Identifier
Values
[[1]] => [1] => 1 => 1
[[1],[1]] => [1,1] => 11 => 1
[[2]] => [2] => 0 => 1
[[1,1]] => [2] => 0 => 1
[[1],[1],[1]] => [1,1,1] => 111 => 1
[[2],[1]] => [2,1] => 01 => 1
[[1,1],[1]] => [2,1] => 01 => 1
[[3]] => [3] => 1 => 1
[[2,1]] => [3] => 1 => 1
[[1,1,1]] => [3] => 1 => 1
[[1],[1],[1],[1]] => [1,1,1,1] => 1111 => 1
[[2],[1],[1]] => [2,1,1] => 011 => 1
[[2],[2]] => [2,2] => 00 => 1
[[1,1],[1],[1]] => [2,1,1] => 011 => 1
[[1,1],[1,1]] => [2,2] => 00 => 1
[[3],[1]] => [3,1] => 11 => 1
[[2,1],[1]] => [3,1] => 11 => 1
[[1,1,1],[1]] => [3,1] => 11 => 1
[[4]] => [4] => 0 => 1
[[3,1]] => [4] => 0 => 1
[[2,2]] => [4] => 0 => 1
[[2,1,1]] => [4] => 0 => 1
[[1,1,1,1]] => [4] => 0 => 1
[[1],[1],[1],[1],[1]] => [1,1,1,1,1] => 11111 => 1
[[2],[1],[1],[1]] => [2,1,1,1] => 0111 => 1
[[2],[2],[1]] => [2,2,1] => 001 => 1
[[1,1],[1],[1],[1]] => [2,1,1,1] => 0111 => 1
[[1,1],[1,1],[1]] => [2,2,1] => 001 => 1
[[3],[1],[1]] => [3,1,1] => 111 => 1
[[3],[2]] => [3,2] => 10 => 1
[[2,1],[1],[1]] => [3,1,1] => 111 => 1
[[2,1],[2]] => [3,2] => 10 => 1
[[2,1],[1,1]] => [3,2] => 10 => 1
[[1,1,1],[1],[1]] => [3,1,1] => 111 => 1
[[1,1,1],[1,1]] => [3,2] => 10 => 1
[[4],[1]] => [4,1] => 01 => 1
[[3,1],[1]] => [4,1] => 01 => 1
[[2,2],[1]] => [4,1] => 01 => 1
[[2,1,1],[1]] => [4,1] => 01 => 1
[[1,1,1,1],[1]] => [4,1] => 01 => 1
[[5]] => [5] => 1 => 1
[[4,1]] => [5] => 1 => 1
[[3,2]] => [5] => 1 => 1
[[3,1,1]] => [5] => 1 => 1
[[2,2,1]] => [5] => 1 => 1
[[2,1,1,1]] => [5] => 1 => 1
[[1,1,1,1,1]] => [5] => 1 => 1
[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1] => 111111 => 1
[[2],[1],[1],[1],[1]] => [2,1,1,1,1] => 01111 => 1
[[2],[2],[1],[1]] => [2,2,1,1] => 0011 => 1
[[2],[2],[2]] => [2,2,2] => 000 => 1
[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => 01111 => 1
[[1,1],[1,1],[1],[1]] => [2,2,1,1] => 0011 => 1
[[1,1],[1,1],[1,1]] => [2,2,2] => 000 => 1
[[3],[1],[1],[1]] => [3,1,1,1] => 1111 => 1
[[3],[2],[1]] => [3,2,1] => 101 => 1
[[3],[3]] => [3,3] => 11 => 1
[[2,1],[1],[1],[1]] => [3,1,1,1] => 1111 => 1
[[2,1],[2],[1]] => [3,2,1] => 101 => 1
[[2,1],[1,1],[1]] => [3,2,1] => 101 => 1
[[2,1],[2,1]] => [3,3] => 11 => 1
[[1,1,1],[1],[1],[1]] => [3,1,1,1] => 1111 => 1
[[1,1,1],[1,1],[1]] => [3,2,1] => 101 => 1
[[1,1,1],[1,1,1]] => [3,3] => 11 => 1
[[4],[1],[1]] => [4,1,1] => 011 => 1
[[4],[2]] => [4,2] => 00 => 1
[[3,1],[1],[1]] => [4,1,1] => 011 => 1
[[3,1],[2]] => [4,2] => 00 => 1
[[3,1],[1,1]] => [4,2] => 00 => 1
[[2,2],[1],[1]] => [4,1,1] => 011 => 1
[[2,2],[2]] => [4,2] => 00 => 1
[[2,2],[1,1]] => [4,2] => 00 => 1
[[2,1,1],[1],[1]] => [4,1,1] => 011 => 1
[[2,1,1],[2]] => [4,2] => 00 => 1
[[2,1,1],[1,1]] => [4,2] => 00 => 1
[[1,1,1,1],[1],[1]] => [4,1,1] => 011 => 1
[[1,1,1,1],[1,1]] => [4,2] => 00 => 1
[[5],[1]] => [5,1] => 11 => 1
[[4,1],[1]] => [5,1] => 11 => 1
[[3,2],[1]] => [5,1] => 11 => 1
[[3,1,1],[1]] => [5,1] => 11 => 1
[[2,2,1],[1]] => [5,1] => 11 => 1
[[2,1,1,1],[1]] => [5,1] => 11 => 1
[[1,1,1,1,1],[1]] => [5,1] => 11 => 1
[[6]] => [6] => 0 => 1
[[5,1]] => [6] => 0 => 1
[[4,2]] => [6] => 0 => 1
[[4,1,1]] => [6] => 0 => 1
[[3,3]] => [6] => 0 => 1
[[3,2,1]] => [6] => 0 => 1
[[3,1,1,1]] => [6] => 0 => 1
[[2,2,2]] => [6] => 0 => 1
[[2,2,1,1]] => [6] => 0 => 1
[[2,1,1,1,1]] => [6] => 0 => 1
[[1,1,1,1,1,1]] => [6] => 0 => 1
[[2],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => 011111 => 1
[[2],[2],[1],[1],[1]] => [2,2,1,1,1] => 00111 => 1
[[2],[2],[2],[1]] => [2,2,2,1] => 0001 => 1
[[1,1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => 011111 => 1
[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => 00111 => 1
[[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => 0001 => 1
>>> Load all 1092 entries. <<<
[[3],[1],[1],[1],[1]] => [3,1,1,1,1] => 11111 => 1
[[3],[2],[1],[1]] => [3,2,1,1] => 1011 => 1
[[3],[2],[2]] => [3,2,2] => 100 => 1
[[3],[3],[1]] => [3,3,1] => 111 => 1
[[2,1],[1],[1],[1],[1]] => [3,1,1,1,1] => 11111 => 1
[[2,1],[2],[1],[1]] => [3,2,1,1] => 1011 => 1
[[2,1],[2],[2]] => [3,2,2] => 100 => 1
[[2,1],[1,1],[1],[1]] => [3,2,1,1] => 1011 => 1
[[2,1],[1,1],[1,1]] => [3,2,2] => 100 => 1
[[2,1],[2,1],[1]] => [3,3,1] => 111 => 1
[[1,1,1],[1],[1],[1],[1]] => [3,1,1,1,1] => 11111 => 1
[[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => 1011 => 1
[[1,1,1],[1,1],[1,1]] => [3,2,2] => 100 => 1
[[1,1,1],[1,1,1],[1]] => [3,3,1] => 111 => 1
[[4],[1],[1],[1]] => [4,1,1,1] => 0111 => 1
[[4],[2],[1]] => [4,2,1] => 001 => 1
[[4],[3]] => [4,3] => 01 => 1
[[3,1],[1],[1],[1]] => [4,1,1,1] => 0111 => 1
[[3,1],[2],[1]] => [4,2,1] => 001 => 1
[[3,1],[1,1],[1]] => [4,2,1] => 001 => 1
[[3,1],[3]] => [4,3] => 01 => 1
[[3,1],[2,1]] => [4,3] => 01 => 1
[[2,2],[1],[1],[1]] => [4,1,1,1] => 0111 => 1
[[2,2],[2],[1]] => [4,2,1] => 001 => 1
[[2,2],[1,1],[1]] => [4,2,1] => 001 => 1
[[2,2],[2,1]] => [4,3] => 01 => 1
[[2,1,1],[1],[1],[1]] => [4,1,1,1] => 0111 => 1
[[2,1,1],[2],[1]] => [4,2,1] => 001 => 1
[[2,1,1],[1,1],[1]] => [4,2,1] => 001 => 1
[[2,1,1],[2,1]] => [4,3] => 01 => 1
[[2,1,1],[1,1,1]] => [4,3] => 01 => 1
[[1,1,1,1],[1],[1],[1]] => [4,1,1,1] => 0111 => 1
[[1,1,1,1],[1,1],[1]] => [4,2,1] => 001 => 1
[[1,1,1,1],[1,1,1]] => [4,3] => 01 => 1
[[5],[1],[1]] => [5,1,1] => 111 => 1
[[5],[2]] => [5,2] => 10 => 1
[[4,1],[1],[1]] => [5,1,1] => 111 => 1
[[4,1],[2]] => [5,2] => 10 => 1
[[4,1],[1,1]] => [5,2] => 10 => 1
[[3,2],[1],[1]] => [5,1,1] => 111 => 1
[[3,2],[2]] => [5,2] => 10 => 1
[[3,2],[1,1]] => [5,2] => 10 => 1
[[3,1,1],[1],[1]] => [5,1,1] => 111 => 1
[[3,1,1],[2]] => [5,2] => 10 => 1
[[3,1,1],[1,1]] => [5,2] => 10 => 1
[[2,2,1],[1],[1]] => [5,1,1] => 111 => 1
[[2,2,1],[2]] => [5,2] => 10 => 1
[[2,2,1],[1,1]] => [5,2] => 10 => 1
[[2,1,1,1],[1],[1]] => [5,1,1] => 111 => 1
[[2,1,1,1],[2]] => [5,2] => 10 => 1
[[2,1,1,1],[1,1]] => [5,2] => 10 => 1
[[1,1,1,1,1],[1],[1]] => [5,1,1] => 111 => 1
[[1,1,1,1,1],[1,1]] => [5,2] => 10 => 1
[[6],[1]] => [6,1] => 01 => 1
[[5,1],[1]] => [6,1] => 01 => 1
[[4,2],[1]] => [6,1] => 01 => 1
[[4,1,1],[1]] => [6,1] => 01 => 1
[[3,3],[1]] => [6,1] => 01 => 1
[[3,2,1],[1]] => [6,1] => 01 => 1
[[3,1,1,1],[1]] => [6,1] => 01 => 1
