Identifier
Values
[[1,2]] => [[2,0],[1]] => [[2,0],[1]] => 3
[[2,2]] => [[2,0],[0]] => [[2,0],[2]] => 4
[[1],[2]] => [[1,1],[1]] => [[1,1],[1]] => 3
[[1,3]] => [[2,0,0],[1,0],[1]] => [[2,0,0],[1,0],[1]] => 4
[[2,3]] => [[2,0,0],[1,0],[0]] => [[2,0,0],[2,0],[1]] => 5
[[3,3]] => [[2,0,0],[0,0],[0]] => [[2,0,0],[2,0],[2]] => 6
[[1],[3]] => [[1,1,0],[1,0],[1]] => [[1,1,0],[1,0],[1]] => 4
[[2],[3]] => [[1,1,0],[1,0],[0]] => [[1,1,0],[1,1],[1]] => 5
[[1,1,2]] => [[3,0],[2]] => [[3,0],[1]] => 4
[[1,2,2]] => [[3,0],[1]] => [[3,0],[2]] => 5
[[2,2,2]] => [[3,0],[0]] => [[3,0],[3]] => 6
[[1,1],[2]] => [[2,1],[2]] => [[2,1],[1]] => 4
[[1,2],[2]] => [[2,1],[1]] => [[2,1],[2]] => 5
[[1,4]] => [[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0],[1,0,0],[1,0],[1]] => 5
[[2,4]] => [[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0],[2,0,0],[1,0],[1]] => 6
[[3,4]] => [[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0],[2,0,0],[2,0],[1]] => 7
[[4,4]] => [[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0],[2,0,0],[2,0],[2]] => 8
[[1],[4]] => [[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0],[1,0,0],[1,0],[1]] => 5
[[2],[4]] => [[1,1,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0],[1,1,0],[1,0],[1]] => 6
[[3],[4]] => [[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0],[1,1,0],[1,1],[1]] => 7
[[1,1,3]] => [[3,0,0],[2,0],[2]] => [[3,0,0],[1,0],[1]] => 5
[[1,2,3]] => [[3,0,0],[2,0],[1]] => [[3,0,0],[2,0],[1]] => 6
[[1,3,3]] => [[3,0,0],[1,0],[1]] => [[3,0,0],[2,0],[2]] => 7
[[2,2,3]] => [[3,0,0],[2,0],[0]] => [[3,0,0],[3,0],[1]] => 7
[[2,3,3]] => [[3,0,0],[1,0],[0]] => [[3,0,0],[3,0],[2]] => 8
[[3,3,3]] => [[3,0,0],[0,0],[0]] => [[3,0,0],[3,0],[3]] => 9
[[1,1],[3]] => [[2,1,0],[2,0],[2]] => [[2,1,0],[1,0],[1]] => 5
[[1,2],[3]] => [[2,1,0],[2,0],[1]] => [[2,1,0],[1,1],[1]] => 6
[[1,3],[2]] => [[2,1,0],[1,1],[1]] => [[2,1,0],[2,0],[1]] => 6
[[1,3],[3]] => [[2,1,0],[1,0],[1]] => [[2,1,0],[2,0],[2]] => 7
[[2,2],[3]] => [[2,1,0],[2,0],[0]] => [[2,1,0],[2,1],[1]] => 7
[[2,3],[3]] => [[2,1,0],[1,0],[0]] => [[2,1,0],[2,1],[2]] => 8
[[1],[2],[3]] => [[1,1,1],[1,1],[1]] => [[1,1,1],[1,1],[1]] => 6
[[1,1,1,2]] => [[4,0],[3]] => [[4,0],[1]] => 5
[[1,1,2,2]] => [[4,0],[2]] => [[4,0],[2]] => 6
[[1,2,2,2]] => [[4,0],[1]] => [[4,0],[3]] => 7
[[2,2,2,2]] => [[4,0],[0]] => [[4,0],[4]] => 8
[[1,1,1],[2]] => [[3,1],[3]] => [[3,1],[1]] => 5
[[1,1,2],[2]] => [[3,1],[2]] => [[3,1],[2]] => 6
[[1,2,2],[2]] => [[3,1],[1]] => [[3,1],[3]] => 7
[[1,1],[2,2]] => [[2,2],[2]] => [[2,2],[2]] => 6
[[1,5]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[2,5]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 7
[[3,5]] => [[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 8
[[4,5]] => [[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 9
[[5,5]] => [[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 10
[[1],[5]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[2],[5]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 7
[[3],[5]] => [[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 8
[[4],[5]] => [[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 9
[[1,1,4]] => [[3,0,0,0],[2,0,0],[2,0],[2]] => [[3,0,0,0],[1,0,0],[1,0],[1]] => 6
[[1,2,4]] => [[3,0,0,0],[2,0,0],[2,0],[1]] => [[3,0,0,0],[2,0,0],[1,0],[1]] => 7
[[1,3,4]] => [[3,0,0,0],[2,0,0],[1,0],[1]] => [[3,0,0,0],[2,0,0],[2,0],[1]] => 8
[[1,4,4]] => [[3,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0],[2,0,0],[2,0],[2]] => 9
[[2,2,4]] => [[3,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0],[3,0,0],[1,0],[1]] => 8
[[2,3,4]] => [[3,0,0,0],[2,0,0],[1,0],[0]] => [[3,0,0,0],[3,0,0],[2,0],[1]] => 9
[[2,4,4]] => [[3,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0],[3,0,0],[2,0],[2]] => 10
[[3,3,4]] => [[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[1]] => 10
[[3,4,4]] => [[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[2]] => 11
[[4,4,4]] => [[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[3]] => 12
[[1,1],[4]] => [[2,1,0,0],[2,0,0],[2,0],[2]] => [[2,1,0,0],[1,0,0],[1,0],[1]] => 6
[[1,2],[4]] => [[2,1,0,0],[2,0,0],[2,0],[1]] => [[2,1,0,0],[1,1,0],[1,0],[1]] => 7
[[1,4],[2]] => [[2,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,0,0],[2,0,0],[1,0],[1]] => 7
[[1,3],[4]] => [[2,1,0,0],[2,0,0],[1,0],[1]] => [[2,1,0,0],[1,1,0],[1,1],[1]] => 8
[[1,4],[3]] => [[2,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,0,0],[2,0,0],[2,0],[1]] => 8
[[1,4],[4]] => [[2,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0],[2,0,0],[2,0],[2]] => 9
[[2,2],[4]] => [[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0],[2,1,0],[1,0],[1]] => 8
[[2,3],[4]] => [[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[1,1],[1]] => 9
[[2,4],[3]] => [[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[2,0],[1]] => 9
[[2,4],[4]] => [[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[2,0],[2]] => 10
[[3,3],[4]] => [[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0],[2,1,0],[2,1],[1]] => 10
[[3,4],[4]] => [[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0],[2,1,0],[2,1],[2]] => 11
[[1],[2],[4]] => [[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,1,1,0],[1,1,0],[1,0],[1]] => 7
[[1],[3],[4]] => [[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,1,1,0],[1,1,0],[1,1],[1]] => 8
[[2],[3],[4]] => [[1,1,1,0],[1,1,0],[1,0],[0]] => [[1,1,1,0],[1,1,1],[1,1],[1]] => 9
[[1,1,1,3]] => [[4,0,0],[3,0],[3]] => [[4,0,0],[1,0],[1]] => 6
[[1,1,2,3]] => [[4,0,0],[3,0],[2]] => [[4,0,0],[2,0],[1]] => 7
[[1,1,3,3]] => [[4,0,0],[2,0],[2]] => [[4,0,0],[2,0],[2]] => 8
[[1,2,2,3]] => [[4,0,0],[3,0],[1]] => [[4,0,0],[3,0],[1]] => 8
[[1,2,3,3]] => [[4,0,0],[2,0],[1]] => [[4,0,0],[3,0],[2]] => 9
[[1,3,3,3]] => [[4,0,0],[1,0],[1]] => [[4,0,0],[3,0],[3]] => 10
[[2,2,2,3]] => [[4,0,0],[3,0],[0]] => [[4,0,0],[4,0],[1]] => 9
[[2,2,3,3]] => [[4,0,0],[2,0],[0]] => [[4,0,0],[4,0],[2]] => 10
[[2,3,3,3]] => [[4,0,0],[1,0],[0]] => [[4,0,0],[4,0],[3]] => 11
[[3,3,3,3]] => [[4,0,0],[0,0],[0]] => [[4,0,0],[4,0],[4]] => 12
[[1,1,1],[3]] => [[3,1,0],[3,0],[3]] => [[3,1,0],[1,0],[1]] => 6
[[1,1,2],[3]] => [[3,1,0],[3,0],[2]] => [[3,1,0],[1,1],[1]] => 7
[[1,1,3],[2]] => [[3,1,0],[2,1],[2]] => [[3,1,0],[2,0],[1]] => 7
[[1,1,3],[3]] => [[3,1,0],[2,0],[2]] => [[3,1,0],[2,0],[2]] => 8
[[1,2,2],[3]] => [[3,1,0],[3,0],[1]] => [[3,1,0],[2,1],[1]] => 8
[[1,2,3],[2]] => [[3,1,0],[2,1],[1]] => [[3,1,0],[3,0],[1]] => 8
