Identifier
-
Mp00134:
Standard tableaux
—descent word⟶
Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001161: Dyck paths ⟶ ℤ
Values
[[1]] => => [1] => [1,0] => 0
[[1,2]] => 0 => [2] => [1,1,0,0] => 0
[[1],[2]] => 1 => [1,1] => [1,0,1,0] => 1
[[1,2,3]] => 00 => [3] => [1,1,1,0,0,0] => 0
[[1,3],[2]] => 10 => [1,2] => [1,0,1,1,0,0] => 1
[[1,2],[3]] => 01 => [2,1] => [1,1,0,0,1,0] => 2
[[1],[2],[3]] => 11 => [1,1,1] => [1,0,1,0,1,0] => 3
[[1,2,3,4]] => 000 => [4] => [1,1,1,1,0,0,0,0] => 0
[[1,3,4],[2]] => 100 => [1,3] => [1,0,1,1,1,0,0,0] => 1
[[1,2,4],[3]] => 010 => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[1,2,3],[4]] => 001 => [3,1] => [1,1,1,0,0,0,1,0] => 3
[[1,3],[2,4]] => 101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
[[1,2],[3,4]] => 010 => [2,2] => [1,1,0,0,1,1,0,0] => 2
[[1,4],[2],[3]] => 110 => [1,1,2] => [1,0,1,0,1,1,0,0] => 3
[[1,3],[2],[4]] => 101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
[[1,2],[3],[4]] => 011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 5
[[1],[2],[3],[4]] => 111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 6
[[1,2,3,4,5]] => 0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[[1,3,4,5],[2]] => 1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[[1,2,4,5],[3]] => 0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[[1,2,3,5],[4]] => 0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
[[1,2,3,4],[5]] => 0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
[[1,3,5],[2,4]] => 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
[[1,2,5],[3,4]] => 0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 2
[[1,3,4],[2,5]] => 1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[[1,2,4],[3,5]] => 0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 6
[[1,2,3],[4,5]] => 0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
[[1,4,5],[2],[3]] => 1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
[[1,3,5],[2],[4]] => 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
[[1,2,5],[3],[4]] => 0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
[[1,3,4],[2],[5]] => 1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
[[1,2,4],[3],[5]] => 0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 6
[[1,2,3],[4],[5]] => 0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 7
[[1,4],[2,5],[3]] => 1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 7
[[1,3],[2,5],[4]] => 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 4
[[1,2],[3,5],[4]] => 0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
[[1,3],[2,4],[5]] => 1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 8
[[1,2],[3,4],[5]] => 0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 6
[[1,5],[2],[3],[4]] => 1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 6
[[1,4],[2],[3],[5]] => 1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 7
[[1,3],[2],[4],[5]] => 1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 8
[[1,2],[3],[4],[5]] => 0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 9
[[1],[2],[3],[4],[5]] => 1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 10
[[1,2,3,4,5,6]] => 00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[1,3,4,5,6],[2]] => 10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[1,2,4,5,6],[3]] => 01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,2,3,5,6],[4]] => 00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,2,3,4,6],[5]] => 00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[[1,2,3,4,5],[6]] => 00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[[1,3,5,6],[2,4]] => 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[[1,2,5,6],[3,4]] => 01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[1,3,4,6],[2,5]] => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,2,4,6],[3,5]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3,6],[4,5]] => 00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,3,4,5],[2,6]] => 10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[[1,2,4,5],[3,6]] => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
[[1,2,3,5],[4,6]] => 00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 8
[[1,2,3,4],[5,6]] => 00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[[1,4,5,6],[2],[3]] => 11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[[1,3,5,6],[2],[4]] => 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[[1,2,5,6],[3],[4]] => 01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[[1,3,4,6],[2],[5]] => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,2,4,6],[3],[5]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3,6],[4],[5]] => 00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 7
[[1,3,4,5],[2],[6]] => 10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[[1,2,4,5],[3],[6]] => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
[[1,2,3,5],[4],[6]] => 00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 8
[[1,2,3,4],[5],[6]] => 00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 9
[[1,3,5],[2,4,6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[[1,2,5],[3,4,6]] => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
[[1,3,4],[2,5,6]] => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,2,4],[3,5,6]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3],[4,5,6]] => 00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[1,4,6],[2,5],[3]] => 11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[[1,3,6],[2,5],[4]] => 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 4
[[1,2,6],[3,5],[4]] => 01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[[1,3,6],[2,4],[5]] => 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[[1,2,6],[3,4],[5]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,4,5],[2,6],[3]] => 11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
[[1,3,5],[2,6],[4]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[[1,2,5],[3,6],[4]] => 01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 10
[[1,3,4],[2,6],[5]] => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[[1,2,4],[3,6],[5]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,2,3],[4,6],[5]] => 00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 7
[[1,3,5],[2,4],[6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[[1,2,5],[3,4],[6]] => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 7
[[1,3,4],[2,5],[6]] => 10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 10
[[1,2,4],[3,5],[6]] => 01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 11
[[1,2,3],[4,5],[6]] => 00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 8
[[1,5,6],[2],[3],[4]] => 11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
[[1,4,6],[2],[3],[5]] => 11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[[1,3,6],[2],[4],[5]] => 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[[1,2,6],[3],[4],[5]] => 01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 9
[[1,4,5],[2],[3],[6]] => 11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 8
[[1,3,5],[2],[4],[6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[[1,2,5],[3],[4],[6]] => 01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 10
[[1,3,4],[2],[5],[6]] => 10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 10
[[1,2,4],[3],[5],[6]] => 01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 11
[[1,2,3],[4],[5],[6]] => 00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 12
[[1,4],[2,5],[3,6]] => 11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 12
[[1,3],[2,5],[4,6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
>>> Load all 980 entries. <<<[[1,2],[3,5],[4,6]] => 01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 10
[[1,3],[2,4],[5,6]] => 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[[1,2],[3,4],[5,6]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
[[1,5],[2,6],[3],[4]] => 11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 11
[[1,4],[2,6],[3],[5]] => 11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[[1,3],[2,6],[4],[5]] => 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 8
[[1,2],[3,6],[4],[5]] => 01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 9
[[1,4],[2,5],[3],[6]] => 11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 12
[[1,3],[2,5],[4],[6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 9
[[1,2],[3,5],[4],[6]] => 01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 10
[[1,3],[2,4],[5],[6]] => 10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 13
[[1,2],[3,4],[5],[6]] => 01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 11
[[1,6],[2],[3],[4],[5]] => 11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 10
[[1,5],[2],[3],[4],[6]] => 11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 11
[[1,4],[2],[3],[5],[6]] => 11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 12
[[1,3],[2],[4],[5],[6]] => 10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 13
[[1,2],[3],[4],[5],[6]] => 01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 14
[[1],[2],[3],[4],[5],[6]] => 11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 15
[[1,2,3,4,5,6,7]] => 000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[1,3,4,5,6,7],[2]] => 100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[[1,2,4,5,6,7],[3]] => 010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[1,2,3,5,6,7],[4]] => 001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[1,2,3,4,6,7],[5]] => 000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[1,2,3,4,5,7],[6]] => 000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[1,2,3,4,5,6],[7]] => 000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[[1,3,5,6,7],[2,4]] => 101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,6,7],[3,4]] => 010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[[1,3,4,6,7],[2,5]] => 100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[1,2,4,6,7],[3,5]] => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[[1,2,3,6,7],[4,5]] => 001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[1,3,4,5,7],[2,6]] => 100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[1,2,4,5,7],[3,6]] => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[[1,2,3,5,7],[4,6]] => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[[1,2,3,4,7],[5,6]] => 000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[1,3,4,5,6],[2,7]] => 100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[1,2,4,5,6],[3,7]] => 010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