[[2,2,2],[1]] => [6,1] => 01 => 1
[[2,2,1,1],[1]] => [6,1] => 01 => 1
[[2,1,1,1,1],[1]] => [6,1] => 01 => 1
[[1,1,1,1,1,1],[1]] => [6,1] => 01 => 1
[[7]] => [7] => 1 => 1
[[6,1]] => [7] => 1 => 1
[[5,2]] => [7] => 1 => 1
[[5,1,1]] => [7] => 1 => 1
[[4,3]] => [7] => 1 => 1
[[4,2,1]] => [7] => 1 => 1
[[4,1,1,1]] => [7] => 1 => 1
[[3,3,1]] => [7] => 1 => 1
[[3,2,2]] => [7] => 1 => 1
[[3,2,1,1]] => [7] => 1 => 1
[[3,1,1,1,1]] => [7] => 1 => 1
[[2,2,2,1]] => [7] => 1 => 1
[[2,2,1,1,1]] => [7] => 1 => 1
[[2,1,1,1,1,1]] => [7] => 1 => 1
[[1,1,1,1,1,1,1]] => [7] => 1 => 1
[[2],[2],[1],[1],[1],[1]] => [2,2,1,1,1,1] => 001111 => 1
[[2],[2],[2],[1],[1]] => [2,2,2,1,1] => 00011 => 1
[[2],[2],[2],[2]] => [2,2,2,2] => 0000 => 1
[[1,1],[1,1],[1],[1],[1],[1]] => [2,2,1,1,1,1] => 001111 => 1
[[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,1,1] => 00011 => 1
[[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2] => 0000 => 1
[[3],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => 111111 => 1
[[3],[2],[1],[1],[1]] => [3,2,1,1,1] => 10111 => 1
[[3],[2],[2],[1]] => [3,2,2,1] => 1001 => 1
[[3],[3],[1],[1]] => [3,3,1,1] => 1111 => 1
[[3],[3],[2]] => [3,3,2] => 110 => 1
[[2,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => 111111 => 1
[[2,1],[2],[1],[1],[1]] => [3,2,1,1,1] => 10111 => 1
[[2,1],[2],[2],[1]] => [3,2,2,1] => 1001 => 1
[[2,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => 10111 => 1
[[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => 1001 => 1
[[2,1],[2,1],[1],[1]] => [3,3,1,1] => 1111 => 1
[[2,1],[2,1],[2]] => [3,3,2] => 110 => 1
[[2,1],[2,1],[1,1]] => [3,3,2] => 110 => 1
[[1,1,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => 111111 => 1
[[1,1,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => 10111 => 1
[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => 1001 => 1
[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => 1111 => 1
[[1,1,1],[1,1,1],[1,1]] => [3,3,2] => 110 => 1
[[4],[1],[1],[1],[1]] => [4,1,1,1,1] => 01111 => 1
[[4],[2],[1],[1]] => [4,2,1,1] => 0011 => 1
[[4],[2],[2]] => [4,2,2] => 000 => 1
[[4],[3],[1]] => [4,3,1] => 011 => 1
[[4],[4]] => [4,4] => 00 => 1
[[3,1],[1],[1],[1],[1]] => [4,1,1,1,1] => 01111 => 1
[[3,1],[2],[1],[1]] => [4,2,1,1] => 0011 => 1
[[3,1],[2],[2]] => [4,2,2] => 000 => 1
[[3,1],[1,1],[1],[1]] => [4,2,1,1] => 0011 => 1
[[3,1],[1,1],[1,1]] => [4,2,2] => 000 => 1
[[3,1],[3],[1]] => [4,3,1] => 011 => 1
[[3,1],[2,1],[1]] => [4,3,1] => 011 => 1
[[3,1],[3,1]] => [4,4] => 00 => 1
[[2,2],[1],[1],[1],[1]] => [4,1,1,1,1] => 01111 => 1
[[2,2],[2],[1],[1]] => [4,2,1,1] => 0011 => 1
[[2,2],[2],[2]] => [4,2,2] => 000 => 1
[[2,2],[1,1],[1],[1]] => [4,2,1,1] => 0011 => 1
[[2,2],[1,1],[1,1]] => [4,2,2] => 000 => 1
[[2,2],[2,1],[1]] => [4,3,1] => 011 => 1
[[2,2],[2,2]] => [4,4] => 00 => 1
[[2,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => 01111 => 1
[[2,1,1],[2],[1],[1]] => [4,2,1,1] => 0011 => 1
[[2,1,1],[2],[2]] => [4,2,2] => 000 => 1
[[2,1,1],[1,1],[1],[1]] => [4,2,1,1] => 0011 => 1
[[2,1,1],[1,1],[1,1]] => [4,2,2] => 000 => 1
[[2,1,1],[2,1],[1]] => [4,3,1] => 011 => 1
[[2,1,1],[1,1,1],[1]] => [4,3,1] => 011 => 1
[[2,1,1],[2,1,1]] => [4,4] => 00 => 1
[[1,1,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => 01111 => 1
[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1] => 0011 => 1
[[1,1,1,1],[1,1],[1,1]] => [4,2,2] => 000 => 1
[[1,1,1,1],[1,1,1],[1]] => [4,3,1] => 011 => 1
[[1,1,1,1],[1,1,1,1]] => [4,4] => 00 => 1
[[5],[1],[1],[1]] => [5,1,1,1] => 1111 => 1
[[5],[2],[1]] => [5,2,1] => 101 => 1
[[5],[3]] => [5,3] => 11 => 1
[[4,1],[1],[1],[1]] => [5,1,1,1] => 1111 => 1
[[4,1],[2],[1]] => [5,2,1] => 101 => 1
[[4,1],[1,1],[1]] => [5,2,1] => 101 => 1
[[4,1],[3]] => [5,3] => 11 => 1
[[4,1],[2,1]] => [5,3] => 11 => 1
[[3,2],[1],[1],[1]] => [5,1,1,1] => 1111 => 1
[[3,2],[2],[1]] => [5,2,1] => 101 => 1
[[3,2],[1,1],[1]] => [5,2,1] => 101 => 1
[[3,2],[3]] => [5,3] => 11 => 1
[[3,2],[2,1]] => [5,3] => 11 => 1
[[3,1,1],[1],[1],[1]] => [5,1,1,1] => 1111 => 1
[[3,1,1],[2],[1]] => [5,2,1] => 101 => 1
[[3,1,1],[1,1],[1]] => [5,2,1] => 101 => 1
[[3,1,1],[3]] => [5,3] => 11 => 1
[[3,1,1],[2,1]] => [5,3] => 11 => 1
[[3,1,1],[1,1,1]] => [5,3] => 11 => 1
[[2,2,1],[1],[1],[1]] => [5,1,1,1] => 1111 => 1
[[2,2,1],[2],[1]] => [5,2,1] => 101 => 1
[[2,2,1],[1,1],[1]] => [5,2,1] => 101 => 1
[[2,2,1],[2,1]] => [5,3] => 11 => 1
[[2,2,1],[1,1,1]] => [5,3] => 11 => 1
[[2,1,1,1],[1],[1],[1]] => [5,1,1,1] => 1111 => 1
[[2,1,1,1],[2],[1]] => [5,2,1] => 101 => 1
[[2,1,1,1],[1,1],[1]] => [5,2,1] => 101 => 1
[[2,1,1,1],[2,1]] => [5,3] => 11 => 1
[[2,1,1,1],[1,1,1]] => [5,3] => 11 => 1
[[1,1,1,1,1],[1],[1],[1]] => [5,1,1,1] => 1111 => 1
[[1,1,1,1,1],[1,1],[1]] => [5,2,1] => 101 => 1
[[1,1,1,1,1],[1,1,1]] => [5,3] => 11 => 1
[[6],[1],[1]] => [6,1,1] => 011 => 1
[[6],[2]] => [6,2] => 00 => 1
[[5,1],[1],[1]] => [6,1,1] => 011 => 1
[[5,1],[2]] => [6,2] => 00 => 1
[[5,1],[1,1]] => [6,2] => 00 => 1
[[4,2],[1],[1]] => [6,1,1] => 011 => 1
[[4,2],[2]] => [6,2] => 00 => 1
[[4,2],[1,1]] => [6,2] => 00 => 1
[[4,1,1],[1],[1]] => [6,1,1] => 011 => 1
[[4,1,1],[2]] => [6,2] => 00 => 1
[[4,1,1],[1,1]] => [6,2] => 00 => 1
[[3,3],[1],[1]] => [6,1,1] => 011 => 1
[[3,3],[2]] => [6,2] => 00 => 1
[[3,3],[1,1]] => [6,2] => 00 => 1
[[3,2,1],[1],[1]] => [6,1,1] => 011 => 1
[[3,2,1],[2]] => [6,2] => 00 => 1
[[3,2,1],[1,1]] => [6,2] => 00 => 1
[[3,1,1,1],[1],[1]] => [6,1,1] => 011 => 1
[[3,1,1,1],[2]] => [6,2] => 00 => 1
[[3,1,1,1],[1,1]] => [6,2] => 00 => 1
[[2,2,2],[1],[1]] => [6,1,1] => 011 => 1
[[2,2,2],[2]] => [6,2] => 00 => 1
[[2,2,2],[1,1]] => [6,2] => 00 => 1
[[2,2,1,1],[1],[1]] => [6,1,1] => 011 => 1
[[2,2,1,1],[2]] => [6,2] => 00 => 1
[[2,2,1,1],[1,1]] => [6,2] => 00 => 1
[[2,1,1,1,1],[1],[1]] => [6,1,1] => 011 => 1
[[2,1,1,1,1],[2]] => [6,2] => 00 => 1
[[2,1,1,1,1],[1,1]] => [6,2] => 00 => 1
[[1,1,1,1,1,1],[1],[1]] => [6,1,1] => 011 => 1
[[1,1,1,1,1,1],[1,1]] => [6,2] => 00 => 1
[[7],[1]] => [7,1] => 11 => 1
[[6,1],[1]] => [7,1] => 11 => 1
[[5,2],[1]] => [7,1] => 11 => 1
[[5,1,1],[1]] => [7,1] => 11 => 1
[[4,3],[1]] => [7,1] => 11 => 1