[[1,2,3],[3]] => [[3,1,0],[2,0],[1]] => [[3,1,0],[2,1],[2]] => 9
[[1,3,3],[2]] => [[3,1,0],[1,1],[1]] => [[3,1,0],[3,0],[2]] => 9
[[1,3,3],[3]] => [[3,1,0],[1,0],[1]] => [[3,1,0],[3,0],[3]] => 10
[[2,2,2],[3]] => [[3,1,0],[3,0],[0]] => [[3,1,0],[3,1],[1]] => 9
[[2,2,3],[3]] => [[3,1,0],[2,0],[0]] => [[3,1,0],[3,1],[2]] => 10
[[2,3,3],[3]] => [[3,1,0],[1,0],[0]] => [[3,1,0],[3,1],[3]] => 11
[[1,1],[2,3]] => [[2,2,0],[2,1],[2]] => [[2,2,0],[2,0],[1]] => 7
[[1,1],[3,3]] => [[2,2,0],[2,0],[2]] => [[2,2,0],[2,0],[2]] => 8
[[1,2],[2,3]] => [[2,2,0],[2,1],[1]] => [[2,2,0],[2,1],[1]] => 8
[[1,2],[3,3]] => [[2,2,0],[2,0],[1]] => [[2,2,0],[2,1],[2]] => 9
>>> Load all 629 entries. <<<
[[2,2],[3,3]] => [[2,2,0],[2,0],[0]] => [[2,2,0],[2,2],[2]] => 10
[[1,1],[2],[3]] => [[2,1,1],[2,1],[2]] => [[2,1,1],[1,1],[1]] => 7
[[1,2],[2],[3]] => [[2,1,1],[2,1],[1]] => [[2,1,1],[2,1],[1]] => 8
[[1,3],[2],[3]] => [[2,1,1],[1,1],[1]] => [[2,1,1],[2,1],[2]] => 9
[[1,1,1,1,2]] => [[5,0],[4]] => [[5,0],[1]] => 6
[[1,1,1,2,2]] => [[5,0],[3]] => [[5,0],[2]] => 7
[[1,1,2,2,2]] => [[5,0],[2]] => [[5,0],[3]] => 8
[[1,2,2,2,2]] => [[5,0],[1]] => [[5,0],[4]] => 9
[[2,2,2,2,2]] => [[5,0],[0]] => [[5,0],[5]] => 10
[[1,1,1,1],[2]] => [[4,1],[4]] => [[4,1],[1]] => 6
[[1,1,1,2],[2]] => [[4,1],[3]] => [[4,1],[2]] => 7
[[1,1,2,2],[2]] => [[4,1],[2]] => [[4,1],[3]] => 8
[[1,2,2,2],[2]] => [[4,1],[1]] => [[4,1],[4]] => 9
[[1,1,1],[2,2]] => [[3,2],[3]] => [[3,2],[2]] => 7
[[1,1,2],[2,2]] => [[3,2],[2]] => [[3,2],[3]] => 8
[[1,6]] => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2,6]] => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 8
[[3,6]] => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 9
[[4,6]] => [[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 10
[[5,6]] => [[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 11
[[6,6]] => [[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 12
[[1],[6]] => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2],[6]] => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 8
[[3],[6]] => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 9
[[4],[6]] => [[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 10
[[5],[6]] => [[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 11
[[1,1,5]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[1,2,5]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 8
[[1,3,5]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 9
[[1,4,5]] => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 10
[[1,5,5]] => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 11
[[2,2,5]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => 9
[[2,3,5]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => 10
[[2,4,5]] => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => 11
[[2,5,5]] => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => 12
[[3,3,5]] => [[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => 11
[[3,4,5]] => [[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => 12
[[3,5,5]] => [[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => 13
[[4,4,5]] => [[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => 13
[[4,5,5]] => [[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => 14
[[5,5,5]] => [[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => 15
[[1,1],[5]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[1,2],[5]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 8
[[1,5],[2]] => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 8
[[1,3],[5]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 9
[[1,5],[3]] => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 9
[[1,4],[5]] => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 10
[[1,5],[4]] => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 10
[[1,5],[5]] => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 11
[[2,2],[5]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => 9
[[2,3],[5]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => 10
[[2,5],[3]] => [[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => 10
[[2,4],[5]] => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => 11
[[2,5],[4]] => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => 11
[[2,5],[5]] => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => 12
[[3,3],[5]] => [[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => 11
[[3,4],[5]] => [[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => 12
[[3,5],[4]] => [[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => 12
[[3,5],[5]] => [[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => 13
[[4,4],[5]] => [[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => 13
[[4,5],[5]] => [[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => 14
[[1],[2],[5]] => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 8
[[1],[3],[5]] => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 9
[[1],[4],[5]] => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 10
[[2],[3],[5]] => [[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => 10
[[2],[4],[5]] => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => 11
[[3],[4],[5]] => [[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => 12
[[1,1,1,4]] => [[4,0,0,0],[3,0,0],[3,0],[3]] => [[4,0,0,0],[1,0,0],[1,0],[1]] => 7
[[1,1,2,4]] => [[4,0,0,0],[3,0,0],[3,0],[2]] => [[4,0,0,0],[2,0,0],[1,0],[1]] => 8
[[1,1,3,4]] => [[4,0,0,0],[3,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[1]] => 9
[[1,1,4,4]] => [[4,0,0,0],[2,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[2]] => 10
[[1,2,2,4]] => [[4,0,0,0],[3,0,0],[3,0],[1]] => [[4,0,0,0],[3,0,0],[1,0],[1]] => 9
[[1,2,3,4]] => [[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[1]] => 10
[[1,2,4,4]] => [[4,0,0,0],[2,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[2]] => 11
[[1,3,3,4]] => [[4,0,0,0],[3,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[1]] => 11
[[1,3,4,4]] => [[4,0,0,0],[2,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[2]] => 12
[[1,4,4,4]] => [[4,0,0,0],[1,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[3]] => 13
[[2,2,2,4]] => [[4,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0],[4,0,0],[1,0],[1]] => 10
[[2,2,3,4]] => [[4,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[1]] => 11
[[2,2,4,4]] => [[4,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[2]] => 12
[[2,3,3,4]] => [[4,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[1]] => 12