[[1,2,3,5,6],[4,7]] => 001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[[1,2,3,4,6],[5,7]] => 000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
[[1,2,3,4,5],[6,7]] => 000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[[1,4,5,6,7],[2],[3]] => 110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[[1,3,5,6,7],[2],[4]] => 101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,5,6,7],[3],[4]] => 011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[[1,3,4,6,7],[2],[5]] => 100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[1,2,4,6,7],[3],[5]] => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[[1,2,3,6,7],[4],[5]] => 001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[[1,3,4,5,7],[2],[6]] => 100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[1,2,4,5,7],[3],[6]] => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[[1,2,3,5,7],[4],[6]] => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[[1,2,3,4,7],[5],[6]] => 000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
[[1,3,4,5,6],[2],[7]] => 100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[[1,2,4,5,6],[3],[7]] => 010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
[[1,2,3,5,6],[4],[7]] => 001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[[1,2,3,4,6],[5],[7]] => 000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
[[1,2,3,4,5],[6],[7]] => 000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 11
[[1,3,5,7],[2,4,6]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,5,7],[3,4,6]] => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[[1,3,4,7],[2,5,6]] => 100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[1,2,4,7],[3,5,6]] => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[[1,2,3,7],[4,5,6]] => 001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[[1,3,5,6],[2,4,7]] => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[1,2,5,6],[3,4,7]] => 010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
[[1,3,4,6],[2,5,7]] => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[[1,2,4,6],[3,5,7]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,2,3,6],[4,5,7]] => 001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[[1,3,4,5],[2,6,7]] => 100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[1,2,4,5],[3,6,7]] => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[[1,2,3,5],[4,6,7]] => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[[1,2,3,4],[5,6,7]] => 000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[[1,4,6,7],[2,5],[3]] => 110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[[1,3,6,7],[2,5],[4]] => 101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[[1,2,6,7],[3,5],[4]] => 011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[[1,3,6,7],[2,4],[5]] => 101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[[1,2,6,7],[3,4],[5]] => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[[1,4,5,7],[2,6],[3]] => 110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[[1,3,5,7],[2,6],[4]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,5,7],[3,6],[4]] => 011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[[1,3,4,7],[2,6],[5]] => 100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[1,2,4,7],[3,6],[5]] => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[[1,2,3,7],[4,6],[5]] => 001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[[1,3,5,7],[2,4],[6]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,5,7],[3,4],[6]] => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[[1,3,4,7],[2,5],[6]] => 100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[[1,2,4,7],[3,5],[6]] => 010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[[1,2,3,7],[4,5],[6]] => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[[1,4,5,6],[2,7],[3]] => 110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[[1,3,5,6],[2,7],[4]] => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[1,2,5,6],[3,7],[4]] => 011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[[1,3,4,6],[2,7],[5]] => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[[1,2,4,6],[3,7],[5]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,2,3,6],[4,7],[5]] => 001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
[[1,3,4,5],[2,7],[6]] => 100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[[1,2,4,5],[3,7],[6]] => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[[1,2,3,5],[4,7],[6]] => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[[1,2,3,4],[5,7],[6]] => 000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 9
[[1,3,5,6],[2,4],[7]] => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[1,2,5,6],[3,4],[7]] => 010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 8
[[1,3,4,6],[2,5],[7]] => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[[1,2,4,6],[3,5],[7]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,2,3,6],[4,5],[7]] => 001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[[1,3,4,5],[2,6],[7]] => 100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[[1,2,4,5],[3,6],[7]] => 010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
[[1,2,3,5],[4,6],[7]] => 001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 14
[[1,2,3,4],[5,6],[7]] => 000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
[[1,5,6,7],[2],[3],[4]] => 111000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[[1,4,6,7],[2],[3],[5]] => 110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[[1,3,6,7],[2],[4],[5]] => 101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[[1,2,6,7],[3],[4],[5]] => 011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[[1,4,5,7],[2],[3],[6]] => 110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[[1,3,5,7],[2],[4],[6]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,5,7],[3],[4],[6]] => 011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[[1,3,4,7],[2],[5],[6]] => 100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[[1,2,4,7],[3],[5],[6]] => 010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[[1,2,3,7],[4],[5],[6]] => 001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 12
[[1,4,5,6],[2],[3],[7]] => 110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[[1,3,5,6],[2],[4],[7]] => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[1,2,5,6],[3],[4],[7]] => 011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[[1,3,4,6],[2],[5],[7]] => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[[1,2,4,6],[3],[5],[7]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,2,3,6],[4],[5],[7]] => 001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
[[1,3,4,5],[2],[6],[7]] => 100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[[1,2,4,5],[3],[6],[7]] => 010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
[[1,2,3,5],[4],[6],[7]] => 001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 14
[[1,2,3,4],[5],[6],[7]] => 000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 15
[[1,4,6],[2,5,7],[3]] => 110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[[1,3,6],[2,5,7],[4]] => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[1,2,6],[3,5,7],[4]] => 011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[[1,3,6],[2,4,7],[5]] => 101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[[1,2,6],[3,4,7],[5]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,4,5],[2,6,7],[3]] => 110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[[1,3,5],[2,6,7],[4]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,5],[3,6,7],[4]] => 011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[[1,3,4],[2,6,7],[5]] => 100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[[1,2,4],[3,6,7],[5]] => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[[1,2,3],[4,6,7],[5]] => 001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[[1,3,5],[2,4,7],[6]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,5],[3,4,7],[6]] => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[[1,3,4],[2,5,7],[6]] => 100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[[1,2,4],[3,5,7],[6]] => 010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[[1,2,3],[4,5,7],[6]] => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[[1,3,5],[2,4,6],[7]] => 101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[[1,2,5],[3,4,6],[7]] => 010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
[[1,3,4],[2,5,6],[7]] => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[[1,2,4],[3,5,6],[7]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,2,3],[4,5,6],[7]] => 001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[[1,4,7],[2,5],[3,6]] => 110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[[1,3,7],[2,5],[4,6]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,7],[3,5],[4,6]] => 011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[[1,3,7],[2,4],[5,6]] => 101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[[1,2,7],[3,4],[5,6]] => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 6
[[1,4,6],[2,5],[3,7]] => 110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[[1,3,6],[2,5],[4,7]] => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[1,2,6],[3,5],[4,7]] => 011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[[1,3,6],[2,4],[5,7]] => 101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[[1,2,6],[3,4],[5,7]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,4,5],[2,6],[3,7]] => 110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[[1,3,5],[2,6],[4,7]] => 101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[[1,2,5],[3,6],[4,7]] => 011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
