Identifier
Values
[[1]] => => [1] => ([],1) => 0
[[1,2]] => 0 => [2] => ([],2) => 0
[[1],[2]] => 1 => [1,1] => ([(0,1)],2) => 1
[[1,2,3]] => 00 => [3] => ([],3) => 0
[[1,3],[2]] => 10 => [1,2] => ([(1,2)],3) => 1
[[1,2],[3]] => 01 => [2,1] => ([(0,2),(1,2)],3) => 2
[[1],[2],[3]] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[[1,2,3,4]] => 000 => [4] => ([],4) => 0
[[1,3,4],[2]] => 100 => [1,3] => ([(2,3)],4) => 1
[[1,2,4],[3]] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,2,3],[4]] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[[1,3],[2,4]] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,2],[3,4]] => 010 => [2,2] => ([(1,3),(2,3)],4) => 2
[[1,4],[2],[3]] => 110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[[1,3],[2],[4]] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 4
[[1,2],[3],[4]] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 5
[[1],[2],[3],[4]] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6
[[1,2,3,4,5]] => 0000 => [5] => ([],5) => 0
[[1,3,4,5],[2]] => 1000 => [1,4] => ([(3,4)],5) => 1
[[1,2,4,5],[3]] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[[1,2,3,5],[4]] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[[1,2,3,4],[5]] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[[1,3,5],[2,4]] => 1010 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,2,5],[3,4]] => 0100 => [2,3] => ([(2,4),(3,4)],5) => 2
[[1,3,4],[2,5]] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 5
[[1,2,4],[3,5]] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[[1,2,3],[4,5]] => 0010 => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[[1,4,5],[2],[3]] => 1100 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 3
[[1,3,5],[2],[4]] => 1010 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,2,5],[3],[4]] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[[1,3,4],[2],[5]] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 5
[[1,2,4],[3],[5]] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[[1,2,3],[4],[5]] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 7
[[1,4],[2,5],[3]] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 7
[[1,3],[2,5],[4]] => 1010 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 4
[[1,2],[3,5],[4]] => 0110 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
[[1,3],[2,4],[5]] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8
[[1,2],[3,4],[5]] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[[1,5],[2],[3],[4]] => 1110 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6
[[1,4],[2],[3],[5]] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 7
[[1,3],[2],[4],[5]] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8
[[1,2],[3],[4],[5]] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 9
[[1],[2],[3],[4],[5]] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10
[[1,2,3,4,5,6]] => 00000 => [6] => ([],6) => 0
[[1,3,4,5,6],[2]] => 10000 => [1,5] => ([(4,5)],6) => 1
[[1,2,4,5,6],[3]] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[[1,2,3,5,6],[4]] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[[1,2,3,4,6],[5]] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[[1,2,3,4,5],[6]] => 00001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[[1,3,5,6],[2,4]] => 10100 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[[1,2,5,6],[3,4]] => 01000 => [2,4] => ([(3,5),(4,5)],6) => 2
[[1,3,4,6],[2,5]] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1,2,4,6],[3,5]] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[[1,2,3,6],[4,5]] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[[1,3,4,5],[2,6]] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 6
[[1,2,4,5],[3,6]] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[[1,2,3,5],[4,6]] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[[1,2,3,4],[5,6]] => 00010 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[[1,4,5,6],[2],[3]] => 11000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 3
[[1,3,5,6],[2],[4]] => 10100 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[[1,2,5,6],[3],[4]] => 01100 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1,3,4,6],[2],[5]] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1,2,4,6],[3],[5]] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[[1,2,3,6],[4],[5]] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[[1,3,4,5],[2],[6]] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 6
[[1,2,4,5],[3],[6]] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[[1,2,3,5],[4],[6]] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[[1,2,3,4],[5],[6]] => 00011 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 9
[[1,3,5],[2,4,6]] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 9
[[1,2,5],[3,4,6]] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[[1,3,4],[2,5,6]] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1,2,4],[3,5,6]] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[[1,2,3],[4,5,6]] => 00100 => [3,3] => ([(2,5),(3,5),(4,5)],6) => 3
[[1,4,6],[2,5],[3]] => 11010 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[[1,3,6],[2,5],[4]] => 10100 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 4
[[1,2,6],[3,5],[4]] => 01100 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1,3,6],[2,4],[5]] => 10110 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[[1,2,6],[3,4],[5]] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[[1,4,5],[2,6],[3]] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[[1,3,5],[2,6],[4]] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 9
[[1,2,5],[3,6],[4]] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
[[1,3,4],[2,6],[5]] => 10010 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1,2,4],[3,6],[5]] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[[1,2,3],[4,6],[5]] => 00110 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[[1,3,5],[2,4],[6]] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 9