[[2,3,4,4]] => [[4,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[2]] => 13
[[2,4,4,4]] => [[4,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[3]] => 14
[[3,3,3,4]] => [[4,0,0,0],[3,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[1]] => 13
[[3,3,4,4]] => [[4,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[2]] => 14
[[3,4,4,4]] => [[4,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[3]] => 15
[[4,4,4,4]] => [[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[4]] => 16
[[1,1,1],[4]] => [[3,1,0,0],[3,0,0],[3,0],[3]] => [[3,1,0,0],[1,0,0],[1,0],[1]] => 7
[[1,1,2],[4]] => [[3,1,0,0],[3,0,0],[3,0],[2]] => [[3,1,0,0],[1,1,0],[1,0],[1]] => 8
[[1,1,4],[2]] => [[3,1,0,0],[2,1,0],[2,1],[2]] => [[3,1,0,0],[2,0,0],[1,0],[1]] => 8
[[1,1,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[2]] => [[3,1,0,0],[1,1,0],[1,1],[1]] => 9
[[1,1,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[1]] => 9
[[1,1,4],[4]] => [[3,1,0,0],[2,0,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[2]] => 10
[[1,2,2],[4]] => [[3,1,0,0],[3,0,0],[3,0],[1]] => [[3,1,0,0],[2,1,0],[1,0],[1]] => 9
[[1,2,4],[2]] => [[3,1,0,0],[2,1,0],[2,1],[1]] => [[3,1,0,0],[3,0,0],[1,0],[1]] => 9
[[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => 10
[[1,2,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => 10
[[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => 10
[[1,2,4],[4]] => [[3,1,0,0],[2,0,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[2]] => 11
[[1,4,4],[2]] => [[3,1,0,0],[1,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[2]] => 11
[[1,3,3],[4]] => [[3,1,0,0],[3,0,0],[1,0],[1]] => [[3,1,0,0],[2,1,0],[2,1],[1]] => 11
[[1,3,4],[3]] => [[3,1,0,0],[2,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[1]] => 11
[[1,3,4],[4]] => [[3,1,0,0],[2,0,0],[1,0],[1]] => [[3,1,0,0],[2,1,0],[2,1],[2]] => 12
[[1,4,4],[3]] => [[3,1,0,0],[1,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[2]] => 12
[[1,4,4],[4]] => [[3,1,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[3]] => 13
[[2,2,2],[4]] => [[3,1,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0],[3,1,0],[1,0],[1]] => 10
[[2,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[1,1],[1]] => 11
[[2,2,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[1]] => 11
[[2,2,4],[4]] => [[3,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[2]] => 12
[[2,3,3],[4]] => [[3,1,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[2,1],[1]] => 12
[[2,3,4],[3]] => [[3,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[1]] => 12
[[2,3,4],[4]] => [[3,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[2,1],[2]] => 13
[[2,4,4],[3]] => [[3,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[2]] => 13
[[2,4,4],[4]] => [[3,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[3]] => 14
[[3,3,3],[4]] => [[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[1]] => 13
[[3,3,4],[4]] => [[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[2]] => 14
[[3,4,4],[4]] => [[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[3]] => 15
[[1,1],[2,4]] => [[2,2,0,0],[2,1,0],[2,1],[2]] => [[2,2,0,0],[2,0,0],[1,0],[1]] => 8
[[1,1],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[1]] => 9
[[1,1],[4,4]] => [[2,2,0,0],[2,0,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[2]] => 10
[[1,2],[2,4]] => [[2,2,0,0],[2,1,0],[2,1],[1]] => [[2,2,0,0],[2,1,0],[1,0],[1]] => 9
[[1,2],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => 10
[[1,3],[2,4]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => 10
[[1,2],[4,4]] => [[2,2,0,0],[2,0,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[2]] => 11
[[1,3],[3,4]] => [[2,2,0,0],[2,1,0],[1,0],[1]] => [[2,2,0,0],[2,1,0],[2,1],[1]] => 11
[[1,3],[4,4]] => [[2,2,0,0],[2,0,0],[1,0],[1]] => [[2,2,0,0],[2,1,0],[2,1],[2]] => 12
[[2,2],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[1]] => 11
[[2,2],[4,4]] => [[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[2]] => 12
[[2,3],[3,4]] => [[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0],[2,2,0],[2,1],[1]] => 12
[[2,3],[4,4]] => [[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0],[2,2,0],[2,1],[2]] => 13
[[3,3],[4,4]] => [[2,2,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0],[2,2,0],[2,2],[2]] => 14
[[1,1],[2],[4]] => [[2,1,1,0],[2,1,0],[2,1],[2]] => [[2,1,1,0],[1,1,0],[1,0],[1]] => 8
[[1,1],[3],[4]] => [[2,1,1,0],[2,1,0],[2,0],[2]] => [[2,1,1,0],[1,1,0],[1,1],[1]] => 9
[[1,2],[2],[4]] => [[2,1,1,0],[2,1,0],[2,1],[1]] => [[2,1,1,0],[2,1,0],[1,0],[1]] => 9
[[1,2],[3],[4]] => [[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => 10
[[1,3],[2],[4]] => [[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[1,1],[1]] => 10
[[1,4],[2],[3]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[1]] => 10
[[1,4],[2],[4]] => [[2,1,1,0],[1,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[2]] => 11
[[1,3],[3],[4]] => [[2,1,1,0],[2,1,0],[1,0],[1]] => [[2,1,1,0],[2,1,0],[2,1],[1]] => 11
[[1,4],[3],[4]] => [[2,1,1,0],[1,1,0],[1,0],[1]] => [[2,1,1,0],[2,1,0],[2,1],[2]] => 12
[[2,2],[3],[4]] => [[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,1,1,0],[2,1,1],[1,1],[1]] => 11
[[2,3],[3],[4]] => [[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,1,1,0],[2,1,1],[2,1],[1]] => 12
[[2,4],[3],[4]] => [[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0],[2,1,1],[2,1],[2]] => 13
[[1],[2],[3],[4]] => [[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1],[1,1],[1]] => 10
[[1,1,1,1,3]] => [[5,0,0],[4,0],[4]] => [[5,0,0],[1,0],[1]] => 7
[[1,1,1,2,3]] => [[5,0,0],[4,0],[3]] => [[5,0,0],[2,0],[1]] => 8
[[1,1,1,3,3]] => [[5,0,0],[3,0],[3]] => [[5,0,0],[2,0],[2]] => 9
[[1,1,2,2,3]] => [[5,0,0],[4,0],[2]] => [[5,0,0],[3,0],[1]] => 9
[[1,1,2,3,3]] => [[5,0,0],[3,0],[2]] => [[5,0,0],[3,0],[2]] => 10
[[1,1,3,3,3]] => [[5,0,0],[2,0],[2]] => [[5,0,0],[3,0],[3]] => 11
[[1,2,2,2,3]] => [[5,0,0],[4,0],[1]] => [[5,0,0],[4,0],[1]] => 10
[[1,2,2,3,3]] => [[5,0,0],[3,0],[1]] => [[5,0,0],[4,0],[2]] => 11
[[1,2,3,3,3]] => [[5,0,0],[2,0],[1]] => [[5,0,0],[4,0],[3]] => 12
[[1,3,3,3,3]] => [[5,0,0],[1,0],[1]] => [[5,0,0],[4,0],[4]] => 13
[[2,2,2,2,3]] => [[5,0,0],[4,0],[0]] => [[5,0,0],[5,0],[1]] => 11
[[2,2,2,3,3]] => [[5,0,0],[3,0],[0]] => [[5,0,0],[5,0],[2]] => 12
[[2,2,3,3,3]] => [[5,0,0],[2,0],[0]] => [[5,0,0],[5,0],[3]] => 13
[[2,3,3,3,3]] => [[5,0,0],[1,0],[0]] => [[5,0,0],[5,0],[4]] => 14