[[4,2,1],[1]] => [7,1] => 11 => 1
[[4,1,1,1],[1]] => [7,1] => 11 => 1
[[3,3,1],[1]] => [7,1] => 11 => 1
[[3,2,2],[1]] => [7,1] => 11 => 1
[[3,2,1,1],[1]] => [7,1] => 11 => 1
[[3,1,1,1,1],[1]] => [7,1] => 11 => 1
[[2,2,2,1],[1]] => [7,1] => 11 => 1
[[2,2,1,1,1],[1]] => [7,1] => 11 => 1
[[2,1,1,1,1,1],[1]] => [7,1] => 11 => 1
[[1,1,1,1,1,1,1],[1]] => [7,1] => 11 => 1
[[8]] => [8] => 0 => 1
[[7,1]] => [8] => 0 => 1
[[6,2]] => [8] => 0 => 1
[[6,1,1]] => [8] => 0 => 1
[[5,3]] => [8] => 0 => 1
[[5,2,1]] => [8] => 0 => 1
[[5,1,1,1]] => [8] => 0 => 1
[[4,4]] => [8] => 0 => 1
[[4,3,1]] => [8] => 0 => 1
[[4,2,2]] => [8] => 0 => 1
[[4,2,1,1]] => [8] => 0 => 1
[[4,1,1,1,1]] => [8] => 0 => 1
[[3,3,2]] => [8] => 0 => 1
[[3,3,1,1]] => [8] => 0 => 1
[[3,2,2,1]] => [8] => 0 => 1
[[3,2,1,1,1]] => [8] => 0 => 1
[[3,1,1,1,1,1]] => [8] => 0 => 1
[[2,2,2,2]] => [8] => 0 => 1
[[2,2,2,1,1]] => [8] => 0 => 1
[[2,2,1,1,1,1]] => [8] => 0 => 1
[[2,1,1,1,1,1,1]] => [8] => 0 => 1
[[1,1,1,1,1,1,1,1]] => [8] => 0 => 1
[[2],[2],[2],[1],[1],[1]] => [2,2,2,1,1,1] => 000111 => 1
[[2],[2],[2],[2],[1]] => [2,2,2,2,1] => 00001 => 1
[[1,1],[1,1],[1,1],[1],[1],[1]] => [2,2,2,1,1,1] => 000111 => 1
[[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1] => 00001 => 1
[[3],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 101111 => 1
[[3],[2],[2],[1],[1]] => [3,2,2,1,1] => 10011 => 1
[[3],[2],[2],[2]] => [3,2,2,2] => 1000 => 1
[[3],[3],[1],[1],[1]] => [3,3,1,1,1] => 11111 => 1
[[3],[3],[2],[1]] => [3,3,2,1] => 1101 => 1
[[3],[3],[3]] => [3,3,3] => 111 => 1
[[2,1],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 101111 => 1
[[2,1],[2],[2],[1],[1]] => [3,2,2,1,1] => 10011 => 1
[[2,1],[2],[2],[2]] => [3,2,2,2] => 1000 => 1
[[2,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 101111 => 1
[[2,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => 10011 => 1
[[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => 1000 => 1
[[2,1],[2,1],[1],[1],[1]] => [3,3,1,1,1] => 11111 => 1
[[2,1],[2,1],[2],[1]] => [3,3,2,1] => 1101 => 1
[[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => 1101 => 1
[[2,1],[2,1],[2,1]] => [3,3,3] => 111 => 1
[[1,1,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => 101111 => 1
[[1,1,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => 10011 => 1
[[1,1,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => 1000 => 1
[[1,1,1],[1,1,1],[1],[1],[1]] => [3,3,1,1,1] => 11111 => 1
[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => 1101 => 1
[[1,1,1],[1,1,1],[1,1,1]] => [3,3,3] => 111 => 1
[[4],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 011111 => 1
[[4],[2],[1],[1],[1]] => [4,2,1,1,1] => 00111 => 1
[[4],[2],[2],[1]] => [4,2,2,1] => 0001 => 1
[[4],[3],[1],[1]] => [4,3,1,1] => 0111 => 1
[[4],[3],[2]] => [4,3,2] => 010 => 1
[[4],[4],[1]] => [4,4,1] => 001 => 1
[[3,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 011111 => 1
[[3,1],[2],[1],[1],[1]] => [4,2,1,1,1] => 00111 => 1
[[3,1],[2],[2],[1]] => [4,2,2,1] => 0001 => 1
[[3,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 00111 => 1
[[3,1],[1,1],[1,1],[1]] => [4,2,2,1] => 0001 => 1
[[3,1],[3],[1],[1]] => [4,3,1,1] => 0111 => 1
[[3,1],[3],[2]] => [4,3,2] => 010 => 1
[[3,1],[2,1],[1],[1]] => [4,3,1,1] => 0111 => 1
[[3,1],[2,1],[2]] => [4,3,2] => 010 => 1
[[3,1],[2,1],[1,1]] => [4,3,2] => 010 => 1
[[3,1],[3,1],[1]] => [4,4,1] => 001 => 1
[[2,2],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 011111 => 1
[[2,2],[2],[1],[1],[1]] => [4,2,1,1,1] => 00111 => 1
[[2,2],[2],[2],[1]] => [4,2,2,1] => 0001 => 1
[[2,2],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 00111 => 1
[[2,2],[1,1],[1,1],[1]] => [4,2,2,1] => 0001 => 1
[[2,2],[2,1],[1],[1]] => [4,3,1,1] => 0111 => 1
[[2,2],[2,1],[2]] => [4,3,2] => 010 => 1
[[2,2],[2,1],[1,1]] => [4,3,2] => 010 => 1
[[2,2],[2,2],[1]] => [4,4,1] => 001 => 1
[[2,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 011111 => 1
[[2,1,1],[2],[1],[1],[1]] => [4,2,1,1,1] => 00111 => 1
[[2,1,1],[2],[2],[1]] => [4,2,2,1] => 0001 => 1
[[2,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 00111 => 1
[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => 0001 => 1
[[2,1,1],[2,1],[1],[1]] => [4,3,1,1] => 0111 => 1
[[2,1,1],[2,1],[2]] => [4,3,2] => 010 => 1
[[2,1,1],[2,1],[1,1]] => [4,3,2] => 010 => 1
[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => 0111 => 1
[[2,1,1],[1,1,1],[1,1]] => [4,3,2] => 010 => 1
[[2,1,1],[2,1,1],[1]] => [4,4,1] => 001 => 1
[[1,1,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => 011111 => 1
[[1,1,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => 00111 => 1
[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => 0001 => 1
[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => 0111 => 1
[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => 010 => 1
[[1,1,1,1],[1,1,1,1],[1]] => [4,4,1] => 001 => 1
[[5],[1],[1],[1],[1]] => [5,1,1,1,1] => 11111 => 1
[[5],[2],[1],[1]] => [5,2,1,1] => 1011 => 1
[[5],[2],[2]] => [5,2,2] => 100 => 1
[[5],[3],[1]] => [5,3,1] => 111 => 1
[[5],[4]] => [5,4] => 10 => 1
[[4,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 11111 => 1
[[4,1],[2],[1],[1]] => [5,2,1,1] => 1011 => 1
[[4,1],[2],[2]] => [5,2,2] => 100 => 1
[[4,1],[1,1],[1],[1]] => [5,2,1,1] => 1011 => 1
[[4,1],[1,1],[1,1]] => [5,2,2] => 100 => 1
[[4,1],[3],[1]] => [5,3,1] => 111 => 1
[[4,1],[2,1],[1]] => [5,3,1] => 111 => 1
[[4,1],[4]] => [5,4] => 10 => 1
[[4,1],[3,1]] => [5,4] => 10 => 1
[[3,2],[1],[1],[1],[1]] => [5,1,1,1,1] => 11111 => 1
[[3,2],[2],[1],[1]] => [5,2,1,1] => 1011 => 1
[[3,2],[2],[2]] => [5,2,2] => 100 => 1
[[3,2],[1,1],[1],[1]] => [5,2,1,1] => 1011 => 1
[[3,2],[1,1],[1,1]] => [5,2,2] => 100 => 1
[[3,2],[3],[1]] => [5,3,1] => 111 => 1
[[3,2],[2,1],[1]] => [5,3,1] => 111 => 1
[[3,2],[3,1]] => [5,4] => 10 => 1
[[3,2],[2,2]] => [5,4] => 10 => 1
[[3,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 11111 => 1
[[3,1,1],[2],[1],[1]] => [5,2,1,1] => 1011 => 1
[[3,1,1],[2],[2]] => [5,2,2] => 100 => 1
[[3,1,1],[1,1],[1],[1]] => [5,2,1,1] => 1011 => 1
[[3,1,1],[1,1],[1,1]] => [5,2,2] => 100 => 1
[[3,1,1],[3],[1]] => [5,3,1] => 111 => 1
