Identifier
-
Mp00134:
Standard tableaux
—descent word⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
St000288: Binary words ⟶ ℤ
Values
[[1,2]] => 0 => 0 => 0
[[1],[2]] => 1 => 1 => 1
[[1,2,3]] => 00 => 00 => 0
[[1,3],[2]] => 10 => 01 => 1
[[1,2],[3]] => 01 => 10 => 1
[[1],[2],[3]] => 11 => 11 => 2
[[1,2,3,4]] => 000 => 000 => 0
[[1,3,4],[2]] => 100 => 001 => 1
[[1,2,4],[3]] => 010 => 010 => 1
[[1,2,3],[4]] => 001 => 100 => 1
[[1,3],[2,4]] => 101 => 101 => 2
[[1,2],[3,4]] => 010 => 010 => 1
[[1,4],[2],[3]] => 110 => 011 => 2
[[1,3],[2],[4]] => 101 => 101 => 2
[[1,2],[3],[4]] => 011 => 110 => 2
[[1],[2],[3],[4]] => 111 => 111 => 3
[[1,2,3,4,5]] => 0000 => 0000 => 0
[[1,3,4,5],[2]] => 1000 => 0001 => 1
[[1,2,4,5],[3]] => 0100 => 0010 => 1
[[1,2,3,5],[4]] => 0010 => 0100 => 1
[[1,2,3,4],[5]] => 0001 => 1000 => 1
[[1,3,5],[2,4]] => 1010 => 0101 => 2
[[1,2,5],[3,4]] => 0100 => 0010 => 1
[[1,3,4],[2,5]] => 1001 => 1001 => 2
[[1,2,4],[3,5]] => 0101 => 1010 => 2
[[1,2,3],[4,5]] => 0010 => 0100 => 1
[[1,4,5],[2],[3]] => 1100 => 0011 => 2
[[1,3,5],[2],[4]] => 1010 => 0101 => 2
[[1,2,5],[3],[4]] => 0110 => 0110 => 2
[[1,3,4],[2],[5]] => 1001 => 1001 => 2
[[1,2,4],[3],[5]] => 0101 => 1010 => 2
[[1,2,3],[4],[5]] => 0011 => 1100 => 2
[[1,4],[2,5],[3]] => 1101 => 1011 => 3
[[1,3],[2,5],[4]] => 1010 => 0101 => 2
[[1,2],[3,5],[4]] => 0110 => 0110 => 2
[[1,3],[2,4],[5]] => 1011 => 1101 => 3
[[1,2],[3,4],[5]] => 0101 => 1010 => 2
[[1,5],[2],[3],[4]] => 1110 => 0111 => 3
[[1,4],[2],[3],[5]] => 1101 => 1011 => 3
[[1,3],[2],[4],[5]] => 1011 => 1101 => 3
[[1,2],[3],[4],[5]] => 0111 => 1110 => 3
[[1],[2],[3],[4],[5]] => 1111 => 1111 => 4
[[1,2,3,4,5,6]] => 00000 => 00000 => 0
[[1,3,4,5,6],[2]] => 10000 => 00001 => 1
[[1,2,4,5,6],[3]] => 01000 => 00010 => 1
[[1,2,3,5,6],[4]] => 00100 => 00100 => 1
[[1,2,3,4,6],[5]] => 00010 => 01000 => 1
[[1,2,3,4,5],[6]] => 00001 => 10000 => 1
[[1,3,5,6],[2,4]] => 10100 => 00101 => 2
[[1,2,5,6],[3,4]] => 01000 => 00010 => 1
[[1,3,4,6],[2,5]] => 10010 => 01001 => 2
[[1,2,4,6],[3,5]] => 01010 => 01010 => 2
[[1,2,3,6],[4,5]] => 00100 => 00100 => 1
[[1,3,4,5],[2,6]] => 10001 => 10001 => 2
[[1,2,4,5],[3,6]] => 01001 => 10010 => 2
[[1,2,3,5],[4,6]] => 00101 => 10100 => 2
[[1,2,3,4],[5,6]] => 00010 => 01000 => 1
[[1,4,5,6],[2],[3]] => 11000 => 00011 => 2
[[1,3,5,6],[2],[4]] => 10100 => 00101 => 2
[[1,2,5,6],[3],[4]] => 01100 => 00110 => 2
[[1,3,4,6],[2],[5]] => 10010 => 01001 => 2
[[1,2,4,6],[3],[5]] => 01010 => 01010 => 2
[[1,2,3,6],[4],[5]] => 00110 => 01100 => 2
[[1,3,4,5],[2],[6]] => 10001 => 10001 => 2
[[1,2,4,5],[3],[6]] => 01001 => 10010 => 2
[[1,2,3,5],[4],[6]] => 00101 => 10100 => 2
[[1,2,3,4],[5],[6]] => 00011 => 11000 => 2