[[1,3,4],[2,6],[5,7]] => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[[1,2,4],[3,6],[5,7]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,2,3],[4,6],[5,7]] => 001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
[[1,3,5],[2,4],[6,7]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,5],[3,4],[6,7]] => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 7
[[1,3,4],[2,5],[6,7]] => 100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[[1,2,4],[3,5],[6,7]] => 010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[[1,2,3],[4,5],[6,7]] => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[[1,5,7],[2,6],[3],[4]] => 111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[[1,4,7],[2,6],[3],[5]] => 110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[[1,3,7],[2,6],[4],[5]] => 101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 8
[[1,2,7],[3,6],[4],[5]] => 011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[[1,4,7],[2,5],[3],[6]] => 110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[[1,3,7],[2,5],[4],[6]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,7],[3,5],[4],[6]] => 011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[[1,3,7],[2,4],[5],[6]] => 101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[[1,2,7],[3,4],[5],[6]] => 010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[[1,5,6],[2,7],[3],[4]] => 111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[[1,4,6],[2,7],[3],[5]] => 110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[[1,3,6],[2,7],[4],[5]] => 101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[[1,2,6],[3,7],[4],[5]] => 011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[[1,4,5],[2,7],[3],[6]] => 110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 8
[[1,3,5],[2,7],[4],[6]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2,5],[3,7],[4],[6]] => 011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[[1,3,4],[2,7],[5],[6]] => 100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 10
[[1,2,4],[3,7],[5],[6]] => 010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[[1,2,3],[4,7],[5],[6]] => 001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 12
[[1,4,6],[2,5],[3],[7]] => 110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[[1,3,6],[2,5],[4],[7]] => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 10
[[1,2,6],[3,5],[4],[7]] => 011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 11
[[1,3,6],[2,4],[5],[7]] => 101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[[1,2,6],[3,4],[5],[7]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,4,5],[2,6],[3],[7]] => 110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[[1,3,5],[2,6],[4],[7]] => 101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[[1,2,5],[3,6],[4],[7]] => 011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
[[1,3,4],[2,6],[5],[7]] => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[[1,2,4],[3,6],[5],[7]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,2,3],[4,6],[5],[7]] => 001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 13
[[1,3,5],[2,4],[6],[7]] => 101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[[1,2,5],[3,4],[6],[7]] => 010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 13
[[1,3,4],[2,5],[6],[7]] => 100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
[[1,2,4],[3,5],[6],[7]] => 010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 17
[[1,2,3],[4,5],[6],[7]] => 001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 14
[[1,6,7],[2],[3],[4],[5]] => 111100 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[[1,5,7],[2],[3],[4],[6]] => 111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[[1,4,7],[2],[3],[5],[6]] => 110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[[1,3,7],[2],[4],[5],[6]] => 101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[[1,2,7],[3],[4],[5],[6]] => 011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[[1,5,6],[2],[3],[4],[7]] => 111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 12
[[1,4,6],[2],[3],[5],[7]] => 110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[[1,3,6],[2],[4],[5],[7]] => 101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[[1,2,6],[3],[4],[5],[7]] => 011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[[1,4,5],[2],[3],[6],[7]] => 110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 14
[[1,3,5],[2],[4],[6],[7]] => 101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[[1,2,5],[3],[4],[6],[7]] => 011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
[[1,3,4],[2],[5],[6],[7]] => 100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 16
[[1,2,4],[3],[5],[6],[7]] => 010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 17
[[1,2,3],[4],[5],[6],[7]] => 001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 18
[[1,5],[2,6],[3,7],[4]] => 111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
[[1,4],[2,6],[3,7],[5]] => 110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[[1,3],[2,6],[4,7],[5]] => 101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[[1,2],[3,6],[4,7],[5]] => 011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[[1,4],[2,5],[3,7],[6]] => 110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[[1,3],[2,5],[4,7],[6]] => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 9
[[1,2],[3,5],[4,7],[6]] => 011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 10
[[1,3],[2,4],[5,7],[6]] => 101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[[1,2],[3,4],[5,7],[6]] => 010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 11
[[1,4],[2,5],[3,6],[7]] => 110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 18
[[1,3],[2,5],[4,6],[7]] => 101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[[1,2],[3,5],[4,6],[7]] => 011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
[[1,3],[2,4],[5,6],[7]] => 101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[[1,2],[3,4],[5,6],[7]] => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 12
[[1,6],[2,7],[3],[4],[5]] => 111101 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
[[1,5],[2,7],[3],[4],[6]] => 111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[[1,4],[2,7],[3],[5],[6]] => 110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[[1,3],[2,7],[4],[5],[6]] => 101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[[1,2],[3,7],[4],[5],[6]] => 011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[[1,5],[2,6],[3],[4],[7]] => 111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
[[1,4],[2,6],[3],[5],[7]] => 110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[[1,3],[2,6],[4],[5],[7]] => 101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[[1,2],[3,6],[4],[5],[7]] => 011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 15
[[1,4],[2,5],[3],[6],[7]] => 110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 18
[[1,3],[2,5],[4],[6],[7]] => 101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[[1,2],[3,5],[4],[6],[7]] => 011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 16
[[1,3],[2,4],[5],[6],[7]] => 101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 19
[[1,2],[3,4],[5],[6],[7]] => 010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 17
[[1,7],[2],[3],[4],[5],[6]] => 111110 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
[[1,6],[2],[3],[4],[5],[7]] => 111101 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 16
[[1,5],[2],[3],[4],[6],[7]] => 111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 17
[[1,4],[2],[3],[5],[6],[7]] => 110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 18
[[1,3],[2],[4],[5],[6],[7]] => 101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 19
[[1,2],[3],[4],[5],[6],[7]] => 011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 20
[[1],[2],[3],[4],[5],[6],[7]] => 111111 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 21
[[1,3,4,5,6,7,8],[2]] => 1000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[[1,2,4,5,6,7,8],[3]] => 0100000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[1,3,5,6,7,8],[2,4]] => 1010000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[[1,2,5,6,7,8],[3,4]] => 0100000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[[1,3,4,6,7,8],[2,5]] => 1001000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[[1,2,4,6,7,8],[3,5]] => 0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,3,4,5,7,8],[2,6]] => 1000100 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[[1,2,4,5,7,8],[3,6]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,4,5,6,8],[2,7]] => 1000010 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[[1,2,4,5,6,8],[3,7]] => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[[1,3,4,5,6,7],[2,8]] => 1000001 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[[1,2,4,5,6,7],[3,8]] => 0100001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
[[1,4,5,6,7,8],[2],[3]] => 1100000 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[[1,3,5,6,7,8],[2],[4]] => 1010000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[[1,2,5,6,7,8],[3],[4]] => 0110000 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,3,4,6,7,8],[2],[5]] => 1001000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[[1,2,4,6,7,8],[3],[5]] => 0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,3,4,5,7,8],[2],[6]] => 1000100 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[[1,2,4,5,7,8],[3],[6]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,4,5,6,8],[2],[7]] => 1000010 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[[1,2,4,5,6,8],[3],[7]] => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[[1,3,4,5,6,7],[2],[8]] => 1000001 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 8
[[1,2,4,5,6,7],[3],[8]] => 0100001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