[[3,1,1],[2,1],[1]] => [5,3,1] => 111 => 1
[[3,1,1],[1,1,1],[1]] => [5,3,1] => 111 => 1
[[3,1,1],[3,1]] => [5,4] => 10 => 1
[[3,1,1],[2,1,1]] => [5,4] => 10 => 1
[[2,2,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 11111 => 1
[[2,2,1],[2],[1],[1]] => [5,2,1,1] => 1011 => 1
[[2,2,1],[2],[2]] => [5,2,2] => 100 => 1
[[2,2,1],[1,1],[1],[1]] => [5,2,1,1] => 1011 => 1
[[2,2,1],[1,1],[1,1]] => [5,2,2] => 100 => 1
[[2,2,1],[2,1],[1]] => [5,3,1] => 111 => 1
[[2,2,1],[1,1,1],[1]] => [5,3,1] => 111 => 1
[[2,2,1],[2,2]] => [5,4] => 10 => 1
[[2,2,1],[2,1,1]] => [5,4] => 10 => 1
[[2,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 11111 => 1
[[2,1,1,1],[2],[1],[1]] => [5,2,1,1] => 1011 => 1
[[2,1,1,1],[2],[2]] => [5,2,2] => 100 => 1
[[2,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => 1011 => 1
[[2,1,1,1],[1,1],[1,1]] => [5,2,2] => 100 => 1
[[2,1,1,1],[2,1],[1]] => [5,3,1] => 111 => 1
[[2,1,1,1],[1,1,1],[1]] => [5,3,1] => 111 => 1
[[2,1,1,1],[2,1,1]] => [5,4] => 10 => 1
[[2,1,1,1],[1,1,1,1]] => [5,4] => 10 => 1
[[1,1,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => 11111 => 1
[[1,1,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => 1011 => 1
[[1,1,1,1,1],[1,1],[1,1]] => [5,2,2] => 100 => 1
[[1,1,1,1,1],[1,1,1],[1]] => [5,3,1] => 111 => 1
[[1,1,1,1,1],[1,1,1,1]] => [5,4] => 10 => 1
[[6],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[6],[2],[1]] => [6,2,1] => 001 => 1
[[6],[3]] => [6,3] => 01 => 1
[[5,1],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[5,1],[2],[1]] => [6,2,1] => 001 => 1
[[5,1],[1,1],[1]] => [6,2,1] => 001 => 1
[[5,1],[3]] => [6,3] => 01 => 1
[[5,1],[2,1]] => [6,3] => 01 => 1
[[4,2],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[4,2],[2],[1]] => [6,2,1] => 001 => 1
[[4,2],[1,1],[1]] => [6,2,1] => 001 => 1
[[4,2],[3]] => [6,3] => 01 => 1
[[4,2],[2,1]] => [6,3] => 01 => 1
[[4,1,1],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[4,1,1],[2],[1]] => [6,2,1] => 001 => 1
[[4,1,1],[1,1],[1]] => [6,2,1] => 001 => 1
[[4,1,1],[3]] => [6,3] => 01 => 1
[[4,1,1],[2,1]] => [6,3] => 01 => 1
[[4,1,1],[1,1,1]] => [6,3] => 01 => 1
[[3,3],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[3,3],[2],[1]] => [6,2,1] => 001 => 1
[[3,3],[1,1],[1]] => [6,2,1] => 001 => 1
[[3,3],[3]] => [6,3] => 01 => 1
[[3,3],[2,1]] => [6,3] => 01 => 1
[[3,2,1],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[3,2,1],[2],[1]] => [6,2,1] => 001 => 1
[[3,2,1],[1,1],[1]] => [6,2,1] => 001 => 1
[[3,2,1],[3]] => [6,3] => 01 => 1
[[3,2,1],[2,1]] => [6,3] => 01 => 1
[[3,2,1],[1,1,1]] => [6,3] => 01 => 1
[[3,1,1,1],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[3,1,1,1],[2],[1]] => [6,2,1] => 001 => 1
[[3,1,1,1],[1,1],[1]] => [6,2,1] => 001 => 1
[[3,1,1,1],[3]] => [6,3] => 01 => 1
[[3,1,1,1],[2,1]] => [6,3] => 01 => 1
[[3,1,1,1],[1,1,1]] => [6,3] => 01 => 1
[[2,2,2],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[2,2,2],[2],[1]] => [6,2,1] => 001 => 1
[[2,2,2],[1,1],[1]] => [6,2,1] => 001 => 1
[[2,2,2],[2,1]] => [6,3] => 01 => 1
[[2,2,2],[1,1,1]] => [6,3] => 01 => 1
[[2,2,1,1],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[2,2,1,1],[2],[1]] => [6,2,1] => 001 => 1
[[2,2,1,1],[1,1],[1]] => [6,2,1] => 001 => 1
[[2,2,1,1],[2,1]] => [6,3] => 01 => 1
[[2,2,1,1],[1,1,1]] => [6,3] => 01 => 1
[[2,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[2,1,1,1,1],[2],[1]] => [6,2,1] => 001 => 1
[[2,1,1,1,1],[1,1],[1]] => [6,2,1] => 001 => 1
[[2,1,1,1,1],[2,1]] => [6,3] => 01 => 1
[[2,1,1,1,1],[1,1,1]] => [6,3] => 01 => 1
[[1,1,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => 0111 => 1
[[1,1,1,1,1,1],[1,1],[1]] => [6,2,1] => 001 => 1
[[1,1,1,1,1,1],[1,1,1]] => [6,3] => 01 => 1
[[7],[1],[1]] => [7,1,1] => 111 => 1
[[7],[2]] => [7,2] => 10 => 1
[[6,1],[1],[1]] => [7,1,1] => 111 => 1
[[6,1],[2]] => [7,2] => 10 => 1
[[6,1],[1,1]] => [7,2] => 10 => 1
[[5,2],[1],[1]] => [7,1,1] => 111 => 1
[[5,2],[2]] => [7,2] => 10 => 1
[[5,2],[1,1]] => [7,2] => 10 => 1
[[5,1,1],[1],[1]] => [7,1,1] => 111 => 1
[[5,1,1],[2]] => [7,2] => 10 => 1
[[5,1,1],[1,1]] => [7,2] => 10 => 1
[[4,3],[1],[1]] => [7,1,1] => 111 => 1
[[4,3],[2]] => [7,2] => 10 => 1
[[4,3],[1,1]] => [7,2] => 10 => 1
[[4,2,1],[1],[1]] => [7,1,1] => 111 => 1
[[4,2,1],[2]] => [7,2] => 10 => 1
[[4,2,1],[1,1]] => [7,2] => 10 => 1
[[4,1,1,1],[1],[1]] => [7,1,1] => 111 => 1
[[4,1,1,1],[2]] => [7,2] => 10 => 1
[[4,1,1,1],[1,1]] => [7,2] => 10 => 1
[[3,3,1],[1],[1]] => [7,1,1] => 111 => 1
[[3,3,1],[2]] => [7,2] => 10 => 1
[[3,3,1],[1,1]] => [7,2] => 10 => 1
[[3,2,2],[1],[1]] => [7,1,1] => 111 => 1
[[3,2,2],[2]] => [7,2] => 10 => 1
[[3,2,2],[1,1]] => [7,2] => 10 => 1
[[3,2,1,1],[1],[1]] => [7,1,1] => 111 => 1
[[3,2,1,1],[2]] => [7,2] => 10 => 1
[[3,2,1,1],[1,1]] => [7,2] => 10 => 1
[[3,1,1,1,1],[1],[1]] => [7,1,1] => 111 => 1
[[3,1,1,1,1],[2]] => [7,2] => 10 => 1
[[3,1,1,1,1],[1,1]] => [7,2] => 10 => 1
[[2,2,2,1],[1],[1]] => [7,1,1] => 111 => 1
[[2,2,2,1],[2]] => [7,2] => 10 => 1
[[2,2,2,1],[1,1]] => [7,2] => 10 => 1
[[2,2,1,1,1],[1],[1]] => [7,1,1] => 111 => 1
[[2,2,1,1,1],[2]] => [7,2] => 10 => 1
[[2,2,1,1,1],[1,1]] => [7,2] => 10 => 1
[[2,1,1,1,1,1],[1],[1]] => [7,1,1] => 111 => 1
[[2,1,1,1,1,1],[2]] => [7,2] => 10 => 1
[[2,1,1,1,1,1],[1,1]] => [7,2] => 10 => 1
[[1,1,1,1,1,1,1],[1],[1]] => [7,1,1] => 111 => 1
[[1,1,1,1,1,1,1],[1,1]] => [7,2] => 10 => 1
[[8],[1]] => [8,1] => 01 => 1
[[7,1],[1]] => [8,1] => 01 => 1
[[6,2],[1]] => [8,1] => 01 => 1
[[6,1,1],[1]] => [8,1] => 01 => 1
[[5,3],[1]] => [8,1] => 01 => 1
[[5,2,1],[1]] => [8,1] => 01 => 1
[[5,1,1,1],[1]] => [8,1] => 01 => 1
[[4,4],[1]] => [8,1] => 01 => 1
[[4,3,1],[1]] => [8,1] => 01 => 1
[[4,2,2],[1]] => [8,1] => 01 => 1
[[4,2,1,1],[1]] => [8,1] => 01 => 1
[[4,1,1,1,1],[1]] => [8,1] => 01 => 1
[[3,3,2],[1]] => [8,1] => 01 => 1
[[3,3,1,1],[1]] => [8,1] => 01 => 1
[[3,2,2,1],[1]] => [8,1] => 01 => 1
[[3,2,1,1,1],[1]] => [8,1] => 01 => 1
[[3,1,1,1,1,1],[1]] => [8,1] => 01 => 1
[[2,2,2,2],[1]] => [8,1] => 01 => 1
[[2,2,2,1,1],[1]] => [8,1] => 01 => 1
[[2,2,1,1,1,1],[1]] => [8,1] => 01 => 1
[[2,1,1,1,1,1,1],[1]] => [8,1] => 01 => 1