[[1,2,5],[3,4],[6]] => 01001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[[1,3,4],[2,5],[6]] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
[[1,2,4],[3,5],[6]] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 11
[[1,2,3],[4,5],[6]] => 00101 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[[1,5,6],[2],[3],[4]] => 11100 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[[1,4,6],[2],[3],[5]] => 11010 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[[1,3,6],[2],[4],[5]] => 10110 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[[1,2,6],[3],[4],[5]] => 01110 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 9
[[1,4,5],[2],[3],[6]] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[[1,3,5],[2],[4],[6]] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 9
[[1,2,5],[3],[4],[6]] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
[[1,3,4],[2],[5],[6]] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
[[1,2,4],[3],[5],[6]] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 11
[[1,2,3],[4],[5],[6]] => 00111 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12
[[1,4],[2,5],[3,6]] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12
[[1,3],[2,5],[4,6]] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 9
>>> Load all 367 entries. <<<
[[1,2],[3,5],[4,6]] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
[[1,3],[2,4],[5,6]] => 10110 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[[1,2],[3,4],[5,6]] => 01010 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
[[1,5],[2,6],[3],[4]] => 11101 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 11
[[1,4],[2,6],[3],[5]] => 11010 => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7
[[1,3],[2,6],[4],[5]] => 10110 => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
[[1,2],[3,6],[4],[5]] => 01110 => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 9
[[1,4],[2,5],[3],[6]] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12
[[1,3],[2,5],[4],[6]] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 9
[[1,2],[3,5],[4],[6]] => 01101 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
[[1,3],[2,4],[5],[6]] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 13
[[1,2],[3,4],[5],[6]] => 01011 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 11
[[1,6],[2],[3],[4],[5]] => 11110 => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
[[1,5],[2],[3],[4],[6]] => 11101 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 11
[[1,4],[2],[3],[5],[6]] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12
[[1,3],[2],[4],[5],[6]] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 13
[[1,2],[3],[4],[5],[6]] => 01111 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 14
[[1],[2],[3],[4],[5],[6]] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15
[[1,2,3,4,5,6,7]] => 000000 => [7] => ([],7) => 0
[[1,3,4,5,6,7],[2]] => 100000 => [1,6] => ([(5,6)],7) => 1
[[1,2,4,5,6,7],[3]] => 010000 => [2,5] => ([(4,6),(5,6)],7) => 2
[[1,2,3,5,6,7],[4]] => 001000 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 3
[[1,2,3,4,6,7],[5]] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[[1,2,3,4,5,7],[6]] => 000010 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[[1,2,3,4,5,6],[7]] => 000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[[1,3,5,6,7],[2,4]] => 101000 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,2,5,6,7],[3,4]] => 010000 => [2,5] => ([(4,6),(5,6)],7) => 2
[[1,3,4,6,7],[2,5]] => 100100 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,2,4,6,7],[3,5]] => 010100 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,2,3,6,7],[4,5]] => 001000 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 3
[[1,3,4,5,7],[2,6]] => 100010 => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,2,4,5,7],[3,6]] => 010010 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,2,3,5,7],[4,6]] => 001010 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,3,4,7],[5,6]] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[[1,3,4,5,6],[2,7]] => 100001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,2,4,5,6],[3,7]] => 010001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,3,5,6],[4,7]] => 001001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,3,4,6],[5,7]] => 000101 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,3,4,5],[6,7]] => 000010 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[[1,4,5,6,7],[2],[3]] => 110000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 3
[[1,3,5,6,7],[2],[4]] => 101000 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,2,5,6,7],[3],[4]] => 011000 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,3,4,6,7],[2],[5]] => 100100 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,2,4,6,7],[3],[5]] => 010100 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,2,3,6,7],[4],[5]] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,4,5,7],[2],[6]] => 100010 => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,2,4,5,7],[3],[6]] => 010010 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,2,3,5,7],[4],[6]] => 001010 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,3,4,7],[5],[6]] => 000110 => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,3,4,5,6],[2],[7]] => 100001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,2,4,5,6],[3],[7]] => 010001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,3,5,6],[4],[7]] => 001001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,3,4,6],[5],[7]] => 000101 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,3,4,5],[6],[7]] => 000011 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,3,5,7],[2,4,6]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,5,7],[3,4,6]] => 010010 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,4,7],[2,5,6]] => 100100 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,2,4,7],[3,5,6]] => 010100 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,2,3,7],[4,5,6]] => 001000 => [3,4] => ([(3,6),(4,6),(5,6)],7) => 3