[[1,3,5,7,8],[2,4,6]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5,7,8],[3,4,6]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,4,7,8],[2,5,6]] => 1001000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[[1,2,4,7,8],[3,5,6]] => 0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,3,5,6,8],[2,4,7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,5,6,8],[3,4,7]] => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[[1,3,4,6,8],[2,5,7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,6,8],[3,5,7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,4,5,8],[2,6,7]] => 1000100 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[[1,2,4,5,8],[3,6,7]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,5,6,7],[2,4,8]] => 1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[[1,2,5,6,7],[3,4,8]] => 0100001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
[[1,3,4,6,7],[2,5,8]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4,6,7],[3,5,8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,4,5,7],[2,6,8]] => 1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[[1,2,4,5,7],[3,6,8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4,5,6],[2,7,8]] => 1000010 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[[1,2,4,5,6],[3,7,8]] => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[[1,4,6,7,8],[2,5],[3]] => 1101000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[[1,3,6,7,8],[2,5],[4]] => 1010000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 4
[[1,2,6,7,8],[3,5],[4]] => 0110000 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[[1,3,6,7,8],[2,4],[5]] => 1011000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[[1,2,6,7,8],[3,4],[5]] => 0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,4,5,7,8],[2,6],[3]] => 1100100 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[[1,3,5,7,8],[2,6],[4]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5,7,8],[3,6],[4]] => 0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[1,3,4,7,8],[2,6],[5]] => 1001000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[[1,2,4,7,8],[3,6],[5]] => 0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,3,5,7,8],[2,4],[6]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5,7,8],[3,4],[6]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,4,7,8],[2,5],[6]] => 1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[[1,2,4,7,8],[3,5],[6]] => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[[1,4,5,6,8],[2,7],[3]] => 1100010 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[[1,3,5,6,8],[2,7],[4]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,5,6,8],[3,7],[4]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,4,6,8],[2,7],[5]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,6,8],[3,7],[5]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,4,5,8],[2,7],[6]] => 1000100 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[[1,2,4,5,8],[3,7],[6]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,5,6,8],[2,4],[7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,5,6,8],[3,4],[7]] => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[[1,3,4,6,8],[2,5],[7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,6,8],[3,5],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,4,5,8],[2,6],[7]] => 1000110 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[[1,2,4,5,8],[3,6],[7]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,4,5,6,7],[2,8],[3]] => 1100001 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[[1,3,5,6,7],[2,8],[4]] => 1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[[1,2,5,6,7],[3,8],[4]] => 0110001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12
[[1,3,4,6,7],[2,8],[5]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4,6,7],[3,8],[5]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,4,5,7],[2,8],[6]] => 1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[[1,2,4,5,7],[3,8],[6]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4,5,6],[2,8],[7]] => 1000010 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[[1,2,4,5,6],[3,8],[7]] => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[[1,3,5,6,7],[2,4],[8]] => 1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[[1,2,5,6,7],[3,4],[8]] => 0100001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 9
[[1,3,4,6,7],[2,5],[8]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4,6,7],[3,5],[8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,4,5,7],[2,6],[8]] => 1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[[1,2,4,5,7],[3,6],[8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4,5,6],[2,7],[8]] => 1000011 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 14
[[1,2,4,5,6],[3,7],[8]] => 0100011 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 15
[[1,5,6,7,8],[2],[3],[4]] => 1110000 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[[1,4,6,7,8],[2],[3],[5]] => 1101000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[[1,3,6,7,8],[2],[4],[5]] => 1011000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[[1,2,6,7,8],[3],[4],[5]] => 0111000 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[[1,4,5,7,8],[2],[3],[6]] => 1100100 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[[1,3,5,7,8],[2],[4],[6]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5,7,8],[3],[4],[6]] => 0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[1,3,4,7,8],[2],[5],[6]] => 1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[[1,2,4,7,8],[3],[5],[6]] => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[[1,4,5,6,8],[2],[3],[7]] => 1100010 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[[1,3,5,6,8],[2],[4],[7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,5,6,8],[3],[4],[7]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,4,6,8],[2],[5],[7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,6,8],[3],[5],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,4,5,8],[2],[6],[7]] => 1000110 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[[1,2,4,5,8],[3],[6],[7]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,4,5,6,7],[2],[3],[8]] => 1100001 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[[1,3,5,6,7],[2],[4],[8]] => 1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[[1,2,5,6,7],[3],[4],[8]] => 0110001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12
[[1,3,4,6,7],[2],[5],[8]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4,6,7],[3],[5],[8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,4,5,7],[2],[6],[8]] => 1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[[1,2,4,5,7],[3],[6],[8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4,5,6],[2],[7],[8]] => 1000011 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 14
[[1,2,4,5,6],[3],[7],[8]] => 0100011 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 15
[[1,3,5,7],[2,4,6,8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3,4,6,8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4,7],[2,5,6,8]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4,7],[3,5,6,8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,5,6],[2,4,7,8]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,5,6],[3,4,7,8]] => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[[1,3,4,6],[2,5,7,8]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,6],[3,5,7,8]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,4,5],[2,6,7,8]] => 1000100 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[[1,2,4,5],[3,6,7,8]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,4,6,8],[2,5,7],[3]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6,8],[2,5,7],[4]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,6,8],[3,5,7],[4]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,6,8],[2,4,7],[5]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6,8],[3,4,7],[5]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,4,5,8],[2,6,7],[3]] => 1100100 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[[1,3,5,8],[2,6,7],[4]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5,8],[3,6,7],[4]] => 0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[1,3,4,8],[2,6,7],[5]] => 1001000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[[1,2,4,8],[3,6,7],[5]] => 0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,3,5,8],[2,4,7],[6]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5,8],[3,4,7],[6]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,4,8],[2,5,7],[6]] => 1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[[1,2,4,8],[3,5,7],[6]] => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[[1,3,5,8],[2,4,6],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5,8],[3,4,6],[7]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,3,4,8],[2,5,6],[7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,8],[3,5,6],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,4,6,7],[2,5,8],[3]] => 1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[[1,3,6,7],[2,5,8],[4]] => 1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[[1,2,6,7],[3,5,8],[4]] => 0110001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12
[[1,3,6,7],[2,4,8],[5]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,6,7],[3,4,8],[5]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,4,5,7],[2,6,8],[3]] => 1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[[1,3,5,7],[2,6,8],[4]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3,6,8],[4]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,4,7],[2,6,8],[5]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4,7],[3,6,8],[5]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,5,7],[2,4,8],[6]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3,4,8],[6]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4,7],[2,5,8],[6]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4,7],[3,5,8],[6]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,4,5,6],[2,7,8],[3]] => 1100010 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[[1,3,5,6],[2,7,8],[4]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,5,6],[3,7,8],[4]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,4,6],[2,7,8],[5]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,6],[3,7,8],[5]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,4,5],[2,7,8],[6]] => 1000100 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 6