[[1,1,1,1,1,1,1,1],[1]] => [8,1] => 01 => 1
[[9]] => [9] => 1 => 1
[[8,1]] => [9] => 1 => 1
[[7,2]] => [9] => 1 => 1
[[7,1,1]] => [9] => 1 => 1
[[6,3]] => [9] => 1 => 1
[[6,2,1]] => [9] => 1 => 1
[[6,1,1,1]] => [9] => 1 => 1
[[5,4]] => [9] => 1 => 1
[[5,3,1]] => [9] => 1 => 1
[[5,2,2]] => [9] => 1 => 1
[[5,2,1,1]] => [9] => 1 => 1
[[5,1,1,1,1]] => [9] => 1 => 1
[[4,4,1]] => [9] => 1 => 1
[[4,3,2]] => [9] => 1 => 1
[[4,3,1,1]] => [9] => 1 => 1
[[4,2,2,1]] => [9] => 1 => 1
[[4,2,1,1,1]] => [9] => 1 => 1
[[4,1,1,1,1,1]] => [9] => 1 => 1
[[3,3,3]] => [9] => 1 => 1
[[3,3,2,1]] => [9] => 1 => 1
[[3,3,1,1,1]] => [9] => 1 => 1
[[3,2,2,2]] => [9] => 1 => 1
[[3,2,2,1,1]] => [9] => 1 => 1
[[3,2,1,1,1,1]] => [9] => 1 => 1
[[3,1,1,1,1,1,1]] => [9] => 1 => 1
[[2,2,2,2,1]] => [9] => 1 => 1
[[2,2,2,1,1,1]] => [9] => 1 => 1
[[2,2,1,1,1,1,1]] => [9] => 1 => 1
[[2,1,1,1,1,1,1,1]] => [9] => 1 => 1
[[1,1,1,1,1,1,1,1,1]] => [9] => 1 => 1
[[2],[2],[2],[2],[1],[1]] => [2,2,2,2,1,1] => 000011 => 1
[[2],[2],[2],[2],[2]] => [2,2,2,2,2] => 00000 => 1
[[1,1],[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,2,1,1] => 000011 => 1
[[1,1],[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2,2] => 00000 => 1
[[3],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => 100111 => 1
[[3],[2],[2],[2],[1]] => [3,2,2,2,1] => 10001 => 1
[[3],[3],[1],[1],[1],[1]] => [3,3,1,1,1,1] => 111111 => 1
[[3],[3],[2],[1],[1]] => [3,3,2,1,1] => 11011 => 1
[[3],[3],[2],[2]] => [3,3,2,2] => 1100 => 1
[[3],[3],[3],[1]] => [3,3,3,1] => 1111 => 1
[[2,1],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => 100111 => 1
[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1] => 10001 => 1
[[2,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => 100111 => 1
[[2,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => 10001 => 1
[[2,1],[2,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => 111111 => 1
[[2,1],[2,1],[2],[1],[1]] => [3,3,2,1,1] => 11011 => 1
[[2,1],[2,1],[2],[2]] => [3,3,2,2] => 1100 => 1
[[2,1],[2,1],[1,1],[1],[1]] => [3,3,2,1,1] => 11011 => 1
[[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2] => 1100 => 1
[[2,1],[2,1],[2,1],[1]] => [3,3,3,1] => 1111 => 1
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => 100111 => 1
[[1,1,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => 10001 => 1
[[1,1,1],[1,1,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => 111111 => 1
[[1,1,1],[1,1,1],[1,1],[1],[1]] => [3,3,2,1,1] => 11011 => 1
[[1,1,1],[1,1,1],[1,1],[1,1]] => [3,3,2,2] => 1100 => 1
[[1,1,1],[1,1,1],[1,1,1],[1]] => [3,3,3,1] => 1111 => 1
[[4],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 001111 => 1
[[4],[2],[2],[1],[1]] => [4,2,2,1,1] => 00011 => 1
[[4],[2],[2],[2]] => [4,2,2,2] => 0000 => 1
[[4],[3],[1],[1],[1]] => [4,3,1,1,1] => 01111 => 1
[[4],[3],[2],[1]] => [4,3,2,1] => 0101 => 1
[[4],[3],[3]] => [4,3,3] => 011 => 1
[[4],[4],[1],[1]] => [4,4,1,1] => 0011 => 1
[[4],[4],[2]] => [4,4,2] => 000 => 1
[[3,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 001111 => 1
[[3,1],[2],[2],[1],[1]] => [4,2,2,1,1] => 00011 => 1
[[3,1],[2],[2],[2]] => [4,2,2,2] => 0000 => 1
[[3,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 001111 => 1
[[3,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 00011 => 1
[[3,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => 0000 => 1
[[3,1],[3],[1],[1],[1]] => [4,3,1,1,1] => 01111 => 1
[[3,1],[3],[2],[1]] => [4,3,2,1] => 0101 => 1
[[3,1],[3],[3]] => [4,3,3] => 011 => 1
[[3,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => 01111 => 1
[[3,1],[2,1],[2],[1]] => [4,3,2,1] => 0101 => 1
[[3,1],[2,1],[1,1],[1]] => [4,3,2,1] => 0101 => 1
[[3,1],[2,1],[2,1]] => [4,3,3] => 011 => 1
[[3,1],[3,1],[1],[1]] => [4,4,1,1] => 0011 => 1
[[3,1],[3,1],[2]] => [4,4,2] => 000 => 1
[[3,1],[3,1],[1,1]] => [4,4,2] => 000 => 1
[[2,2],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 001111 => 1
[[2,2],[2],[2],[1],[1]] => [4,2,2,1,1] => 00011 => 1
[[2,2],[2],[2],[2]] => [4,2,2,2] => 0000 => 1
[[2,2],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 001111 => 1
[[2,2],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 00011 => 1
[[2,2],[1,1],[1,1],[1,1]] => [4,2,2,2] => 0000 => 1
[[2,2],[2,1],[1],[1],[1]] => [4,3,1,1,1] => 01111 => 1
[[2,2],[2,1],[2],[1]] => [4,3,2,1] => 0101 => 1
[[2,2],[2,1],[1,1],[1]] => [4,3,2,1] => 0101 => 1
[[2,2],[2,1],[2,1]] => [4,3,3] => 011 => 1
[[2,2],[2,2],[1],[1]] => [4,4,1,1] => 0011 => 1
[[2,2],[2,2],[2]] => [4,4,2] => 000 => 1
[[2,2],[2,2],[1,1]] => [4,4,2] => 000 => 1
[[2,1,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 001111 => 1
[[2,1,1],[2],[2],[1],[1]] => [4,2,2,1,1] => 00011 => 1
[[2,1,1],[2],[2],[2]] => [4,2,2,2] => 0000 => 1
[[2,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 001111 => 1
[[2,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 00011 => 1
[[2,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => 0000 => 1
[[2,1,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => 01111 => 1
[[2,1,1],[2,1],[2],[1]] => [4,3,2,1] => 0101 => 1
[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1] => 0101 => 1
[[2,1,1],[2,1],[2,1]] => [4,3,3] => 011 => 1
[[2,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => 01111 => 1
[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => 0101 => 1
[[2,1,1],[1,1,1],[1,1,1]] => [4,3,3] => 011 => 1
[[2,1,1],[2,1,1],[1],[1]] => [4,4,1,1] => 0011 => 1
[[2,1,1],[2,1,1],[2]] => [4,4,2] => 000 => 1
[[2,1,1],[2,1,1],[1,1]] => [4,4,2] => 000 => 1
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => 001111 => 1
[[1,1,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => 00011 => 1
[[1,1,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => 0000 => 1
[[1,1,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => 01111 => 1
[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => 0101 => 1
[[1,1,1,1],[1,1,1],[1,1,1]] => [4,3,3] => 011 => 1
[[1,1,1,1],[1,1,1,1],[1],[1]] => [4,4,1,1] => 0011 => 1
[[1,1,1,1],[1,1,1,1],[1,1]] => [4,4,2] => 000 => 1
[[5],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 111111 => 1
