[6,7,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[7,7,7]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[1,7],[2]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,7],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,7],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,7],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,7],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,7],[7]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,7],[3]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,7],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,7],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,7],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[2,7],[7]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,7],[4]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,7],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,7],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[3,7],[7]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[4,7],[5]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[4,7],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[4,7],[7]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[5,7],[6]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[5,7],[7]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[6,7],[7]] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 1
[[1,1,1,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,2,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,3,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,1,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,2,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,3,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,3,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,3,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,4,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,4,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,4,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,5,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,5,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,6,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,2,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,3,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,2,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,3,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,3,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,4,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,4,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,4,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,5,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,5,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[2,6,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,3,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,3,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,4,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,4,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,4,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,5,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,5,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[3,6,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,4,4,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,4,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,4,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,5,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,5,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[4,6,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[5,5,5,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[5,5,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[5,6,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[6,6,6,6]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[1,2,6],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,3,6],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,4,6],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,5,6],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,6,6],[2]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,3,6],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,4,6],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,5,6],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,6,6],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,4,6],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,5,6],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,6,6],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,5,6],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,6,6],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,6,6],[6]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,3,6],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,4,6],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,5,6],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,6,6],[3]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,4,6],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,5,6],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,6,6],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,5,6],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,6,6],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[2,6,6],[6]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,4,6],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,5,6],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,6,6],[4]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,5,6],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,6,6],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[3,6,6],[6]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[4,5,6],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[4,6,6],[5]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[4,6,6],[6]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[5,6,6],[6]] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0] => 1
[[1,1,1,1,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,2,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,1,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,2,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,2,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,3,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,3,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,3,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,1,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,2,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,3,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,3,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,3,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,3,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,3,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,3,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,4,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,4,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,4,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,5,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,2,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,2,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,3,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,3,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,3,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,2,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,3,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,3,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,3,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,3,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,4,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,4,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,4,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[2,5,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,3,3,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,3,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,3,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,3,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,4,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,4,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,4,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[3,5,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[4,4,4,4,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[4,4,4,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[4,4,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[4,5,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[5,5,5,5,5]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,2,2,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,3,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,4,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,2,5,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,5,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,5,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,5,5,5],[2]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,3,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,4,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,5,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,5,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,5,5,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,4,5],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,4,5,5],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,5,5,5],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,5,5,5],[5]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,3,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,4,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,3,5,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,4,4,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,4,5,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,5,5,5],[3]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,4,4,5],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,4,5,5],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,5,5,5],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[2,5,5,5],[5]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,4,4,5],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,4,5,5],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,5,5,5],[4]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[3,5,5,5],[5]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[4,5,5,5],[5]] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,1,1,1,1,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,1,2,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,1,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,1,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,2,2,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,2,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,2,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,1,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,2,2,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,2,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,2,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,2,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,3,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,3,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,3,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,1,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,2,2,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,2,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,2,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,3,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,3,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,3,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,2,2,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,2,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,2,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,2,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,3,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,3,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,3,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,2,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[3,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[3,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[3,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[3,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[3,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[4,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,2,2,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,3,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,2,4,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,3,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,3,4,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,2,4,4,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3,3,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3,4,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,4,4,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,4,4,4,4],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3,3,4],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,3,4,4],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,4,4,4],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,4,4,4,4],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,4,4,4,4],[4]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,3,3,3,4],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,3,3,4,4],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,3,4,4,4],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,4,4,4,4],[3]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[2,4,4,4,4],[4]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[3,4,4,4,4],[4]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,1,1,1,1,1,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,1,1,2,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,1,1,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,1,2,2,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,1,2,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,1,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,1,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,1,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[2,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[2,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[2,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[2,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[2,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[2,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[3,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,2,2,2,2,3],[2]] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,2,2,3,3],[2]] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,2,3,3,3],[2]] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,2,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,3,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[2,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[1]] => [1] => [1,0] => [1,0] => 0
[[2]] => [1] => [1,0] => [1,0] => 0
[[1,1]] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[[3]] => [1] => [1,0] => [1,0] => 0
[[1,1,1]] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[[4]] => [1] => [1,0] => [1,0] => 0
[[1,1,1,1]] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[[5]] => [1] => [1,0] => [1,0] => 0
[[1,1,1,1,1]] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[[6]] => [1] => [1,0] => [1,0] => 0
[[1,1,1,1,1,1]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
decomposition reverse
Description
This map is recursively defined as follows.
The unique empty path of semilength $0$ is sent to itself.
Let $D$ be a Dyck path of semilength $n > 0$ and decompose it into $1 D_1 0 D_2$ with Dyck paths $D_1, D_2$ of respective semilengths $n_1$ and $n_2$ such that $n_1$ is minimal. One then has $n_1+n_2 = n-1$.
Now let $\tilde D_1$ and $\tilde D_2$ be the recursively defined respective images of $D_1$ and $D_2$ under this map. The image of $D$ is then defined as $1 \tilde D_2 0 \tilde D_1$.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.