[[3,3,3,3,3]] => [[5,0,0],[0,0],[0]] => [[5,0,0],[5,0],[5]] => 15
[[1,1,1,1],[3]] => [[4,1,0],[4,0],[4]] => [[4,1,0],[1,0],[1]] => 7
[[1,1,1,2],[3]] => [[4,1,0],[4,0],[3]] => [[4,1,0],[1,1],[1]] => 8
[[1,1,1,3],[2]] => [[4,1,0],[3,1],[3]] => [[4,1,0],[2,0],[1]] => 8
[[1,1,1,3],[3]] => [[4,1,0],[3,0],[3]] => [[4,1,0],[2,0],[2]] => 9
[[1,1,2,2],[3]] => [[4,1,0],[4,0],[2]] => [[4,1,0],[2,1],[1]] => 9
[[1,1,2,3],[2]] => [[4,1,0],[3,1],[2]] => [[4,1,0],[3,0],[1]] => 9
[[1,1,2,3],[3]] => [[4,1,0],[3,0],[2]] => [[4,1,0],[2,1],[2]] => 10
[[1,1,3,3],[2]] => [[4,1,0],[2,1],[2]] => [[4,1,0],[3,0],[2]] => 10
[[1,1,3,3],[3]] => [[4,1,0],[2,0],[2]] => [[4,1,0],[3,0],[3]] => 11
[[1,2,2,2],[3]] => [[4,1,0],[4,0],[1]] => [[4,1,0],[3,1],[1]] => 10
[[1,2,2,3],[2]] => [[4,1,0],[3,1],[1]] => [[4,1,0],[4,0],[1]] => 10
[[1,2,2,3],[3]] => [[4,1,0],[3,0],[1]] => [[4,1,0],[3,1],[2]] => 11
[[1,2,3,3],[2]] => [[4,1,0],[2,1],[1]] => [[4,1,0],[4,0],[2]] => 11
[[1,2,3,3],[3]] => [[4,1,0],[2,0],[1]] => [[4,1,0],[3,1],[3]] => 12
[[1,3,3,3],[2]] => [[4,1,0],[1,1],[1]] => [[4,1,0],[4,0],[3]] => 12
[[1,3,3,3],[3]] => [[4,1,0],[1,0],[1]] => [[4,1,0],[4,0],[4]] => 13
[[2,2,2,2],[3]] => [[4,1,0],[4,0],[0]] => [[4,1,0],[4,1],[1]] => 11
[[2,2,2,3],[3]] => [[4,1,0],[3,0],[0]] => [[4,1,0],[4,1],[2]] => 12
[[2,2,3,3],[3]] => [[4,1,0],[2,0],[0]] => [[4,1,0],[4,1],[3]] => 13
[[2,3,3,3],[3]] => [[4,1,0],[1,0],[0]] => [[4,1,0],[4,1],[4]] => 14
[[1,1,1],[2,3]] => [[3,2,0],[3,1],[3]] => [[3,2,0],[2,0],[1]] => 8
[[1,1,1],[3,3]] => [[3,2,0],[3,0],[3]] => [[3,2,0],[2,0],[2]] => 9
[[1,1,2],[2,3]] => [[3,2,0],[3,1],[2]] => [[3,2,0],[2,1],[1]] => 9
[[1,1,3],[2,2]] => [[3,2,0],[2,2],[2]] => [[3,2,0],[3,0],[1]] => 9
[[1,1,2],[3,3]] => [[3,2,0],[3,0],[2]] => [[3,2,0],[2,1],[2]] => 10
[[1,1,3],[2,3]] => [[3,2,0],[2,1],[2]] => [[3,2,0],[3,0],[2]] => 10
[[1,1,3],[3,3]] => [[3,2,0],[2,0],[2]] => [[3,2,0],[3,0],[3]] => 11
[[1,2,2],[2,3]] => [[3,2,0],[3,1],[1]] => [[3,2,0],[3,1],[1]] => 10
[[1,2,2],[3,3]] => [[3,2,0],[3,0],[1]] => [[3,2,0],[2,2],[2]] => 11
[[1,2,3],[2,3]] => [[3,2,0],[2,1],[1]] => [[3,2,0],[3,1],[2]] => 11
[[1,2,3],[3,3]] => [[3,2,0],[2,0],[1]] => [[3,2,0],[3,1],[3]] => 12
[[2,2,2],[3,3]] => [[3,2,0],[3,0],[0]] => [[3,2,0],[3,2],[2]] => 12
[[2,2,3],[3,3]] => [[3,2,0],[2,0],[0]] => [[3,2,0],[3,2],[3]] => 13
[[1,1,1],[2],[3]] => [[3,1,1],[3,1],[3]] => [[3,1,1],[1,1],[1]] => 8
[[1,1,2],[2],[3]] => [[3,1,1],[3,1],[2]] => [[3,1,1],[2,1],[1]] => 9
[[1,1,3],[2],[3]] => [[3,1,1],[2,1],[2]] => [[3,1,1],[2,1],[2]] => 10
[[1,2,2],[2],[3]] => [[3,1,1],[3,1],[1]] => [[3,1,1],[3,1],[1]] => 10
[[1,2,3],[2],[3]] => [[3,1,1],[2,1],[1]] => [[3,1,1],[3,1],[2]] => 11
[[1,3,3],[2],[3]] => [[3,1,1],[1,1],[1]] => [[3,1,1],[3,1],[3]] => 12
[[1,1],[2,2],[3]] => [[2,2,1],[2,2],[2]] => [[2,2,1],[2,1],[1]] => 9
[[1,1],[2,3],[3]] => [[2,2,1],[2,1],[2]] => [[2,2,1],[2,1],[2]] => 10
[[1,2],[2,3],[3]] => [[2,2,1],[2,1],[1]] => [[2,2,1],[2,2],[2]] => 11
[[1,1,1,1,1,2]] => [[6,0],[5]] => [[6,0],[1]] => 7
[[1,1,1,1,2,2]] => [[6,0],[4]] => [[6,0],[2]] => 8
[[1,1,1,2,2,2]] => [[6,0],[3]] => [[6,0],[3]] => 9
[[1,1,2,2,2,2]] => [[6,0],[2]] => [[6,0],[4]] => 10
[[1,2,2,2,2,2]] => [[6,0],[1]] => [[6,0],[5]] => 11
[[2,2,2,2,2,2]] => [[6,0],[0]] => [[6,0],[6]] => 12
[[1,1,1,1,1],[2]] => [[5,1],[5]] => [[5,1],[1]] => 7
[[1,1,1,1,2],[2]] => [[5,1],[4]] => [[5,1],[2]] => 8
[[1,1,1,2,2],[2]] => [[5,1],[3]] => [[5,1],[3]] => 9
[[1,1,2,2,2],[2]] => [[5,1],[2]] => [[5,1],[4]] => 10
[[1,2,2,2,2],[2]] => [[5,1],[1]] => [[5,1],[5]] => 11
[[1,1,1,1],[2,2]] => [[4,2],[4]] => [[4,2],[2]] => 8
[[1,1,1,2],[2,2]] => [[4,2],[3]] => [[4,2],[3]] => 9
[[1,1,2,2],[2,2]] => [[4,2],[2]] => [[4,2],[4]] => 10
[[1,1,1],[2,2,2]] => [[3,3],[3]] => [[3,3],[3]] => 9
[[1,1,1,1],[4]] => [[4,1,0,0],[4,0,0],[4,0],[4]] => [[4,1,0,0],[1,0,0],[1,0],[1]] => 8
[[1,1,1,2],[4]] => [[4,1,0,0],[4,0,0],[4,0],[3]] => [[4,1,0,0],[1,1,0],[1,0],[1]] => 9
[[1,1,1,4],[2]] => [[4,1,0,0],[3,1,0],[3,1],[3]] => [[4,1,0,0],[2,0,0],[1,0],[1]] => 9
[[1,1,1,3],[4]] => [[4,1,0,0],[4,0,0],[3,0],[3]] => [[4,1,0,0],[1,1,0],[1,1],[1]] => 10
[[1,1,1,4],[3]] => [[4,1,0,0],[3,1,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[1]] => 10
[[1,1,1,4],[4]] => [[4,1,0,0],[3,0,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[2]] => 11
[[1,1,2,2],[4]] => [[4,1,0,0],[4,0,0],[4,0],[2]] => [[4,1,0,0],[2,1,0],[1,0],[1]] => 10
[[1,1,2,4],[2]] => [[4,1,0,0],[3,1,0],[3,1],[2]] => [[4,1,0,0],[3,0,0],[1,0],[1]] => 10
[[1,1,2,3],[4]] => [[4,1,0,0],[4,0,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[1,1],[1]] => 11
[[1,1,2,4],[3]] => [[4,1,0,0],[3,1,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[1]] => 11
[[1,1,3,4],[2]] => [[4,1,0,0],[3,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[1]] => 11
[[1,1,2,4],[4]] => [[4,1,0,0],[3,0,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[2]] => 12
[[1,1,4,4],[2]] => [[4,1,0,0],[2,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[2]] => 12
[[1,1,3,3],[4]] => [[4,1,0,0],[4,0,0],[2,0],[2]] => [[4,1,0,0],[2,1,0],[2,1],[1]] => 12
[[1,1,3,4],[3]] => [[4,1,0,0],[3,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[1]] => 12
[[1,1,3,4],[4]] => [[4,1,0,0],[3,0,0],[2,0],[2]] => [[4,1,0,0],[2,1,0],[2,1],[2]] => 13
[[1,1,4,4],[3]] => [[4,1,0,0],[2,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[2]] => 13
[[1,1,4,4],[4]] => [[4,1,0,0],[2,0,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[3]] => 14
[[1,2,2,2],[4]] => [[4,1,0,0],[4,0,0],[4,0],[1]] => [[4,1,0,0],[3,1,0],[1,0],[1]] => 11
[[1,2,2,4],[2]] => [[4,1,0,0],[3,1,0],[3,1],[1]] => [[4,1,0,0],[4,0,0],[1,0],[1]] => 11
[[1,2,2,3],[4]] => [[4,1,0,0],[4,0,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[1,1],[1]] => 12
[[1,2,2,4],[3]] => [[4,1,0,0],[3,1,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[1]] => 12
[[1,2,3,4],[2]] => [[4,1,0,0],[3,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[1]] => 12
[[1,2,2,4],[4]] => [[4,1,0,0],[3,0,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[2]] => 13
[[1,2,4,4],[2]] => [[4,1,0,0],[2,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[2]] => 13
[[1,2,3,3],[4]] => [[4,1,0,0],[4,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[2,1],[1]] => 13
[[1,2,3,4],[3]] => [[4,1,0,0],[3,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[1]] => 13
[[1,3,3,4],[2]] => [[4,1,0,0],[3,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[1]] => 13