[[1,2,4,5],[3,7,8],[6]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,5,6],[2,4,8],[7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,5,6],[3,4,8],[7]] => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[[1,3,4,6],[2,5,8],[7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,6],[3,5,8],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,4,5],[2,6,8],[7]] => 1000110 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[[1,2,4,5],[3,6,8],[7]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,3,5,7],[2,4,6],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3,4,6],[8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4,7],[2,5,6],[8]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4,7],[3,5,6],[8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,5,6],[2,4,7],[8]] => 1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[[1,2,5,6],[3,4,7],[8]] => 0100011 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 15
[[1,3,4,6],[2,5,7],[8]] => 1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[[1,2,4,6],[3,5,7],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,3,4,5],[2,6,7],[8]] => 1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[[1,2,4,5],[3,6,7],[8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,4,7,8],[2,5],[3,6]] => 1101100 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[[1,3,7,8],[2,5],[4,6]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,7,8],[3,5],[4,6]] => 0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[1,3,7,8],[2,4],[5,6]] => 1011000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[[1,2,7,8],[3,4],[5,6]] => 0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[[1,4,6,8],[2,5],[3,7]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6,8],[2,5],[4,7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,6,8],[3,5],[4,7]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,6,8],[2,4],[5,7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6,8],[3,4],[5,7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,4,5,8],[2,6],[3,7]] => 1100110 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[[1,3,5,8],[2,6],[4,7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5,8],[3,6],[4,7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3,4,8],[2,6],[5,7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,8],[3,6],[5,7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,5,8],[2,4],[6,7]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5,8],[3,4],[6,7]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,4,8],[2,5],[6,7]] => 1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[[1,2,4,8],[3,5],[6,7]] => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[[1,4,6,7],[2,5],[3,8]] => 1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[[1,3,6,7],[2,5],[4,8]] => 1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[[1,2,6,7],[3,5],[4,8]] => 0110001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12
[[1,3,6,7],[2,4],[5,8]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,6,7],[3,4],[5,8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,4,5,7],[2,6],[3,8]] => 1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[[1,3,5,7],[2,6],[4,8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3,6],[4,8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,4,7],[2,6],[5,8]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4,7],[3,6],[5,8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,5,7],[2,4],[6,8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3,4],[6,8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4,7],[2,5],[6,8]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4,7],[3,5],[6,8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,4,5,6],[2,7],[3,8]] => 1100011 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[[1,3,5,6],[2,7],[4,8]] => 1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[[1,2,5,6],[3,7],[4,8]] => 0110011 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[[1,3,4,6],[2,7],[5,8]] => 1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[[1,2,4,6],[3,7],[5,8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,3,4,5],[2,7],[6,8]] => 1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[[1,2,4,5],[3,7],[6,8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,5,6],[2,4],[7,8]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,5,6],[3,4],[7,8]] => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[[1,3,4,6],[2,5],[7,8]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,6],[3,5],[7,8]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,4,5],[2,6],[7,8]] => 1000110 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[[1,2,4,5],[3,6],[7,8]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,5,7,8],[2,6],[3],[4]] => 1110100 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[[1,4,7,8],[2,6],[3],[5]] => 1101000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[[1,3,7,8],[2,6],[4],[5]] => 1011000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 8
[[1,2,7,8],[3,6],[4],[5]] => 0111000 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[[1,4,7,8],[2,5],[3],[6]] => 1101100 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[[1,3,7,8],[2,5],[4],[6]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,7,8],[3,5],[4],[6]] => 0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[1,3,7,8],[2,4],[5],[6]] => 1011100 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[[1,2,7,8],[3,4],[5],[6]] => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[[1,5,6,8],[2,7],[3],[4]] => 1110010 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[[1,4,6,8],[2,7],[3],[5]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6,8],[2,7],[4],[5]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6,8],[3,7],[4],[5]] => 0111010 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[[1,4,5,8],[2,7],[3],[6]] => 1100100 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[[1,3,5,8],[2,7],[4],[6]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5,8],[3,7],[4],[6]] => 0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[1,3,4,8],[2,7],[5],[6]] => 1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[[1,2,4,8],[3,7],[5],[6]] => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[[1,4,6,8],[2,5],[3],[7]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6,8],[2,5],[4],[7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,6,8],[3,5],[4],[7]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,6,8],[2,4],[5],[7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6,8],[3,4],[5],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,4,5,8],[2,6],[3],[7]] => 1100110 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[[1,3,5,8],[2,6],[4],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5,8],[3,6],[4],[7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3,4,8],[2,6],[5],[7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,8],[3,6],[5],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,5,8],[2,4],[6],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5,8],[3,4],[6],[7]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,3,4,8],[2,5],[6],[7]] => 1001110 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[[1,2,4,8],[3,5],[6],[7]] => 0101110 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[[1,5,6,7],[2,8],[3],[4]] => 1110001 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[[1,4,6,7],[2,8],[3],[5]] => 1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[[1,3,6,7],[2,8],[4],[5]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,6,7],[3,8],[4],[5]] => 0111001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[[1,4,5,7],[2,8],[3],[6]] => 1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[[1,3,5,7],[2,8],[4],[6]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3,8],[4],[6]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,4,7],[2,8],[5],[6]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4,7],[3,8],[5],[6]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,4,5,6],[2,8],[3],[7]] => 1100010 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 9
[[1,3,5,6],[2,8],[4],[7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,5,6],[3,8],[4],[7]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,4,6],[2,8],[5],[7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4,6],[3,8],[5],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,4,5],[2,8],[6],[7]] => 1000110 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 12
[[1,2,4,5],[3,8],[6],[7]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,4,6,7],[2,5],[3],[8]] => 1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[[1,3,6,7],[2,5],[4],[8]] => 1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 11
[[1,2,6,7],[3,5],[4],[8]] => 0110001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 12
[[1,3,6,7],[2,4],[5],[8]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,6,7],[3,4],[5],[8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,4,5,7],[2,6],[3],[8]] => 1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[[1,3,5,7],[2,6],[4],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3,6],[4],[8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,4,7],[2,6],[5],[8]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4,7],[3,6],[5],[8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,5,7],[2,4],[6],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3,4],[6],[8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4,7],[2,5],[6],[8]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4,7],[3,5],[6],[8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,4,5,6],[2,7],[3],[8]] => 1100011 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[[1,3,5,6],[2,7],[4],[8]] => 1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[[1,2,5,6],[3,7],[4],[8]] => 0110011 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[[1,3,4,6],[2,7],[5],[8]] => 1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[[1,2,4,6],[3,7],[5],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,3,4,5],[2,7],[6],[8]] => 1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 13