[[5],[2],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[5],[2],[2],[1]] => [5,2,2,1] => 1001 => 1
[[5],[3],[1],[1]] => [5,3,1,1] => 1111 => 1
[[5],[3],[2]] => [5,3,2] => 110 => 1
[[5],[4],[1]] => [5,4,1] => 101 => 1
[[5],[5]] => [5,5] => 11 => 1
[[4,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 111111 => 1
[[4,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[4,1],[2],[2],[1]] => [5,2,2,1] => 1001 => 1
[[4,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[4,1],[1,1],[1,1],[1]] => [5,2,2,1] => 1001 => 1
[[4,1],[3],[1],[1]] => [5,3,1,1] => 1111 => 1
[[4,1],[3],[2]] => [5,3,2] => 110 => 1
[[4,1],[2,1],[1],[1]] => [5,3,1,1] => 1111 => 1
[[4,1],[2,1],[2]] => [5,3,2] => 110 => 1
[[4,1],[2,1],[1,1]] => [5,3,2] => 110 => 1
[[4,1],[4],[1]] => [5,4,1] => 101 => 1
[[4,1],[3,1],[1]] => [5,4,1] => 101 => 1
[[4,1],[4,1]] => [5,5] => 11 => 1
[[3,2],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 111111 => 1
[[3,2],[2],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[3,2],[2],[2],[1]] => [5,2,2,1] => 1001 => 1
[[3,2],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[3,2],[1,1],[1,1],[1]] => [5,2,2,1] => 1001 => 1
[[3,2],[3],[1],[1]] => [5,3,1,1] => 1111 => 1
[[3,2],[3],[2]] => [5,3,2] => 110 => 1
[[3,2],[2,1],[1],[1]] => [5,3,1,1] => 1111 => 1
[[3,2],[2,1],[2]] => [5,3,2] => 110 => 1
[[3,2],[2,1],[1,1]] => [5,3,2] => 110 => 1
[[3,2],[3,1],[1]] => [5,4,1] => 101 => 1
[[3,2],[2,2],[1]] => [5,4,1] => 101 => 1
[[3,2],[3,2]] => [5,5] => 11 => 1
[[3,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 111111 => 1
[[3,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[3,1,1],[2],[2],[1]] => [5,2,2,1] => 1001 => 1
[[3,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[3,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => 1001 => 1
[[3,1,1],[3],[1],[1]] => [5,3,1,1] => 1111 => 1
[[3,1,1],[3],[2]] => [5,3,2] => 110 => 1
[[3,1,1],[2,1],[1],[1]] => [5,3,1,1] => 1111 => 1
[[3,1,1],[2,1],[2]] => [5,3,2] => 110 => 1
[[3,1,1],[2,1],[1,1]] => [5,3,2] => 110 => 1
[[3,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => 1111 => 1
[[3,1,1],[1,1,1],[1,1]] => [5,3,2] => 110 => 1
[[3,1,1],[3,1],[1]] => [5,4,1] => 101 => 1
[[3,1,1],[2,1,1],[1]] => [5,4,1] => 101 => 1
[[3,1,1],[3,1,1]] => [5,5] => 11 => 1
[[2,2,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 111111 => 1
[[2,2,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[2,2,1],[2],[2],[1]] => [5,2,2,1] => 1001 => 1
[[2,2,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[2,2,1],[1,1],[1,1],[1]] => [5,2,2,1] => 1001 => 1
[[2,2,1],[2,1],[1],[1]] => [5,3,1,1] => 1111 => 1
[[2,2,1],[2,1],[2]] => [5,3,2] => 110 => 1
[[2,2,1],[2,1],[1,1]] => [5,3,2] => 110 => 1
[[2,2,1],[1,1,1],[1],[1]] => [5,3,1,1] => 1111 => 1
[[2,2,1],[1,1,1],[1,1]] => [5,3,2] => 110 => 1
[[2,2,1],[2,2],[1]] => [5,4,1] => 101 => 1
[[2,2,1],[2,1,1],[1]] => [5,4,1] => 101 => 1
[[2,2,1],[2,2,1]] => [5,5] => 11 => 1
[[2,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 111111 => 1
[[2,1,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[2,1,1,1],[2],[2],[1]] => [5,2,2,1] => 1001 => 1
[[2,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[2,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => 1001 => 1
[[2,1,1,1],[2,1],[1],[1]] => [5,3,1,1] => 1111 => 1
[[2,1,1,1],[2,1],[2]] => [5,3,2] => 110 => 1
[[2,1,1,1],[2,1],[1,1]] => [5,3,2] => 110 => 1
[[2,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => 1111 => 1
[[2,1,1,1],[1,1,1],[1,1]] => [5,3,2] => 110 => 1
[[2,1,1,1],[2,1,1],[1]] => [5,4,1] => 101 => 1
[[2,1,1,1],[1,1,1,1],[1]] => [5,4,1] => 101 => 1
[[2,1,1,1],[2,1,1,1]] => [5,5] => 11 => 1
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => 111111 => 1
[[1,1,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => 10111 => 1
[[1,1,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => 1001 => 1
[[1,1,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => 1111 => 1
[[1,1,1,1,1],[1,1,1],[1,1]] => [5,3,2] => 110 => 1
[[1,1,1,1,1],[1,1,1,1],[1]] => [5,4,1] => 101 => 1
[[1,1,1,1,1],[1,1,1,1,1]] => [5,5] => 11 => 1
[[6],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[6],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[6],[2],[2]] => [6,2,2] => 000 => 1
[[6],[3],[1]] => [6,3,1] => 011 => 1
[[6],[4]] => [6,4] => 00 => 1
[[5,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[5,1],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[5,1],[2],[2]] => [6,2,2] => 000 => 1
[[5,1],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[5,1],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[5,1],[3],[1]] => [6,3,1] => 011 => 1
[[5,1],[2,1],[1]] => [6,3,1] => 011 => 1
[[5,1],[4]] => [6,4] => 00 => 1
[[5,1],[3,1]] => [6,4] => 00 => 1
[[4,2],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[4,2],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[4,2],[2],[2]] => [6,2,2] => 000 => 1
[[4,2],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[4,2],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[4,2],[3],[1]] => [6,3,1] => 011 => 1
[[4,2],[2,1],[1]] => [6,3,1] => 011 => 1
[[4,2],[4]] => [6,4] => 00 => 1
[[4,2],[3,1]] => [6,4] => 00 => 1
[[4,2],[2,2]] => [6,4] => 00 => 1
[[4,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[4,1,1],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[4,1,1],[2],[2]] => [6,2,2] => 000 => 1
[[4,1,1],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[4,1,1],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[4,1,1],[3],[1]] => [6,3,1] => 011 => 1
[[4,1,1],[2,1],[1]] => [6,3,1] => 011 => 1
[[4,1,1],[1,1,1],[1]] => [6,3,1] => 011 => 1
[[4,1,1],[4]] => [6,4] => 00 => 1
[[4,1,1],[3,1]] => [6,4] => 00 => 1
[[4,1,1],[2,1,1]] => [6,4] => 00 => 1
[[3,3],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[3,3],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[3,3],[2],[2]] => [6,2,2] => 000 => 1
[[3,3],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[3,3],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[3,3],[3],[1]] => [6,3,1] => 011 => 1
[[3,3],[2,1],[1]] => [6,3,1] => 011 => 1
[[3,3],[3,1]] => [6,4] => 00 => 1
[[3,3],[2,2]] => [6,4] => 00 => 1