[[1,2,3,4],[4]] => [[4,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[2,1],[2]] => 14
[[1,2,4,4],[3]] => [[4,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[2]] => 14
[[1,3,4,4],[2]] => [[4,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[2]] => 14
[[1,2,4,4],[4]] => [[4,1,0,0],[2,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[3]] => 15
[[1,4,4,4],[2]] => [[4,1,0,0],[1,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[3]] => 15
[[1,3,3,3],[4]] => [[4,1,0,0],[4,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[1]] => 14
[[1,3,3,4],[3]] => [[4,1,0,0],[3,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[1]] => 14
[[1,3,3,4],[4]] => [[4,1,0,0],[3,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[2]] => 15
[[1,3,4,4],[3]] => [[4,1,0,0],[2,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[2]] => 15
[[1,3,4,4],[4]] => [[4,1,0,0],[2,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[3]] => 16
[[1,4,4,4],[3]] => [[4,1,0,0],[1,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[3]] => 16
[[1,4,4,4],[4]] => [[4,1,0,0],[1,0,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[4]] => 17
[[2,2,2,2],[4]] => [[4,1,0,0],[4,0,0],[4,0],[0]] => [[4,1,0,0],[4,1,0],[1,0],[1]] => 12
[[2,2,2,3],[4]] => [[4,1,0,0],[4,0,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[1,1],[1]] => 13
[[2,2,2,4],[3]] => [[4,1,0,0],[3,1,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[1]] => 13
[[2,2,2,4],[4]] => [[4,1,0,0],[3,0,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[2]] => 14
[[2,2,3,3],[4]] => [[4,1,0,0],[4,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[2,1],[1]] => 14
[[2,2,3,4],[3]] => [[4,1,0,0],[3,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[1]] => 14
[[2,2,3,4],[4]] => [[4,1,0,0],[3,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[2,1],[2]] => 15
[[2,2,4,4],[3]] => [[4,1,0,0],[2,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[2]] => 15
[[2,2,4,4],[4]] => [[4,1,0,0],[2,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[3]] => 16
[[2,3,3,3],[4]] => [[4,1,0,0],[4,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[1]] => 15
[[2,3,3,4],[3]] => [[4,1,0,0],[3,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[1]] => 15
[[2,3,3,4],[4]] => [[4,1,0,0],[3,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[2]] => 16
[[2,3,4,4],[3]] => [[4,1,0,0],[2,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[2]] => 16
[[2,3,4,4],[4]] => [[4,1,0,0],[2,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[3]] => 17
[[2,4,4,4],[3]] => [[4,1,0,0],[1,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[3]] => 17
[[2,4,4,4],[4]] => [[4,1,0,0],[1,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[4]] => 18
[[3,3,3,3],[4]] => [[4,1,0,0],[4,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[1]] => 16
[[3,3,3,4],[4]] => [[4,1,0,0],[3,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[2]] => 17
[[3,3,4,4],[4]] => [[4,1,0,0],[2,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[3]] => 18
[[3,4,4,4],[4]] => [[4,1,0,0],[1,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[4]] => 19
[[1,1,1],[2,4]] => [[3,2,0,0],[3,1,0],[3,1],[3]] => [[3,2,0,0],[2,0,0],[1,0],[1]] => 9
[[1,1,1],[3,4]] => [[3,2,0,0],[3,1,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[1]] => 10
[[1,1,1],[4,4]] => [[3,2,0,0],[3,0,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[2]] => 11
[[1,1,2],[2,4]] => [[3,2,0,0],[3,1,0],[3,1],[2]] => [[3,2,0,0],[2,1,0],[1,0],[1]] => 10
[[1,1,4],[2,2]] => [[3,2,0,0],[2,2,0],[2,2],[2]] => [[3,2,0,0],[3,0,0],[1,0],[1]] => 10
[[1,1,2],[3,4]] => [[3,2,0,0],[3,1,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[1]] => 11
[[1,1,3],[2,4]] => [[3,2,0,0],[3,1,0],[2,1],[2]] => [[3,2,0,0],[2,1,0],[1,1],[1]] => 11
[[1,1,4],[2,3]] => [[3,2,0,0],[2,2,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[1]] => 11
[[1,1,2],[4,4]] => [[3,2,0,0],[3,0,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[2]] => 12
[[1,1,4],[2,4]] => [[3,2,0,0],[2,1,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[2]] => 12
[[1,1,3],[3,4]] => [[3,2,0,0],[3,1,0],[2,0],[2]] => [[3,2,0,0],[2,1,0],[2,1],[1]] => 12
[[1,1,4],[3,3]] => [[3,2,0,0],[2,2,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[1]] => 12
[[1,1,3],[4,4]] => [[3,2,0,0],[3,0,0],[2,0],[2]] => [[3,2,0,0],[2,1,0],[2,1],[2]] => 13
[[1,1,4],[3,4]] => [[3,2,0,0],[2,1,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[2]] => 13
[[1,1,4],[4,4]] => [[3,2,0,0],[2,0,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[3]] => 14
[[1,2,2],[2,4]] => [[3,2,0,0],[3,1,0],[3,1],[1]] => [[3,2,0,0],[3,1,0],[1,0],[1]] => 11
[[1,2,2],[3,4]] => [[3,2,0,0],[3,1,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[1]] => 12
[[1,2,3],[2,4]] => [[3,2,0,0],[3,1,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[1,1],[1]] => 12
[[1,2,4],[2,3]] => [[3,2,0,0],[2,2,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[1]] => 12
[[1,2,2],[4,4]] => [[3,2,0,0],[3,0,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[2]] => 13
[[1,2,4],[2,4]] => [[3,2,0,0],[2,1,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[2]] => 13
[[1,2,3],[3,4]] => [[3,2,0,0],[3,1,0],[2,0],[1]] => [[3,2,0,0],[2,2,0],[2,1],[1]] => 13
[[1,2,4],[3,3]] => [[3,2,0,0],[2,2,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[1]] => 13
[[1,3,3],[2,4]] => [[3,2,0,0],[3,1,0],[1,1],[1]] => [[3,2,0,0],[3,1,0],[2,1],[1]] => 13
[[1,2,3],[4,4]] => [[3,2,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0],[2,2,0],[2,1],[2]] => 14
[[1,2,4],[3,4]] => [[3,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[2]] => 14
[[1,3,4],[2,4]] => [[3,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0],[3,1,0],[2,1],[2]] => 14
[[1,2,4],[4,4]] => [[3,2,0,0],[2,0,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[3]] => 15
[[1,3,3],[3,4]] => [[3,2,0,0],[3,1,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[1]] => 14
[[1,3,3],[4,4]] => [[3,2,0,0],[3,0,0],[1,0],[1]] => [[3,2,0,0],[2,2,0],[2,2],[2]] => 15
[[1,3,4],[3,4]] => [[3,2,0,0],[2,1,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[2]] => 15
[[1,3,4],[4,4]] => [[3,2,0,0],[2,0,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[3]] => 16
[[2,2,2],[3,4]] => [[3,2,0,0],[3,1,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[1]] => 13
[[2,2,2],[4,4]] => [[3,2,0,0],[3,0,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[2]] => 14
[[2,2,3],[3,4]] => [[3,2,0,0],[3,1,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[2,1],[1]] => 14