[[1,2,4,5],[3,7],[6],[8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,5,6],[2,4],[7],[8]] => 1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[[1,2,5,6],[3,4],[7],[8]] => 0100011 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 15
[[1,3,4,6],[2,5],[7],[8]] => 1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[[1,2,4,6],[3,5],[7],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,3,4,5],[2,6],[7],[8]] => 1000111 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 19
[[1,2,4,5],[3,6],[7],[8]] => 0100111 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20
[[1,6,7,8],[2],[3],[4],[5]] => 1111000 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[[1,5,7,8],[2],[3],[4],[6]] => 1110100 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[[1,4,7,8],[2],[3],[5],[6]] => 1101100 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[[1,3,7,8],[2],[4],[5],[6]] => 1011100 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[[1,2,7,8],[3],[4],[5],[6]] => 0111100 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[[1,5,6,8],[2],[3],[4],[7]] => 1110010 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[[1,4,6,8],[2],[3],[5],[7]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6,8],[2],[4],[5],[7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6,8],[3],[4],[5],[7]] => 0111010 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[[1,4,5,8],[2],[3],[6],[7]] => 1100110 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[[1,3,5,8],[2],[4],[6],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5,8],[3],[4],[6],[7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3,4,8],[2],[5],[6],[7]] => 1001110 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[[1,2,4,8],[3],[5],[6],[7]] => 0101110 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[[1,5,6,7],[2],[3],[4],[8]] => 1110001 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 13
[[1,4,6,7],[2],[3],[5],[8]] => 1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[[1,3,6,7],[2],[4],[5],[8]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,6,7],[3],[4],[5],[8]] => 0111001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[[1,4,5,7],[2],[3],[6],[8]] => 1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[[1,3,5,7],[2],[4],[6],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5,7],[3],[4],[6],[8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,4,7],[2],[5],[6],[8]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4,7],[3],[5],[6],[8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,4,5,6],[2],[3],[7],[8]] => 1100011 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 16
[[1,3,5,6],[2],[4],[7],[8]] => 1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[[1,2,5,6],[3],[4],[7],[8]] => 0110011 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[[1,3,4,6],[2],[5],[7],[8]] => 1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[[1,2,4,6],[3],[5],[7],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,3,4,5],[2],[6],[7],[8]] => 1000111 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 19
[[1,2,4,5],[3],[6],[7],[8]] => 0100111 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20
[[1,4,7],[2,5,8],[3,6]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3,7],[2,5,8],[4,6]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,7],[3,5,8],[4,6]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,7],[2,4,8],[5,6]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,7],[3,4,8],[5,6]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,4,6],[2,5,8],[3,7]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6],[2,5,8],[4,7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,6],[3,5,8],[4,7]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,6],[2,4,8],[5,7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6],[3,4,8],[5,7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,4,5],[2,6,8],[3,7]] => 1100110 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[[1,3,5],[2,6,8],[4,7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5],[3,6,8],[4,7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3,4],[2,6,8],[5,7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4],[3,6,8],[5,7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,5],[2,4,8],[6,7]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5],[3,4,8],[6,7]] => 0100100 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[[1,3,4],[2,5,8],[6,7]] => 1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[[1,2,4],[3,5,8],[6,7]] => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[[1,4,6],[2,5,7],[3,8]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3,6],[2,5,7],[4,8]] => 1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[[1,2,6],[3,5,7],[4,8]] => 0110011 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[[1,3,6],[2,4,7],[5,8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2,6],[3,4,7],[5,8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,4,5],[2,6,7],[3,8]] => 1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[[1,3,5],[2,6,7],[4,8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5],[3,6,7],[4,8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,4],[2,6,7],[5,8]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4],[3,6,7],[5,8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,5],[2,4,7],[6,8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5],[3,4,7],[6,8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4],[2,5,7],[6,8]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4],[3,5,7],[6,8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,3,5],[2,4,6],[7,8]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5],[3,4,6],[7,8]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,3,4],[2,5,6],[7,8]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4],[3,5,6],[7,8]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,5,7],[2,6,8],[3],[4]] => 1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[[1,4,7],[2,6,8],[3],[5]] => 1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[[1,3,7],[2,6,8],[4],[5]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,7],[3,6,8],[4],[5]] => 0111001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[[1,4,7],[2,5,8],[3],[6]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3,7],[2,5,8],[4],[6]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,7],[3,5,8],[4],[6]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,7],[2,4,8],[5],[6]] => 1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[[1,2,7],[3,4,8],[5],[6]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,5,6],[2,7,8],[3],[4]] => 1110010 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[[1,4,6],[2,7,8],[3],[5]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6],[2,7,8],[4],[5]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6],[3,7,8],[4],[5]] => 0111010 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[[1,4,5],[2,7,8],[3],[6]] => 1100100 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[[1,3,5],[2,7,8],[4],[6]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,5],[3,7,8],[4],[6]] => 0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[1,3,4],[2,7,8],[5],[6]] => 1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 10
[[1,2,4],[3,7,8],[5],[6]] => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[[1,4,6],[2,5,8],[3],[7]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6],[2,5,8],[4],[7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,6],[3,5,8],[4],[7]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,6],[2,4,8],[5],[7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6],[3,4,8],[5],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,4,5],[2,6,8],[3],[7]] => 1100110 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[[1,3,5],[2,6,8],[4],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5],[3,6,8],[4],[7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3,4],[2,6,8],[5],[7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4],[3,6,8],[5],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,5],[2,4,8],[6],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5],[3,4,8],[6],[7]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,3,4],[2,5,8],[6],[7]] => 1001110 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[[1,2,4],[3,5,8],[6],[7]] => 0101110 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[[1,4,6],[2,5,7],[3],[8]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3,6],[2,5,7],[4],[8]] => 1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[[1,2,6],[3,5,7],[4],[8]] => 0110011 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[[1,3,6],[2,4,7],[5],[8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2,6],[3,4,7],[5],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,4,5],[2,6,7],[3],[8]] => 1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[[1,3,5],[2,6,7],[4],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5],[3,6,7],[4],[8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,4],[2,6,7],[5],[8]] => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[[1,2,4],[3,6,7],[5],[8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,3,5],[2,4,7],[6],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5],[3,4,7],[6],[8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4],[2,5,7],[6],[8]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4],[3,5,7],[6],[8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,3,5],[2,4,6],[7],[8]] => 1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[[1,2,5],[3,4,6],[7],[8]] => 0100111 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20
[[1,3,4],[2,5,6],[7],[8]] => 1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[[1,2,4],[3,5,6],[7],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,5,8],[2,6],[3,7],[4]] => 1110110 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[[1,4,8],[2,6],[3,7],[5]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,8],[2,6],[4,7],[5]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,8],[3,6],[4,7],[5]] => 0111010 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[[1,4,8],[2,5],[3,7],[6]] => 1101100 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[[1,3,8],[2,5],[4,7],[6]] => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 9