[[1,3,5,6],[2,4,7]] => 101001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,5,6],[3,4,7]] => 010001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,3,4,6],[2,5,7]] => 100101 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,4,6],[3,5,7]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,2,3,6],[4,5,7]] => 001001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,3,4,5],[2,6,7]] => 100010 => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,2,4,5],[3,6,7]] => 010010 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,2,3,5],[4,6,7]] => 001010 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,3,4],[5,6,7]] => 000100 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[[1,4,6,7],[2,5],[3]] => 110100 => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,6,7],[2,5],[4]] => 101000 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,2,6,7],[3,5],[4]] => 011000 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,3,6,7],[2,4],[5]] => 101100 => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,6,7],[3,4],[5]] => 010100 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,4,5,7],[2,6],[3]] => 110010 => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,3,5,7],[2,6],[4]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,5,7],[3,6],[4]] => 011010 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,3,4,7],[2,6],[5]] => 100100 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,2,4,7],[3,6],[5]] => 010100 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,2,3,7],[4,6],[5]] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,5,7],[2,4],[6]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,5,7],[3,4],[6]] => 010010 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,4,7],[2,5],[6]] => 100110 => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,4,7],[3,5],[6]] => 010110 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,3,7],[4,5],[6]] => 001010 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,4,5,6],[2,7],[3]] => 110001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,3,5,6],[2,7],[4]] => 101001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,5,6],[3,7],[4]] => 011001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,3,4,6],[2,7],[5]] => 100101 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,4,6],[3,7],[5]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,2,3,6],[4,7],[5]] => 001101 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,4,5],[2,7],[6]] => 100010 => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,2,4,5],[3,7],[6]] => 010010 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,2,3,5],[4,7],[6]] => 001010 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,3,4],[5,7],[6]] => 000110 => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,3,5,6],[2,4],[7]] => 101001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,5,6],[3,4],[7]] => 010001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,3,4,6],[2,5],[7]] => 100101 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,4,6],[3,5],[7]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,2,3,6],[4,5],[7]] => 001001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,3,4,5],[2,6],[7]] => 100011 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,2,4,5],[3,6],[7]] => 010011 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,2,3,5],[4,6],[7]] => 001011 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2,3,4],[5,6],[7]] => 000101 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,5,6,7],[2],[3],[4]] => 111000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,4,6,7],[2],[3],[5]] => 110100 => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,6,7],[2],[4],[5]] => 101100 => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,6,7],[3],[4],[5]] => 011100 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,4,5,7],[2],[3],[6]] => 110010 => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,3,5,7],[2],[4],[6]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,5,7],[3],[4],[6]] => 011010 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,3,4,7],[2],[5],[6]] => 100110 => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,4,7],[3],[5],[6]] => 010110 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,3,7],[4],[5],[6]] => 001110 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,4,5,6],[2],[3],[7]] => 110001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,3,5,6],[2],[4],[7]] => 101001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,5,6],[3],[4],[7]] => 011001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,3,4,6],[2],[5],[7]] => 100101 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,4,6],[3],[5],[7]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,2,3,6],[4],[5],[7]] => 001101 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,4,5],[2],[6],[7]] => 100011 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,2,4,5],[3],[6],[7]] => 010011 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,2,3,5],[4],[6],[7]] => 001011 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2,3,4],[5],[6],[7]] => 000111 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,4,6],[2,5,7],[3]] => 110101 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,6],[2,5,7],[4]] => 101001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,6],[3,5,7],[4]] => 011001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,3,6],[2,4,7],[5]] => 101101 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2,6],[3,4,7],[5]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,4,5],[2,6,7],[3]] => 110010 => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,3,5],[2,6,7],[4]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,5],[3,6,7],[4]] => 011010 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,3,4],[2,6,7],[5]] => 100100 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,2,4],[3,6,7],[5]] => 010100 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,2,3],[4,6,7],[5]] => 