[[2,2,4],[3,3]] => [[3,2,0,0],[2,2,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[1]] => 14
[[2,2,3],[4,4]] => [[3,2,0,0],[3,0,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[2,1],[2]] => 15
[[2,2,4],[3,4]] => [[3,2,0,0],[2,1,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[2]] => 15
[[2,2,4],[4,4]] => [[3,2,0,0],[2,0,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[3]] => 16
[[2,3,3],[3,4]] => [[3,2,0,0],[3,1,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[1]] => 15
[[2,3,3],[4,4]] => [[3,2,0,0],[3,0,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[2,2],[2]] => 16
[[2,3,4],[3,4]] => [[3,2,0,0],[2,1,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[2]] => 16
[[2,3,4],[4,4]] => [[3,2,0,0],[2,0,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[3]] => 17
[[3,3,3],[4,4]] => [[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,2,0,0],[3,2,0],[3,2],[2]] => 17
[[3,3,4],[4,4]] => [[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,2,0,0],[3,2,0],[3,2],[3]] => 18
[[1,1,1],[2],[4]] => [[3,1,1,0],[3,1,0],[3,1],[3]] => [[3,1,1,0],[1,1,0],[1,0],[1]] => 9
[[1,1,1],[3],[4]] => [[3,1,1,0],[3,1,0],[3,0],[3]] => [[3,1,1,0],[1,1,0],[1,1],[1]] => 10
[[1,1,2],[2],[4]] => [[3,1,1,0],[3,1,0],[3,1],[2]] => [[3,1,1,0],[2,1,0],[1,0],[1]] => 10
[[1,1,2],[3],[4]] => [[3,1,1,0],[3,1,0],[3,0],[2]] => [[3,1,1,0],[1,1,1],[1,1],[1]] => 11
[[1,1,3],[2],[4]] => [[3,1,1,0],[3,1,0],[2,1],[2]] => [[3,1,1,0],[2,1,0],[1,1],[1]] => 11
[[1,1,4],[2],[3]] => [[3,1,1,0],[2,1,1],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[1]] => 11
[[1,1,4],[2],[4]] => [[3,1,1,0],[2,1,0],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[2]] => 12
[[1,1,3],[3],[4]] => [[3,1,1,0],[3,1,0],[2,0],[2]] => [[3,1,1,0],[2,1,0],[2,1],[1]] => 12
[[1,1,4],[3],[4]] => [[3,1,1,0],[2,1,0],[2,0],[2]] => [[3,1,1,0],[2,1,0],[2,1],[2]] => 13
[[1,2,2],[2],[4]] => [[3,1,1,0],[3,1,0],[3,1],[1]] => [[3,1,1,0],[3,1,0],[1,0],[1]] => 11
[[1,2,2],[3],[4]] => [[3,1,1,0],[3,1,0],[3,0],[1]] => [[3,1,1,0],[2,1,1],[1,1],[1]] => 12
[[1,2,3],[2],[4]] => [[3,1,1,0],[3,1,0],[2,1],[1]] => [[3,1,1,0],[3,1,0],[1,1],[1]] => 12
[[1,2,4],[2],[3]] => [[3,1,1,0],[2,1,1],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[1]] => 12
[[1,2,4],[2],[4]] => [[3,1,1,0],[2,1,0],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[2]] => 13
[[1,2,3],[3],[4]] => [[3,1,1,0],[3,1,0],[2,0],[1]] => [[3,1,1,0],[2,1,1],[2,1],[1]] => 13
[[1,3,3],[2],[4]] => [[3,1,1,0],[3,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[2,1],[1]] => 13
[[1,3,4],[2],[3]] => [[3,1,1,0],[2,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[1]] => 13
[[1,2,4],[3],[4]] => [[3,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0],[2,1,1],[2,1],[2]] => 14
[[1,3,4],[2],[4]] => [[3,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[2,1],[2]] => 14
[[1,4,4],[2],[3]] => [[3,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[2]] => 14
[[1,4,4],[2],[4]] => [[3,1,1,0],[1,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[3]] => 15
[[1,3,3],[3],[4]] => [[3,1,1,0],[3,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[1]] => 14
[[1,3,4],[3],[4]] => [[3,1,1,0],[2,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[2]] => 15
[[1,4,4],[3],[4]] => [[3,1,1,0],[1,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[3]] => 16
[[2,2,2],[3],[4]] => [[3,1,1,0],[3,1,0],[3,0],[0]] => [[3,1,1,0],[3,1,1],[1,1],[1]] => 13
[[2,2,3],[3],[4]] => [[3,1,1,0],[3,1,0],[2,0],[0]] => [[3,1,1,0],[3,1,1],[2,1],[1]] => 14
[[2,2,4],[3],[4]] => [[3,1,1,0],[2,1,0],[2,0],[0]] => [[3,1,1,0],[3,1,1],[2,1],[2]] => 15
[[2,3,3],[3],[4]] => [[3,1,1,0],[3,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[1]] => 15
[[2,3,4],[3],[4]] => [[3,1,1,0],[2,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[2]] => 16
[[2,4,4],[3],[4]] => [[3,1,1,0],[1,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[3]] => 17
[[1,1],[2,2],[4]] => [[2,2,1,0],[2,2,0],[2,2],[2]] => [[2,2,1,0],[2,1,0],[1,0],[1]] => 10
[[1,1],[2,3],[4]] => [[2,2,1,0],[2,2,0],[2,1],[2]] => [[2,2,1,0],[2,1,0],[1,1],[1]] => 11
[[1,1],[2,4],[3]] => [[2,2,1,0],[2,1,1],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[1]] => 11
[[1,1],[2,4],[4]] => [[2,2,1,0],[2,1,0],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[2]] => 12
[[1,1],[3,3],[4]] => [[2,2,1,0],[2,2,0],[2,0],[2]] => [[2,2,1,0],[2,1,0],[2,1],[1]] => 12
[[1,1],[3,4],[4]] => [[2,2,1,0],[2,1,0],[2,0],[2]] => [[2,2,1,0],[2,1,0],[2,1],[2]] => 13
[[1,2],[2,3],[4]] => [[2,2,1,0],[2,2,0],[2,1],[1]] => [[2,2,1,0],[2,1,1],[1,1],[1]] => 12
[[1,2],[2,4],[3]] => [[2,2,1,0],[2,1,1],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[1]] => 12
[[1,2],[2,4],[4]] => [[2,2,1,0],[2,1,0],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[2]] => 13
[[1,2],[3,3],[4]] => [[2,2,1,0],[2,2,0],[2,0],[1]] => [[2,2,1,0],[2,1,1],[2,1],[1]] => 13
[[1,3],[2,4],[3]] => [[2,2,1,0],[2,1,1],[1,1],[1]] => [[2,2,1,0],[2,2,0],[2,1],[1]] => 13
[[1,2],[3,4],[4]] => [[2,2,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0],[2,1,1],[2,1],[2]] => 14
[[1,3],[2,4],[4]] => [[2,2,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0],[2,2,0],[2,1],[2]] => 14
[[1,3],[3,4],[4]] => [[2,2,1,0],[2,1,0],[1,0],[1]] => [[2,2,1,0],[2,2,0],[2,2],[2]] => 15
[[2,2],[3,3],[4]] => [[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2,1,0],[2,2,1],[2,1],[1]] => 14
[[2,2],[3,4],[4]] => [[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2,1,0],[2,2,1],[2,1],[2]] => 15
[[2,3],[3,4],[4]] => [[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,2,1,0],[2,2,1],[2,2],[2]] => 16
[[1,1],[2],[3],[4]] => [[2,1,1,1],[2,1,1],[2,1],[2]] => [[2,1,1,1],[1,1,1],[1,1],[1]] => 11
[[1,2],[2],[3],[4]] => [[2,1,1,1],[2,1,1],[2,1],[1]] => [[2,1,1,1],[2,1,1],[1,1],[1]] => 12
[[1,3],[2],[3],[4]] => [[2,1,1,1],[2,1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1],[2,1],[1]] => 13
[[1,4],[2],[3],[4]] => [[2,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1],[2,1],[2]] => 14
[[1,1,1],[2,2,3]] => [[3,3,0],[3,2],[3]] => [[3,3,0],[3,0],[1]] => 10
[[1,1,1],[2,3,3]] => [[3,3,0],[3,1],[3]] => [[3,3,0],[3,0],[2]] => 11
[[1,1,1],[3,3,3]] => [[3,3,0],[3,0],[3]] => [[3,3,0],[3,0],[3]] => 12
[[1,1,2],[2,2,3]] => [[3,3,0],[3,2],[2]] => [[3,3,0],[3,1],[1]] => 11
[[1,1,2],[2,3,3]] => [[3,3,0],[3,1],[2]] => [[3,3,0],[3,1],[2]] => 12
[[1,1,2],[3,3,3]] => [[3,3,0],[3,0],[2]] => [[3,3,0],[3,1],[3]] => 13