[[3,2,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[3,2,1],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[3,2,1],[2],[2]] => [6,2,2] => 000 => 1
[[3,2,1],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[3,2,1],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[3,2,1],[3],[1]] => [6,3,1] => 011 => 1
[[3,2,1],[2,1],[1]] => [6,3,1] => 011 => 1
[[3,2,1],[1,1,1],[1]] => [6,3,1] => 011 => 1
[[3,2,1],[3,1]] => [6,4] => 00 => 1
[[3,2,1],[2,2]] => [6,4] => 00 => 1
[[3,2,1],[2,1,1]] => [6,4] => 00 => 1
[[3,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[3,1,1,1],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[3,1,1,1],[2],[2]] => [6,2,2] => 000 => 1
[[3,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[3,1,1,1],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[3,1,1,1],[3],[1]] => [6,3,1] => 011 => 1
[[3,1,1,1],[2,1],[1]] => [6,3,1] => 011 => 1
[[3,1,1,1],[1,1,1],[1]] => [6,3,1] => 011 => 1
[[3,1,1,1],[3,1]] => [6,4] => 00 => 1
[[3,1,1,1],[2,1,1]] => [6,4] => 00 => 1
[[3,1,1,1],[1,1,1,1]] => [6,4] => 00 => 1
[[2,2,2],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[2,2,2],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[2,2,2],[2],[2]] => [6,2,2] => 000 => 1
[[2,2,2],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[2,2,2],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[2,2,2],[2,1],[1]] => [6,3,1] => 011 => 1
[[2,2,2],[1,1,1],[1]] => [6,3,1] => 011 => 1
[[2,2,2],[2,2]] => [6,4] => 00 => 1
[[2,2,2],[2,1,1]] => [6,4] => 00 => 1
[[2,2,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[2,2,1,1],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[2,2,1,1],[2],[2]] => [6,2,2] => 000 => 1
[[2,2,1,1],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[2,2,1,1],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[2,2,1,1],[2,1],[1]] => [6,3,1] => 011 => 1
[[2,2,1,1],[1,1,1],[1]] => [6,3,1] => 011 => 1
[[2,2,1,1],[2,2]] => [6,4] => 00 => 1
[[2,2,1,1],[2,1,1]] => [6,4] => 00 => 1
[[2,2,1,1],[1,1,1,1]] => [6,4] => 00 => 1
[[2,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[2,1,1,1,1],[2],[1],[1]] => [6,2,1,1] => 0011 => 1
[[2,1,1,1,1],[2],[2]] => [6,2,2] => 000 => 1
[[2,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[2,1,1,1,1],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[2,1,1,1,1],[2,1],[1]] => [6,3,1] => 011 => 1
[[2,1,1,1,1],[1,1,1],[1]] => [6,3,1] => 011 => 1
[[2,1,1,1,1],[2,1,1]] => [6,4] => 00 => 1
[[2,1,1,1,1],[1,1,1,1]] => [6,4] => 00 => 1
[[1,1,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => 01111 => 1
[[1,1,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => 0011 => 1
[[1,1,1,1,1,1],[1,1],[1,1]] => [6,2,2] => 000 => 1
[[1,1,1,1,1,1],[1,1,1],[1]] => [6,3,1] => 011 => 1
[[1,1,1,1,1,1],[1,1,1,1]] => [6,4] => 00 => 1
[[7],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[7],[2],[1]] => [7,2,1] => 101 => 1
[[7],[3]] => [7,3] => 11 => 1
[[6,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[6,1],[2],[1]] => [7,2,1] => 101 => 1
[[6,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[6,1],[3]] => [7,3] => 11 => 1
[[6,1],[2,1]] => [7,3] => 11 => 1
[[5,2],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[5,2],[2],[1]] => [7,2,1] => 101 => 1
[[5,2],[1,1],[1]] => [7,2,1] => 101 => 1
[[5,2],[3]] => [7,3] => 11 => 1
[[5,2],[2,1]] => [7,3] => 11 => 1
[[5,1,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[5,1,1],[2],[1]] => [7,2,1] => 101 => 1
[[5,1,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[5,1,1],[3]] => [7,3] => 11 => 1
[[5,1,1],[2,1]] => [7,3] => 11 => 1
[[5,1,1],[1,1,1]] => [7,3] => 11 => 1
[[4,3],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[4,3],[2],[1]] => [7,2,1] => 101 => 1
[[4,3],[1,1],[1]] => [7,2,1] => 101 => 1
[[4,3],[3]] => [7,3] => 11 => 1
[[4,3],[2,1]] => [7,3] => 11 => 1
[[4,2,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[4,2,1],[2],[1]] => [7,2,1] => 101 => 1
[[4,2,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[4,2,1],[3]] => [7,3] => 11 => 1
[[4,2,1],[2,1]] => [7,3] => 11 => 1
[[4,2,1],[1,1,1]] => [7,3] => 11 => 1
[[4,1,1,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[4,1,1,1],[2],[1]] => [7,2,1] => 101 => 1
[[4,1,1,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[4,1,1,1],[3]] => [7,3] => 11 => 1
[[4,1,1,1],[2,1]] => [7,3] => 11 => 1
[[4,1,1,1],[1,1,1]] => [7,3] => 11 => 1
[[3,3,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[3,3,1],[2],[1]] => [7,2,1] => 101 => 1
[[3,3,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[3,3,1],[3]] => [7,3] => 11 => 1
[[3,3,1],[2,1]] => [7,3] => 11 => 1
[[3,3,1],[1,1,1]] => [7,3] => 11 => 1
[[3,2,2],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[3,2,2],[2],[1]] => [7,2,1] => 101 => 1
[[3,2,2],[1,1],[1]] => [7,2,1] => 101 => 1
[[3,2,2],[3]] => [7,3] => 11 => 1
[[3,2,2],[2,1]] => [7,3] => 11 => 1
[[3,2,2],[1,1,1]] => [7,3] => 11 => 1
[[3,2,1,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[3,2,1,1],[2],[1]] => [7,2,1] => 101 => 1
[[3,2,1,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[3,2,1,1],[3]] => [7,3] => 11 => 1
[[3,2,1,1],[2,1]] => [7,3] => 11 => 1
[[3,2,1,1],[1,1,1]] => [7,3] => 11 => 1
[[3,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[3,1,1,1,1],[2],[1]] => [7,2,1] => 101 => 1
[[3,1,1,1,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[3,1,1,1,1],[3]] => [7,3] => 11 => 1
[[3,1,1,1,1],[2,1]] => [7,3] => 11 => 1
[[3,1,1,1,1],[1,1,1]] => [7,3] => 11 => 1
[[2,2,2,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[2,2,2,1],[2],[1]] => [7,2,1] => 101 => 1
[[2,2,2,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[2,2,2,1],[2,1]] => [7,3] => 11 => 1
[[2,2,2,1],[1,1,1]] => [7,3] => 11 => 1
[[2,2,1,1,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[2,2,1,1,1],[2],[1]] => [7,2,1] => 101 => 1
[[2,2,1,1,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[2,2,1,1,1],[2,1]] => [7,3] => 11 => 1
[[2,2,1,1,1],[1,1,1]] => [7,3] => 11 => 1
[[2,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[2,1,1,1,1,1],[2],[1]] => [7,2,1] => 101 => 1
[[2,1,1,1,1,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[2,1,1,1,1,1],[2,1]] => [7,3] => 11 => 1
[[2,1,1,1,1,1],[1,1,1]] => [7,3] => 11 => 1
