Identifier
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] => 1
[[1],[2],[3]] => 11 => [1,1,1] => [1,0,1,0,1,0] => 2
[[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] => 1
[[1,2,3],[4]] => 001 => [3,1] => [1,1,1,0,0,0,1,0] => 1
[[1,3],[2,4]] => 101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[[1,2],[3,4]] => 010 => [2,2] => [1,1,0,0,1,1,0,0] => 1
[[1,4],[2],[3]] => 110 => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[[1,3],[2],[4]] => 101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[[1,2],[3],[4]] => 011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[[1],[2],[3],[4]] => 111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 3
[[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] => 1
[[1,2,3,5],[4]] => 0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,2,3,4],[5]] => 0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[[1,3,5],[2,4]] => 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5],[3,4]] => 0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[[1,3,4],[2,5]] => 1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[[1,2,4],[3,5]] => 0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,2,3],[4,5]] => 0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[[1,4,5],[2],[3]] => 1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[[1,3,5],[2],[4]] => 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[[1,2,5],[3],[4]] => 0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[1,3,4],[2],[5]] => 1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[[1,2,4],[3],[5]] => 0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,2,3],[4],[5]] => 0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
[[1,4],[2,5],[3]] => 1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[1,3],[2,5],[4]] => 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[[1,2],[3,5],[4]] => 0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[[1,3],[2,4],[5]] => 1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[1,2],[3,4],[5]] => 0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[[1,5],[2],[3],[4]] => 1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 3
[[1,4],[2],[3],[5]] => 1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 3
[[1,3],[2],[4],[5]] => 1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 3
[[1,2],[3],[4],[5]] => 0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 3
[[1],[2],[3],[4],[5]] => 1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[[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] => 1
[[1,2,3,5,6],[4]] => 00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,4,6],[5]] => 00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5],[6]] => 00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[1,3,5,6],[2,4]] => 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[1,2,5,6],[3,4]] => 01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[[1,3,4,6],[2,5]] => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,4,6],[3,5]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3,6],[4,5]] => 00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,3,4,5],[2,6]] => 10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4,5],[3,6]] => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3,5],[4,6]] => 00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3,4],[5,6]] => 00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[[1,4,5,6],[2],[3]] => 11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[1,3,5,6],[2],[4]] => 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[1,2,5,6],[3],[4]] => 01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[1,3,4,6],[2],[5]] => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,4,6],[3],[5]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3,6],[4],[5]] => 00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[1,3,4,5],[2],[6]] => 10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[[1,2,4,5],[3],[6]] => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,2,3,5],[4],[6]] => 00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,2,3,4],[5],[6]] => 00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[[1,3,5],[2,4,6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5],[3,4,6]] => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,3,4],[2,5,6]] => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,4],[3,5,6]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3],[4,5,6]] => 00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[[1,4,6],[2,5],[3]] => 11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[1,3,6],[2,5],[4]] => 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[[1,2,6],[3,5],[4]] => 01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 2
[[1,3,6],[2,4],[5]] => 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[1,2,6],[3,4],[5]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,4,5],[2,6],[3]] => 11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[[1,3,5],[2,6],[4]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5],[3,6],[4]] => 01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[1,3,4],[2,6],[5]] => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[[1,2,4],[3,6],[5]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,2,3],[4,6],[5]] => 00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 2
[[1,3,5],[2,4],[6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5],[3,4],[6]] => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[[1,3,4],[2,5],[6]] => 10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[[1,2,4],[3,5],[6]] => 01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[1,2,3],[4,5],[6]] => 00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[[1,5,6],[2],[3],[4]] => 11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[[1,4,6],[2],[3],[5]] => 11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[1,3,6],[2],[4],[5]] => 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[1,2,6],[3],[4],[5]] => 01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[1,4,5],[2],[3],[6]] => 11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
[[1,3,5],[2],[4],[6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[[1,2,5],[3],[4],[6]] => 01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[1,3,4],[2],[5],[6]] => 10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[[1,2,4],[3],[5],[6]] => 01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[1,2,3],[4],[5],[6]] => 00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[[1,4],[2,5],[3,6]] => 11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[1,3],[2,5],[4,6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
>>> Load all 352 entries. <<<
[[1,2],[3,5],[4,6]] => 01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[1,3],[2,4],[5,6]] => 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[1,2],[3,4],[5,6]] => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[1,5],[2,6],[3],[4]] => 11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[1,4],[2,6],[3],[5]] => 11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[[1,3],[2,6],[4],[5]] => 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[[1,2],[3,6],[4],[5]] => 01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[[1,4],[2,5],[3],[6]] => 11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[1,3],[2,5],[4],[6]] => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[[1,2],[3,5],[4],[6]] => 01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[[1,3],[2,4],[5],[6]] => 10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[1,2],[3,4],[5],[6]] => 01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[[1,6],[2],[3],[4],[5]] => 11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[[1,5],[2],[3],[4],[6]] => 11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[[1,4],[2],[3],[5],[6]] => 11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[[1,3],[2],[4],[5],[6]] => 10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[[1,2],[3],[4],[5],[6]] => 01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 4
[[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] => 5
[[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] => 1
[[1,2,3,5,6,7],[4]] => 001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[1,2,3,4,6,7],[5]] => 000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[1,2,3,4,5,7],[6]] => 000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[1,2,3,4,5,6],[7]] => 000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[[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] => 2
[[1,2,5,6,7],[3,4]] => 010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[[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] => 2
[[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] => 2
[[1,2,3,6,7],[4,5]] => 001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[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] => 2
[[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] => 2
[[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] => 2
[[1,2,3,4,7],[5,6]] => 000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[1,2,3,4,5],[6,7]] => 000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[[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] => 2
[[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] => 2
[[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] => 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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 3
[[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] => 2
[[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] => 2
[[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] => 2
[[1,2,3,7],[4,5,6]] => 001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[[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] => 3
[[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] => 2
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[1,2,3,4],[5,6,7]] => 000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[[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] => 3
[[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] => 2
[[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] => 2
[[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] => 3
[[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] => 2
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 3
[[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] => 2
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 3
[[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] => 2
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 2
[[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] => 2
[[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] => 3
[[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] => 2
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 3
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 3
[[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] => 3
[[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] => 2
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 3
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 3
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 3
[[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] => 4
[[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] => 4
[[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] => 3
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 5
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 3
[[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] => 3
[[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] => 4
[[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] => 3
[[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] => 5
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 3
[[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] => 5
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 5
[[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] => 4
[[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] => 4
[[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] => 4
[[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] => 5
[[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] => 4
[[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] => 4
[[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] => 5
[[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] => 4
[[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] => 5
[[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] => 5
[[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] => 5
[[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] => 5
[[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] => 5
[[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] => 5
[[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] => 6
[] => => [1] => [1,0] => 0
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Description
The number of valleys of the Dyck path.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
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.