[[1,2,2],[2,3,3]] => [[3,3,0],[3,1],[1]] => [[3,3,0],[3,2],[2]] => 13
[[1,2,2],[3,3,3]] => [[3,3,0],[3,0],[1]] => [[3,3,0],[3,2],[3]] => 14
[[2,2,2],[3,3,3]] => [[3,3,0],[3,0],[0]] => [[3,3,0],[3,3],[3]] => 15
[[1,1,1],[2,2],[3]] => [[3,2,1],[3,2],[3]] => [[3,2,1],[2,1],[1]] => 10
[[1,1,1],[2,3],[3]] => [[3,2,1],[3,1],[3]] => [[3,2,1],[2,1],[2]] => 11
[[1,1,2],[2,2],[3]] => [[3,2,1],[3,2],[2]] => [[3,2,1],[3,1],[1]] => 11
[[1,1,2],[2,3],[3]] => [[3,2,1],[3,1],[2]] => [[3,2,1],[2,2],[2]] => 12
[[1,1,3],[2,2],[3]] => [[3,2,1],[2,2],[2]] => [[3,2,1],[3,1],[2]] => 12
[[1,1,3],[2,3],[3]] => [[3,2,1],[2,1],[2]] => [[3,2,1],[3,1],[3]] => 13
[[1,2,2],[2,3],[3]] => [[3,2,1],[3,1],[1]] => [[3,2,1],[3,2],[2]] => 13
[[1,2,3],[2,3],[3]] => [[3,2,1],[2,1],[1]] => [[3,2,1],[3,2],[3]] => 14
[[1,1],[2,2],[3,3]] => [[2,2,2],[2,2],[2]] => [[2,2,2],[2,2],[2]] => 12
[[1,2,3,4,5]] => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 15
[[1,2,3,4],[5]] => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 15
[[1,2,3,5],[4]] => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 15
[[1,2,4,5],[3]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 15
[[1,3,4,5],[2]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 15
[[1,2,3],[4,5]] => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 15
[[1,2,4],[3,5]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 15
[[1,2,5],[3,4]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 15
[[1,3,4],[2,5]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 15
[[1,3,5],[2,4]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 15
[[1,2,3],[4],[5]] => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 15
[[1,2,4],[3],[5]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 15
[[1,2,5],[3],[4]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 15
[[1,3,4],[2],[5]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 15
[[1,3,5],[2],[4]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 15
[[1,4,5],[2],[3]] => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 15
[[1,2],[3,4],[5]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 15
[[1,2],[3,5],[4]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 15
[[1,3],[2,4],[5]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 15
[[1,3],[2,5],[4]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 15
[[1,4],[2,5],[3]] => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 15
[[1,2],[3],[4],[5]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => 15
[[1,3],[2],[4],[5]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 15
[[1,4],[2],[3],[5]] => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 15
[[1,5],[2],[3],[4]] => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 15
[[1],[2],[3],[4],[5]] => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => 15
[[1]] => [[1]] => [[1]] => 1
[[1,1,1,1],[2,2,2],[3,3],[4]] => [[4,3,2,1],[4,3,2],[4,3],[4]] => [[4,3,2,1],[3,2,1],[2,1],[1]] => 20
[[1,1,1,2],[2,2,2],[3,3],[4]] => [[4,3,2,1],[4,3,2],[4,3],[3]] => [[4,3,2,1],[4,2,1],[2,1],[1]] => 21
[[1,1,1,1],[2,2,3],[3,3],[4]] => [[4,3,2,1],[4,3,2],[4,2],[4]] => [[4,3,2,1],[3,2,1],[3,1],[1]] => 21
[[1,1,1,3],[2,2,3],[3,3],[4]] => [[4,3,2,1],[4,3,2],[3,2],[3]] => [[4,3,2,1],[4,2,1],[4,1],[1]] => 23
[[1,1,2,2],[2,2,3],[3,3],[4]] => [[4,3,2,1],[4,3,2],[4,2],[2]] => [[4,3,2,1],[4,3,1],[3,1],[1]] => 23
[[1,1,2,3],[2,2,3],[3,3],[4]] => [[4,3,2,1],[4,3,2],[3,2],[2]] => [[4,3,2,1],[4,3,1],[4,1],[1]] => 24
[[1,1,1,1],[2,2,2],[3,4],[4]] => [[4,3,2,1],[4,3,1],[4,3],[4]] => [[4,3,2,1],[3,2,1],[2,1],[2]] => 21
[[1,1,1,2],[2,2,2],[3,4],[4]] => [[4,3,2,1],[4,3,1],[4,3],[3]] => [[4,3,2,1],[4,2,1],[2,1],[2]] => 22
[[1,1,1,3],[2,2,3],[3,4],[4]] => [[4,3,2,1],[4,3,1],[3,2],[3]] => [[4,3,2,1],[4,2,1],[3,2],[2]] => 24
[[1,1,1,1],[2,2,4],[3,4],[4]] => [[4,3,2,1],[4,2,1],[4,2],[4]] => [[4,3,2,1],[3,2,1],[3,1],[3]] => 23
[[1,1,1,4],[2,2,4],[3,4],[4]] => [[4,3,2,1],[3,2,1],[3,2],[3]] => [[4,3,2,1],[4,2,1],[4,1],[4]] => 26
[[1,1,2,2],[2,2,4],[3,4],[4]] => [[4,3,2,1],[4,2,1],[4,2],[2]] => [[4,3,2,1],[4,3,1],[3,1],[3]] => 25
[[1,1,2,3],[2,2,4],[3,4],[4]] => [[4,3,2,1],[4,2,1],[3,2],[2]] => [[4,3,2,1],[4,3,1],[3,2],[3]] => 26
[[1,1,2,4],[2,2,4],[3,4],[4]] => [[4,3,2,1],[3,2,1],[3,2],[2]] => [[4,3,2,1],[4,3,1],[4,1],[4]] => 27
[[1,1,1,1],[2,3,3],[3,4],[4]] => [[4,3,2,1],[4,3,1],[4,1],[4]] => [[4,3,2,1],[3,2,1],[3,2],[2]] => 23
[[1,1,1,3],[2,3,3],[3,4],[4]] => [[4,3,2,1],[4,3,1],[3,1],[3]] => [[4,3,2,1],[4,2,1],[4,2],[2]] => 25
[[1,1,1,1],[2,3,4],[3,4],[4]] => [[4,3,2,1],[4,2,1],[4,1],[4]] => [[4,3,2,1],[3,2,1],[3,2],[3]] => 24
[[1,1,1,4],[2,3,4],[3,4],[4]] => [[4,3,2,1],[3,2,1],[3,1],[3]] => [[4,3,2,1],[4,2,1],[4,2],[4]] => 27
[[1,1,3,3],[2,3,4],[3,4],[4]] => [[4,3,2,1],[4,2,1],[2,1],[2]] => [[4,3,2,1],[4,3,1],[4,3],[3]] => 28
[[1,1,3,4],[2,3,4],[3,4],[4]] => [[4,3,2,1],[3,2,1],[2,1],[2]] => [[4,3,2,1],[4,3,1],[4,3],[4]] => 29
[[1,2,2,2],[2,3,3],[3,4],[4]] => [[4,3,2,1],[4,3,1],[4,1],[1]] => [[4,3,2,1],[4,3,2],[3,2],[2]] => 26
[[1,2,2,3],[2,3,3],[3,4],[4]] => [[4,3,2,1],[4,3,1],[3,1],[1]] => [[4,3,2,1],[4,3,2],[4,2],[2]] => 27
[[1,2,2,2],[2,3,4],[3,4],[4]] => [[4,3,2,1],[4,2,1],[4,1],[1]] => [[4,3,2,1],[4,3,2],[3,2],[3]] => 27
[[1,2,2,4],[2,3,4],[3,4],[4]] => [[4,3,2,1],[3,2,1],[3,1],[1]] => [[4,3,2,1],[4,3,2],[4,2],[4]] => 29
[[1,2,3,3],[2,3,4],[3,4],[4]] => [[4,3,2,1],[4,2,1],[2,1],[1]] => [[4,3,2,1],[4,3,2],[4,3],[3]] => 29
[[1,2,3,4],[2,3,4],[3,4],[4]] => [[4,3,2,1],[3,2,1],[2,1],[1]] => [[4,3,2,1],[4,3,2],[4,3],[4]] => 30
[[2]] => [[1,0],[0]] => [[1,0],[1]] => 2
[[1,1]] => [[2]] => [[2]] => 2
[[3]] => [[1,0,0],[0,0],[0]] => [[1,0,0],[1,0],[1]] => 3
[[1,1,1]] => [[3]] => [[3]] => 3
[[4]] => [[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0],[1,0,0],[1,0],[1]] => 4
[[1,1,1,1]] => [[4]] => [[4]] => 4
[[5]] => [[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 5
[[1,1,1,1,1]] => [[5]] => [[5]] => 5
[[6]] => [[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[1,2,3,4,5,6]] => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 21
[[1,2,3,4,5],[6]] => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 21
[[1,2,3,4,6],[5]] => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 21
[[1,2,3,4],[5],[6]] => [[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 21
[[1,2,3,5,6],[4]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 21
[[1,2,3,5],[4,6]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 21