[[1,1,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => 1111 => 1
[[1,1,1,1,1,1,1],[1,1],[1]] => [7,2,1] => 101 => 1
[[1,1,1,1,1,1,1],[1,1,1]] => [7,3] => 11 => 1
[[8],[1],[1]] => [8,1,1] => 011 => 1
[[8],[2]] => [8,2] => 00 => 1
[[7,1],[1],[1]] => [8,1,1] => 011 => 1
[[7,1],[2]] => [8,2] => 00 => 1
[[7,1],[1,1]] => [8,2] => 00 => 1
[[6,2],[1],[1]] => [8,1,1] => 011 => 1
[[6,2],[2]] => [8,2] => 00 => 1
[[6,2],[1,1]] => [8,2] => 00 => 1
[[6,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[6,1,1],[2]] => [8,2] => 00 => 1
[[6,1,1],[1,1]] => [8,2] => 00 => 1
[[5,3],[1],[1]] => [8,1,1] => 011 => 1
[[5,3],[2]] => [8,2] => 00 => 1
[[5,3],[1,1]] => [8,2] => 00 => 1
[[5,2,1],[1],[1]] => [8,1,1] => 011 => 1
[[5,2,1],[2]] => [8,2] => 00 => 1
[[5,2,1],[1,1]] => [8,2] => 00 => 1
[[5,1,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[5,1,1,1],[2]] => [8,2] => 00 => 1
[[5,1,1,1],[1,1]] => [8,2] => 00 => 1
[[4,4],[1],[1]] => [8,1,1] => 011 => 1
[[4,4],[2]] => [8,2] => 00 => 1
[[4,4],[1,1]] => [8,2] => 00 => 1
[[4,3,1],[1],[1]] => [8,1,1] => 011 => 1
[[4,3,1],[2]] => [8,2] => 00 => 1
[[4,3,1],[1,1]] => [8,2] => 00 => 1
[[4,2,2],[1],[1]] => [8,1,1] => 011 => 1
[[4,2,2],[2]] => [8,2] => 00 => 1
[[4,2,2],[1,1]] => [8,2] => 00 => 1
[[4,2,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[4,2,1,1],[2]] => [8,2] => 00 => 1
[[4,2,1,1],[1,1]] => [8,2] => 00 => 1
[[4,1,1,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[4,1,1,1,1],[2]] => [8,2] => 00 => 1
[[4,1,1,1,1],[1,1]] => [8,2] => 00 => 1
[[3,3,2],[1],[1]] => [8,1,1] => 011 => 1
[[3,3,2],[2]] => [8,2] => 00 => 1
[[3,3,2],[1,1]] => [8,2] => 00 => 1
[[3,3,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[3,3,1,1],[2]] => [8,2] => 00 => 1
[[3,3,1,1],[1,1]] => [8,2] => 00 => 1
[[3,2,2,1],[1],[1]] => [8,1,1] => 011 => 1
[[3,2,2,1],[2]] => [8,2] => 00 => 1
[[3,2,2,1],[1,1]] => [8,2] => 00 => 1
[[3,2,1,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[3,2,1,1,1],[2]] => [8,2] => 00 => 1
[[3,2,1,1,1],[1,1]] => [8,2] => 00 => 1
[[3,1,1,1,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[3,1,1,1,1,1],[2]] => [8,2] => 00 => 1
[[3,1,1,1,1,1],[1,1]] => [8,2] => 00 => 1
[[2,2,2,2],[1],[1]] => [8,1,1] => 011 => 1
[[2,2,2,2],[2]] => [8,2] => 00 => 1
[[2,2,2,2],[1,1]] => [8,2] => 00 => 1
[[2,2,2,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[2,2,2,1,1],[2]] => [8,2] => 00 => 1
[[2,2,2,1,1],[1,1]] => [8,2] => 00 => 1
[[2,2,1,1,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[2,2,1,1,1,1],[2]] => [8,2] => 00 => 1
[[2,2,1,1,1,1],[1,1]] => [8,2] => 00 => 1
[[2,1,1,1,1,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[2,1,1,1,1,1,1],[2]] => [8,2] => 00 => 1
[[2,1,1,1,1,1,1],[1,1]] => [8,2] => 00 => 1
[[1,1,1,1,1,1,1,1],[1],[1]] => [8,1,1] => 011 => 1
[[1,1,1,1,1,1,1,1],[1,1]] => [8,2] => 00 => 1
[[9],[1]] => [9,1] => 11 => 1
[[8,1],[1]] => [9,1] => 11 => 1
[[7,2],[1]] => [9,1] => 11 => 1
[[7,1,1],[1]] => [9,1] => 11 => 1
[[6,3],[1]] => [9,1] => 11 => 1
[[6,2,1],[1]] => [9,1] => 11 => 1
[[6,1,1,1],[1]] => [9,1] => 11 => 1
[[5,4],[1]] => [9,1] => 11 => 1
[[5,3,1],[1]] => [9,1] => 11 => 1
[[5,2,2],[1]] => [9,1] => 11 => 1
[[5,2,1,1],[1]] => [9,1] => 11 => 1
[[5,1,1,1,1],[1]] => [9,1] => 11 => 1
[[4,4,1],[1]] => [9,1] => 11 => 1
[[4,3,2],[1]] => [9,1] => 11 => 1
[[4,3,1,1],[1]] => [9,1] => 11 => 1
[[4,2,2,1],[1]] => [9,1] => 11 => 1
[[4,2,1,1,1],[1]] => [9,1] => 11 => 1
[[4,1,1,1,1,1],[1]] => [9,1] => 11 => 1
[[3,3,3],[1]] => [9,1] => 11 => 1
[[3,3,2,1],[1]] => [9,1] => 11 => 1
[[3,3,1,1,1],[1]] => [9,1] => 11 => 1
[[3,2,2,2],[1]] => [9,1] => 11 => 1
[[3,2,2,1,1],[1]] => [9,1] => 11 => 1
[[3,2,1,1,1,1],[1]] => [9,1] => 11 => 1
[[3,1,1,1,1,1,1],[1]] => [9,1] => 11 => 1
[[2,2,2,2,1],[1]] => [9,1] => 11 => 1
[[2,2,2,1,1,1],[1]] => [9,1] => 11 => 1
[[2,2,1,1,1,1,1],[1]] => [9,1] => 11 => 1
[[2,1,1,1,1,1,1,1],[1]] => [9,1] => 11 => 1
[[1,1,1,1,1,1,1,1,1],[1]] => [9,1] => 11 => 1
[[10]] => [10] => 0 => 1
[[9,1]] => [10] => 0 => 1
[[8,2]] => [10] => 0 => 1
[[8,1,1]] => [10] => 0 => 1
[[7,3]] => [10] => 0 => 1
[[7,2,1]] => [10] => 0 => 1
[[7,1,1,1]] => [10] => 0 => 1
[[6,4]] => [10] => 0 => 1
[[6,3,1]] => [10] => 0 => 1
[[6,2,2]] => [10] => 0 => 1
[[6,2,1,1]] => [10] => 0 => 1
[[6,1,1,1,1]] => [10] => 0 => 1
[[5,5]] => [10] => 0 => 1
[[5,4,1]] => [10] => 0 => 1
[[5,3,2]] => [10] => 0 => 1
[[5,3,1,1]] => [10] => 0 => 1
[[5,2,2,1]] => [10] => 0 => 1
[[5,2,1,1,1]] => [10] => 0 => 1
[[5,1,1,1,1,1]] => [10] => 0 => 1
[[4,4,2]] => [10] => 0 => 1
[[4,4,1,1]] => [10] => 0 => 1
[[4,3,3]] => [10] => 0 => 1
[[4,3,2,1]] => [10] => 0 => 1
[[4,3,1,1,1]] => [10] => 0 => 1
[[4,2,2,2]] => [10] => 0 => 1
[[4,2,2,1,1]] => [10] => 0 => 1
[[4,2,1,1,1,1]] => [10] => 0 => 1
[[4,1,1,1,1,1,1]] => [10] => 0 => 1
[[3,3,3,1]] => [10] => 0 => 1
[[3,3,2,2]] => [10] => 0 => 1
[[3,3,2,1,1]] => [10] => 0 => 1
[[3,3,1,1,1,1]] => [10] => 0 => 1
[[3,2,2,2,1]] => [10] => 0 => 1
[[3,2,2,1,1,1]] => [10] => 0 => 1
[[3,2,1,1,1,1,1]] => [10] => 0 => 1
[[3,1,1,1,1,1,1,1]] => [10] => 0 => 1
[[2,2,2,2,2]] => [10] => 0 => 1
[[2,2,2,2,1,1]] => [10] => 0 => 1
[[2,2,2,1,1,1,1]] => [10] => 0 => 1
[[2,2,1,1,1,1,1,1]] => [10] => 0 => 1
[[2,1,1,1,1,1,1,1,1]] => [10] => 0 => 1
[[1,1,1,1,1,1,1,1,1,1]] => [10] => 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 minimal chains with small intervals between a binary word and the top element.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. Let $P$ be the lattice on binary words of length $n$, where the covering elements of a word are obtained by replacing a valley with a peak. An interval $[w_1, w_2]$ in $P$ is small if $w_2$ is obtained from $w_1$ by replacing some valleys with peaks.
This statistic counts the number of chains $w = w_1 < \dots < w_d = 1\dots 1$ to the top element of minimal length.
For example, there are two such chains for the word $0110$:
$$ 0110 < 1011 < 1101 < 1110 < 1111 $$
and
$$ 0110 < 1010 < 1101 < 1110 < 1111. $$
Map
to partition
Description
The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
Map
odd parts
Description
Return the binary word indicating which parts of the partition are odd.