001100 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,5],[2,4,7],[6]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,5],[3,4,7],[6]] => 010010 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,4],[2,5,7],[6]] => 100110 => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,4],[3,5,7],[6]] => 010110 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,3],[4,5,7],[6]] => 001010 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,3,5],[2,4,6],[7]] => 101011 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,2,5],[3,4,6],[7]] => 010011 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,4],[2,5,6],[7]] => 100101 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,4],[3,5,6],[7]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,2,3],[4,5,6],[7]] => 001001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,4,7],[2,5],[3,6]] => 110110 => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,3,7],[2,5],[4,6]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,7],[3,5],[4,6]] => 011010 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,3,7],[2,4],[5,6]] => 101100 => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,7],[3,4],[5,6]] => 010100 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[[1,4,6],[2,5],[3,7]] => 110101 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,6],[2,5],[4,7]] => 101001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,6],[3,5],[4,7]] => 011001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,3,6],[2,4],[5,7]] => 101101 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2,6],[3,4],[5,7]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,4,5],[2,6],[3,7]] => 110011 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,3,5],[2,6],[4,7]] => 101011 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,2,5],[3,6],[4,7]] => 011011 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 16
[[1,3,4],[2,6],[5,7]] => 100101 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,4],[3,6],[5,7]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,2,3],[4,6],[5,7]] => 001101 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,5],[2,4],[6,7]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,5],[3,4],[6,7]] => 010010 => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,4],[2,5],[6,7]] => 100110 => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,4],[3,5],[6,7]] => 010110 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,3],[4,5],[6,7]] => 001010 => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,5,7],[2,6],[3],[4]] => 111010 => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,4,7],[2,6],[3],[5]] => 110100 => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,7],[2,6],[4],[5]] => 101100 => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,2,7],[3,6],[4],[5]] => 011100 => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,4,7],[2,5],[3],[6]] => 110110 => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,3,7],[2,5],[4],[6]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,7],[3,5],[4],[6]] => 011010 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,3,7],[2,4],[5],[6]] => 101110 => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,2,7],[3,4],[5],[6]] => 010110 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,5,6],[2,7],[3],[4]] => 111001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,4,6],[2,7],[3],[5]] => 110101 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,6],[2,7],[4],[5]] => 101101 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2,6],[3,7],[4],[5]] => 011101 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,4,5],[2,7],[3],[6]] => 110010 => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 8
[[1,3,5],[2,7],[4],[6]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2,5],[3,7],[4],[6]] => 011010 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,3,4],[2,7],[5],[6]] => 100110 => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,4],[3,7],[5],[6]] => 010110 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,3],[4,7],[5],[6]] => 001110 => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,4,6],[2,5],[3],[7]] => 110101 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,6],[2,5],[4],[7]] => 101001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,2,6],[3,5],[4],[7]] => 011001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,3,6],[2,4],[5],[7]] => 101101 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2,6],[3,4],[5],[7]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,4,5],[2,6],[3],[7]] => 110011 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,3,5],[2,6],[4],[7]] => 101011 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,2,5],[3,6],[4],[7]] => 011011 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 16
[[1,3,4],[2,6],[5],[7]] => 100101 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,2,4],[3,6],[5],[7]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,2,3],[4,6],[5],[7]] => 001101 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,5],[2,4],[6],[7]] => 101011 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,2,5],[3,4],[6],[7]] => 010011 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,4],[2,5],[6],[7]] => 100111 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 16
[[1,2,4],[3,5],[6],[7]] => 010111 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 17