[[1,2,3,5],[4],[6]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 21
[[1,2,3,4],[5,6]] => [[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 21
[[1,2,3,6],[4],[5]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 21
[[1,2,3],[4],[5],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => 21
[[1,2,4,5,6],[3]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 21
[[1,2,4,5],[3,6]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 21
[[1,2,4,6],[3,5]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 21
[[1,2,4],[3,5],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 21
[[1,2,4,5],[3],[6]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 21
[[1,2,4,6],[3],[5]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 21
[[1,2,4],[3],[5],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 21
[[1,2,3,6],[4,5]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 21
[[1,2,3],[4,5],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 21
[[1,2,5,6],[3],[4]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 21
[[1,2,5],[3,6],[4]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 21
[[1,2,5],[3],[4],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 21
[[1,2,3],[4,6],[5]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 21
[[1,2,4],[3,6],[5]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 21
[[1,2,6],[3],[4],[5]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 21
[[1,2],[3],[4],[5],[6]] => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => 21
[[1,3,4,5,6],[2]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 21
[[1,3,4,5],[2,6]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 21
[[1,3,4,6],[2,5]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 21
[[1,3,4],[2,5],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 21
[[1,3,5,6],[2,4]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 21
[[1,3,5],[2,4,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 21
[[1,3,5],[2,4],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 21
[[1,3,4],[2,5,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 21
[[1,3,6],[2,4],[5]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 21
[[1,3],[2,4],[5],[6]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => 21
[[1,3,4,5],[2],[6]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 21
[[1,3,4,6],[2],[5]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 21
[[1,3,4],[2],[5],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 21
[[1,3,5,6],[2],[4]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 21
[[1,3,5],[2,6],[4]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 21
[[1,3,5],[2],[4],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 21
[[1,3,4],[2,6],[5]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 21
[[1,3,6],[2],[4],[5]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 21
[[1,3],[2],[4],[5],[6]] => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => 21
[[1,2,5,6],[3,4]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 21
[[1,2,5],[3,4,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 21
[[1,2,5],[3,4],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 21
[[1,2,4],[3,5,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 21
[[1,2,6],[3,4],[5]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 21
[[1,2],[3,4],[5],[6]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 21
[[1,4,5,6],[2],[3]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 21
[[1,4,5],[2,6],[3]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 21
[[1,4,6],[2,5],[3]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 21
[[1,4],[2,5],[3,6]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 21
[[1,4],[2,5],[3],[6]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 21
[[1,4,5],[2],[3],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 21
[[1,4,6],[2],[3],[5]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 21
[[1,4],[2],[3],[5],[6]] => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 21
[[1,2,3],[4,5,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 21
[[1,2,6],[3,5],[4]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 21
[[1,2],[3,5],[4],[6]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 21
[[1,3,6],[2,5],[4]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 21
[[1,3],[2,5],[4,6]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 21
[[1,3],[2,5],[4],[6]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 21
[[1,2],[3,5],[4,6]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 21
[[1,5,6],[2],[3],[4]] => [[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 21
[[1,5],[2,6],[3],[4]] => [[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 21
[[1,5],[2],[3],[4],[6]] => [[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 21
[[1,2],[3,6],[4],[5]] => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 21
[[1,3],[2,4],[5,6]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 21
[[1,3],[2,6],[4],[5]] => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 21
[[1,2],[3,4],[5,6]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 21
[[1,4],[2,6],[3],[5]] => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 21
[[1,6],[2],[3],[4],[5]] => [[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 21
[[1],[2],[3],[4],[5],[6]] => [[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => 21
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 sum of the entries of the Gelfand-Tsetlin pattern.
Map
to Gelfand-Tsetlin pattern
Description
Return the Gelfand-Tsetlin pattern corresponding to the semistandard tableau.
Map
Schuetzenberger involution
Description
Applies the Schuetzenberger involution to a Gelfand-Tsetlin pattern.
The Schuetzenberger involution is usually regarded as an involution on semistandard Young tableaux with a fixed bound on the size of the entries. It is also known as evacuation, and in the context of crystal graphs of type $A$ it realizes Lusztig's involution.
In the language of tableaux it is defined as follows. Consider a semistandard tableau with no entry larger than $n$. Use Schuetzenberger's jeu de taquin to slide all entries equal to $1$ to the outer border of the tableau. Do the same for all entries equal to $2$, restricting the tableau to the entries larger than $2$, and so on, until the tableau is a reverse semistandard tableau. Finally, replace each entry with its complement with respect to $n$, that is, replace $e$ with $n+1-e$.