[[1,2,8],[3,5],[4,7],[6]] => 0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 10
[[1,3,8],[2,4],[5,7],[6]] => 1011100 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[[1,2,8],[3,4],[5,7],[6]] => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 11
[[1,4,8],[2,5],[3,6],[7]] => 1101110 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[[1,3,8],[2,5],[4,6],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,8],[3,5],[4,6],[7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3,8],[2,4],[5,6],[7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,8],[3,4],[5,6],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,5,7],[2,6],[3,8],[4]] => 1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[[1,4,7],[2,6],[3,8],[5]] => 1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[[1,3,7],[2,6],[4,8],[5]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,7],[3,6],[4,8],[5]] => 0111001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[[1,4,7],[2,5],[3,8],[6]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3,7],[2,5],[4,8],[6]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,7],[3,5],[4,8],[6]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,7],[2,4],[5,8],[6]] => 1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[[1,2,7],[3,4],[5,8],[6]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,5,6],[2,7],[3,8],[4]] => 1110011 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[[1,4,6],[2,7],[3,8],[5]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3,6],[2,7],[4,8],[5]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2,6],[3,7],[4,8],[5]] => 0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[[1,4,5],[2,7],[3,8],[6]] => 1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[[1,3,5],[2,7],[4,8],[6]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5],[3,7],[4,8],[6]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,4],[2,7],[5,8],[6]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4],[3,7],[5,8],[6]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,4,6],[2,5],[3,8],[7]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6],[2,5],[4,8],[7]] => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 10
[[1,2,6],[3,5],[4,8],[7]] => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[[1,3,6],[2,4],[5,8],[7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6],[3,4],[5,8],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,4,5],[2,6],[3,8],[7]] => 1100110 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[[1,3,5],[2,6],[4,8],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5],[3,6],[4,8],[7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3,4],[2,6],[5,8],[7]] => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 11
[[1,2,4],[3,6],[5,8],[7]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,3,5],[2,4],[6,8],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5],[3,4],[6,8],[7]] => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[[1,3,4],[2,5],[6,8],[7]] => 1001110 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[[1,2,4],[3,5],[6,8],[7]] => 0101110 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[[1,4,7],[2,5],[3,6],[8]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3,7],[2,5],[4,6],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,7],[3,5],[4,6],[8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,7],[2,4],[5,6],[8]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,7],[3,4],[5,6],[8]] => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 13
[[1,4,6],[2,5],[3,7],[8]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3,6],[2,5],[4,7],[8]] => 1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[[1,2,6],[3,5],[4,7],[8]] => 0110011 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[[1,3,6],[2,4],[5,7],[8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2,6],[3,4],[5,7],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,4,5],[2,6],[3,7],[8]] => 1100111 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[[1,3,5],[2,6],[4,7],[8]] => 1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[[1,2,5],[3,6],[4,7],[8]] => 0110111 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
[[1,3,4],[2,6],[5,7],[8]] => 1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[[1,2,4],[3,6],[5,7],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,3,5],[2,4],[6,7],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5],[3,4],[6,7],[8]] => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[[1,3,4],[2,5],[6,7],[8]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4],[3,5],[6,7],[8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,6,8],[2,7],[3],[4],[5]] => 1111010 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[[1,5,8],[2,7],[3],[4],[6]] => 1110100 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 11
[[1,4,8],[2,7],[3],[5],[6]] => 1101100 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 12
[[1,3,8],[2,7],[4],[5],[6]] => 1011100 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 13
[[1,2,8],[3,7],[4],[5],[6]] => 0111100 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 14
[[1,5,8],[2,6],[3],[4],[7]] => 1110110 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[[1,4,8],[2,6],[3],[5],[7]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,8],[2,6],[4],[5],[7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,8],[3,6],[4],[5],[7]] => 0111010 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[[1,4,8],[2,5],[3],[6],[7]] => 1101110 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[[1,3,8],[2,5],[4],[6],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,8],[3,5],[4],[6],[7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3,8],[2,4],[5],[6],[7]] => 1011110 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[[1,2,8],[3,4],[5],[6],[7]] => 0101110 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[[1,6,7],[2,8],[3],[4],[5]] => 1111001 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[[1,5,7],[2,8],[3],[4],[6]] => 1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[[1,4,7],[2,8],[3],[5],[6]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3,7],[2,8],[4],[5],[6]] => 1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[[1,2,7],[3,8],[4],[5],[6]] => 0111101 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
[[1,5,6],[2,8],[3],[4],[7]] => 1110010 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[[1,4,6],[2,8],[3],[5],[7]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3,6],[2,8],[4],[5],[7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2,6],[3,8],[4],[5],[7]] => 0111010 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[[1,4,5],[2,8],[3],[6],[7]] => 1100110 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 14
[[1,3,5],[2,8],[4],[6],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2,5],[3,8],[4],[6],[7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3,4],[2,8],[5],[6],[7]] => 1001110 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 16
[[1,2,4],[3,8],[5],[6],[7]] => 0101110 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[[1,5,7],[2,6],[3],[4],[8]] => 1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[[1,4,7],[2,6],[3],[5],[8]] => 1101001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[[1,3,7],[2,6],[4],[5],[8]] => 1011001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 15
[[1,2,7],[3,6],[4],[5],[8]] => 0111001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 16
[[1,4,7],[2,5],[3],[6],[8]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3,7],[2,5],[4],[6],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,7],[3,5],[4],[6],[8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,7],[2,4],[5],[6],[8]] => 1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[[1,2,7],[3,4],[5],[6],[8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,5,6],[2,7],[3],[4],[8]] => 1110011 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[[1,4,6],[2,7],[3],[5],[8]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3,6],[2,7],[4],[5],[8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2,6],[3,7],[4],[5],[8]] => 0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[[1,4,5],[2,7],[3],[6],[8]] => 1100101 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 15
[[1,3,5],[2,7],[4],[6],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2,5],[3,7],[4],[6],[8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3,4],[2,7],[5],[6],[8]] => 1001101 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 17
[[1,2,4],[3,7],[5],[6],[8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,4,6],[2,5],[3],[7],[8]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3,6],[2,5],[4],[7],[8]] => 1010011 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[[1,2,6],[3,5],[4],[7],[8]] => 0110011 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 18
[[1,3,6],[2,4],[5],[7],[8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2,6],[3,4],[5],[7],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,4,5],[2,6],[3],[7],[8]] => 1100111 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[[1,3,5],[2,6],[4],[7],[8]] => 1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[[1,2,5],[3,6],[4],[7],[8]] => 0110111 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
[[1,3,4],[2,6],[5],[7],[8]] => 1001011 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 18
[[1,2,4],[3,6],[5],[7],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,3,5],[2,4],[6],[7],[8]] => 1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[[1,2,5],[3,4],[6],[7],[8]] => 0100111 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 20
[[1,3,4],[2,5],[6],[7],[8]] => 1001111 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 23
[[1,2,4],[3,5],[6],[7],[8]] => 0101111 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 24