[[1,2,3],[4,5],[6],[7]] => 001011 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,6,7],[2],[3],[4],[5]] => 111100 => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,5,7],[2],[3],[4],[6]] => 111010 => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,4,7],[2],[3],[5],[6]] => 110110 => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,3,7],[2],[4],[5],[6]] => 101110 => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,2,7],[3],[4],[5],[6]] => 011110 => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,5,6],[2],[3],[4],[7]] => 111001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,4,6],[2],[3],[5],[7]] => 110101 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3,6],[2],[4],[5],[7]] => 101101 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2,6],[3],[4],[5],[7]] => 011101 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,4,5],[2],[3],[6],[7]] => 110011 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,3,5],[2],[4],[6],[7]] => 101011 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,2,5],[3],[4],[6],[7]] => 011011 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 16
[[1,3,4],[2],[5],[6],[7]] => 100111 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 16
[[1,2,4],[3],[5],[6],[7]] => 010111 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 17
[[1,2,3],[4],[5],[6],[7]] => 001111 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
[[1,5],[2,6],[3,7],[4]] => 111011 => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 17
[[1,4],[2,6],[3,7],[5]] => 110101 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3],[2,6],[4,7],[5]] => 101101 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2],[3,6],[4,7],[5]] => 011101 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,4],[2,5],[3,7],[6]] => 110110 => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,3],[2,5],[4,7],[6]] => 101010 => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 9
[[1,2],[3,5],[4,7],[6]] => 011010 => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 10
[[1,3],[2,4],[5,7],[6]] => 101110 => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,2],[3,4],[5,7],[6]] => 010110 => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,4],[2,5],[3,6],[7]] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
[[1,3],[2,5],[4,6],[7]] => 101011 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,2],[3,5],[4,6],[7]] => 011011 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 16
[[1,3],[2,4],[5,6],[7]] => 101101 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2],[3,4],[5,6],[7]] => 010101 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,6],[2,7],[3],[4],[5]] => 111101 => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 16
[[1,5],[2,7],[3],[4],[6]] => 111010 => [1,1,1,2,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 11
[[1,4],[2,7],[3],[5],[6]] => 110110 => [1,1,2,1,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
[[1,3],[2,7],[4],[5],[6]] => 101110 => [1,2,1,1,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,2],[3,7],[4],[5],[6]] => 011110 => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,5],[2,6],[3],[4],[7]] => 111011 => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 17
[[1,4],[2,6],[3],[5],[7]] => 110101 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 13
[[1,3],[2,6],[4],[5],[7]] => 101101 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 14
[[1,2],[3,6],[4],[5],[7]] => 011101 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,4],[2,5],[3],[6],[7]] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
[[1,3],[2,5],[4],[6],[7]] => 101011 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,2],[3,5],[4],[6],[7]] => 011011 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 16
[[1,3],[2,4],[5],[6],[7]] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 19
[[1,2],[3,4],[5],[6],[7]] => 010111 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 17
[[1,7],[2],[3],[4],[5],[6]] => 111110 => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 15
[[1,6],[2],[3],[4],[5],[7]] => 111101 => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 16
[[1,5],[2],[3],[4],[6],[7]] => 111011 => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 17
[[1,4],[2],[3],[5],[6],[7]] => 110111 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
[[1,3],[2],[4],[5],[6],[7]] => 101111 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 19
[[1,2],[3],[4],[5],[6],[7]] => 011111 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 20
[[1],[2],[3],[4],[5],[6],[7]] => 111111 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 21
[[1,4],[2,5],[3,6],[7],[8]] => 1101111 => [1,1,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 25
[[1,7],[2,8],[3],[4],[5],[6]] => 1111101 => [1,1,1,1,1,2,1] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 22
[[1,4],[2,5],[3],[6],[7],[8]] => 1101111 => [1,1,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 25
[[1,3],[2,4],[5],[6],[7],[8]] => 1011111 => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 26
[[1,7],[2],[3],[4],[5],[6],[8]] => 1111101 => [1,1,1,1,1,2,1] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 22
[[1,4],[2],[3],[5],[6],[7],[8]] => 1101111 => [1,1,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 25
[[1,3],[2],[4],[5],[6],[7],[8]] => 1011111 => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 26
[[1,2],[3],[4],[5],[6],[7],[8]] => 0111111 => [2,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 27
[[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 28
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111 => [2,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 35
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => [1,1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 36
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111 => [2,1,1,1,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 44
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => [1,1,1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 45
[[1,4],[2,5],[3,6],[7],[8],[9]] => 11011111 => [1,1,2,1,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 33
[] => => [1] => ([],1) => 0
[[1,4],[2,5],[3],[6],[7],[8],[9]] => 11011111 => [1,1,2,1,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 33
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Description
The number of edges of a graph.
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.
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
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.