[[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 15
[[1,6,8],[2],[3],[4],[5],[7]] => 1111010 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[[1,5,8],[2],[3],[4],[6],[7]] => 1110110 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[[1,4,8],[2],[3],[5],[6],[7]] => 1101110 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[[1,3,8],[2],[4],[5],[6],[7]] => 1011110 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[[1,2,8],[3],[4],[5],[6],[7]] => 0111110 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
[[1,6,7],[2],[3],[4],[5],[8]] => 1111001 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 17
[[1,5,7],[2],[3],[4],[6],[8]] => 1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[[1,4,7],[2],[3],[5],[6],[8]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3,7],[2],[4],[5],[6],[8]] => 1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[[1,2,7],[3],[4],[5],[6],[8]] => 0111101 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
[[1,5,6],[2],[3],[4],[7],[8]] => 1110011 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 19
[[1,4,6],[2],[3],[5],[7],[8]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3,6],[2],[4],[5],[7],[8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2,6],[3],[4],[5],[7],[8]] => 0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[[1,4,5],[2],[3],[6],[7],[8]] => 1100111 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 21
[[1,3,5],[2],[4],[6],[7],[8]] => 1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[[1,2,5],[3],[4],[6],[7],[8]] => 0110111 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
[[1,3,4],[2],[5],[6],[7],[8]] => 1001111 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 23
[[1,2,4],[3],[5],[6],[7],[8]] => 0101111 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 24
[[1,5],[2,6],[3,7],[4,8]] => 1110111 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
[[1,4],[2,6],[3,7],[5,8]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3],[2,6],[4,7],[5,8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2],[3,6],[4,7],[5,8]] => 0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[[1,4],[2,5],[3,7],[6,8]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3],[2,5],[4,7],[6,8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2],[3,5],[4,7],[6,8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3],[2,4],[5,7],[6,8]] => 1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[[1,2],[3,4],[5,7],[6,8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,4],[2,5],[3,6],[7,8]] => 1101110 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[[1,3],[2,5],[4,6],[7,8]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2],[3,5],[4,6],[7,8]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3],[2,4],[5,6],[7,8]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2],[3,4],[5,6],[7,8]] => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 12
[[1,6],[2,7],[3,8],[4],[5]] => 1111011 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
[[1,5],[2,7],[3,8],[4],[6]] => 1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[[1,4],[2,7],[3,8],[5],[6]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3],[2,7],[4,8],[5],[6]] => 1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[[1,2],[3,7],[4,8],[5],[6]] => 0111101 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
[[1,5],[2,6],[3,8],[4],[7]] => 1110110 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[[1,4],[2,6],[3,8],[5],[7]] => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 13
[[1,3],[2,6],[4,8],[5],[7]] => 1011010 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 14
[[1,2],[3,6],[4,8],[5],[7]] => 0111010 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 15
[[1,4],[2,5],[3,8],[6],[7]] => 1101110 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[[1,3],[2,5],[4,8],[6],[7]] => 1010110 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 15
[[1,2],[3,5],[4,8],[6],[7]] => 0110110 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[[1,3],[2,4],[5,8],[6],[7]] => 1011110 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[[1,2],[3,4],[5,8],[6],[7]] => 0101110 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 17
[[1,5],[2,6],[3,7],[4],[8]] => 1110111 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
[[1,4],[2,6],[3,7],[5],[8]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3],[2,6],[4,7],[5],[8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2],[3,6],[4,7],[5],[8]] => 0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[[1,4],[2,5],[3,7],[6],[8]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3],[2,5],[4,7],[6],[8]] => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 16
[[1,2],[3,5],[4,7],[6],[8]] => 0110101 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 17
[[1,3],[2,4],[5,7],[6],[8]] => 1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[[1,2],[3,4],[5,7],[6],[8]] => 0101101 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 18
[[1,4],[2,5],[3,6],[7],[8]] => 1101111 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 25
[[1,3],[2,5],[4,6],[7],[8]] => 1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[[1,2],[3,5],[4,6],[7],[8]] => 0110111 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
[[1,3],[2,4],[5,6],[7],[8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2],[3,4],[5,6],[7],[8]] => 0101011 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 19
[[1,7],[2,8],[3],[4],[5],[6]] => 1111101 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
[[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 16
[[1,5],[2,8],[3],[4],[6],[7]] => 1110110 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 17
[[1,4],[2,8],[3],[5],[6],[7]] => 1101110 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[[1,3],[2,8],[4],[5],[6],[7]] => 1011110 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 19
[[1,2],[3,8],[4],[5],[6],[7]] => 0111110 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 20
[[1,6],[2,7],[3],[4],[5],[8]] => 1111011 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
[[1,5],[2,7],[3],[4],[6],[8]] => 1110101 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[[1,4],[2,7],[3],[5],[6],[8]] => 1101101 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 19
[[1,3],[2,7],[4],[5],[6],[8]] => 1011101 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 20
[[1,2],[3,7],[4],[5],[6],[8]] => 0111101 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 21
[[1,5],[2,6],[3],[4],[7],[8]] => 1110111 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
[[1,4],[2,6],[3],[5],[7],[8]] => 1101011 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 20
[[1,3],[2,6],[4],[5],[7],[8]] => 1011011 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 21
[[1,2],[3,6],[4],[5],[7],[8]] => 0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 22
[[1,4],[2,5],[3],[6],[7],[8]] => 1101111 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 25
[[1,3],[2,5],[4],[6],[7],[8]] => 1010111 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 22
[[1,2],[3,5],[4],[6],[7],[8]] => 0110111 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 23
[[1,3],[2,4],[5],[6],[7],[8]] => 1011111 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 26
[[1,2],[3,4],[5],[6],[7],[8]] => 0101111 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 24
[[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 21
[[1,7],[2],[3],[4],[5],[6],[8]] => 1111101 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 22
[[1,6],[2],[3],[4],[5],[7],[8]] => 1111011 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 23
[[1,5],[2],[3],[4],[6],[7],[8]] => 1110111 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 24
[[1,4],[2],[3],[5],[6],[7],[8]] => 1101111 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 25
[[1,3],[2],[4],[5],[6],[7],[8]] => 1011111 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 26
[[1,2],[3],[4],[5],[6],[7],[8]] => 0111111 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 27
[[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 28
[] => => [1] => [1,0] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,1,1,1 1,1,2,2,2,1,1 1,1,2,3,4,4,4,3,2,1,1 1,1,2,4,5,7,9,9,9,9,7,5,4,2,1,1 1,1,2,4,6,9,13,16,19,22,23,23,22,19,16,13,9,6,4,2,1,1
F1=1
F2=1+q
F3=1+q+q2+q3
F4=1+q+2 q2+2 q3+2 q4+q5+q6
F5=1+q+2 q2+3 q3+4 q4+4 q5+4 q6+3 q7+2 q8+q9+q10
F6=1+q+2 q2+4 q3+5 q4+7 q5+9 q6+9 q7+9 q8+9 q9+7 q10+5 q11+4 q12+2 q13+q14+q15
F7=1+q+2 q2+4 q3+6 q4+9 q5+13 q6+16 q7+19 q8+22 q9+23 q10+23 q11+22 q12+19 q13+16 q14+13 q15+9 q16+6 q17+4 q18+2 q19+q20+q21
Description
The major index north count of a Dyck path.
The descent set des(D) of a Dyck path D=D1⋯D2n with Di∈{N,E} is given by all indices i such that Di=E and Di+1=N. This is, the positions of the valleys of D.
The major index of a Dyck path is then the sum of the positions of the valleys, ∑i∈des(D)i, see St000027The major index of a Dyck path..
The major index north count is given by ∑i∈des(D)#{j≤i∣Dj=N}.
The descent set des(D) of a Dyck path D=D1⋯D2n with Di∈{N,E} is given by all indices i such that Di=E and Di+1=N. This is, the positions of the valleys of D.
The major index of a Dyck path is then the sum of the positions of the valleys, ∑i∈des(D)i, see St000027The major index of a Dyck path..
The major index north count is given by ∑i∈des(D)#{j≤i∣Dj=N}.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size n we set wi=1 if i+1 is in a lower row than i, and 0 otherwise, for 1≤i<n.
For a standard Young tableau of size n we set wi=1 if i+1 is in a lower row than i, and 0 otherwise, for 1≤i<n.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending 1 to a binary word w, the i-th part of the composition equals 1 plus the number of zeros after the i-th 1 in w.
This map is not surjective, since the empty composition does not have a preimage.
Prepending 1 to a binary word w, the i-th part of the composition equals 1 plus the number of zeros after the i-th 1 in w.
This map is not surjective, since the empty composition does not have a preimage.
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