[[1,3,5],[2,4,6]] => 10101 => 10101 => 3
[[1,2,5],[3,4,6]] => 01001 => 10010 => 2
[[1,3,4],[2,5,6]] => 10010 => 01001 => 2
[[1,2,4],[3,5,6]] => 01010 => 01010 => 2
[[1,2,3],[4,5,6]] => 00100 => 00100 => 1
[[1,4,6],[2,5],[3]] => 11010 => 01011 => 3
[[1,3,6],[2,5],[4]] => 10100 => 00101 => 2
[[1,2,6],[3,5],[4]] => 01100 => 00110 => 2
[[1,3,6],[2,4],[5]] => 10110 => 01101 => 3
[[1,2,6],[3,4],[5]] => 01010 => 01010 => 2
[[1,4,5],[2,6],[3]] => 11001 => 10011 => 3
[[1,3,5],[2,6],[4]] => 10101 => 10101 => 3
[[1,2,5],[3,6],[4]] => 01101 => 10110 => 3
[[1,3,4],[2,6],[5]] => 10010 => 01001 => 2
[[1,2,4],[3,6],[5]] => 01010 => 01010 => 2
[[1,2,3],[4,6],[5]] => 00110 => 01100 => 2
[[1,3,5],[2,4],[6]] => 10101 => 10101 => 3
[[1,2,5],[3,4],[6]] => 01001 => 10010 => 2
[[1,3,4],[2,5],[6]] => 10011 => 11001 => 3
[[1,2,4],[3,5],[6]] => 01011 => 11010 => 3
[[1,2,3],[4,5],[6]] => 00101 => 10100 => 2
[[1,5,6],[2],[3],[4]] => 11100 => 00111 => 3
[[1,4,6],[2],[3],[5]] => 11010 => 01011 => 3
[[1,3,6],[2],[4],[5]] => 10110 => 01101 => 3
[[1,2,6],[3],[4],[5]] => 01110 => 01110 => 3
[[1,4,5],[2],[3],[6]] => 11001 => 10011 => 3
[[1,3,5],[2],[4],[6]] => 10101 => 10101 => 3
[[1,2,5],[3],[4],[6]] => 01101 => 10110 => 3
[[1,3,4],[2],[5],[6]] => 10011 => 11001 => 3
[[1,2,4],[3],[5],[6]] => 01011 => 11010 => 3
[[1,2,3],[4],[5],[6]] => 00111 => 11100 => 3
[[1,4],[2,5],[3,6]] => 11011 => 11011 => 4
[[1,3],[2,5],[4,6]] => 10101 => 10101 => 3
[[1,2],[3,5],[4,6]] => 01101 => 10110 => 3
>>> Load all 2220 entries. <<<[[1,3],[2,4],[5,6]] => 10110 => 01101 => 3
[[1,2],[3,4],[5,6]] => 01010 => 01010 => 2
[[1,5],[2,6],[3],[4]] => 11101 => 10111 => 4
[[1,4],[2,6],[3],[5]] => 11010 => 01011 => 3
[[1,3],[2,6],[4],[5]] => 10110 => 01101 => 3
[[1,2],[3,6],[4],[5]] => 01110 => 01110 => 3
[[1,4],[2,5],[3],[6]] => 11011 => 11011 => 4
[[1,3],[2,5],[4],[6]] => 10101 => 10101 => 3
[[1,2],[3,5],[4],[6]] => 01101 => 10110 => 3
[[1,3],[2,4],[5],[6]] => 10111 => 11101 => 4
[[1,2],[3,4],[5],[6]] => 01011 => 11010 => 3
[[1,6],[2],[3],[4],[5]] => 11110 => 01111 => 4
[[1,5],[2],[3],[4],[6]] => 11101 => 10111 => 4
[[1,4],[2],[3],[5],[6]] => 11011 => 11011 => 4
[[1,3],[2],[4],[5],[6]] => 10111 => 11101 => 4
[[1,2],[3],[4],[5],[6]] => 01111 => 11110 => 4
[[1],[2],[3],[4],[5],[6]] => 11111 => 11111 => 5
[[1,2,3,4,5,6,7]] => 000000 => 000000 => 0
[[1,3,4,5,6,7],[2]] => 100000 => 000001 => 1
[[1,2,4,5,6,7],[3]] => 010000 => 000010 => 1
[[1,2,3,5,6,7],[4]] => 001000 => 000100 => 1
[[1,2,3,4,6,7],[5]] => 000100 => 001000 => 1
[[1,2,3,4,5,7],[6]] => 000010 => 010000 => 1
[[1,2,3,4,5,6],[7]] => 000001 => 100000 => 1
[[1,3,5,6,7],[2,4]] => 101000 => 000101 => 2
[[1,2,5,6,7],[3,4]] => 010000 => 000010 => 1
[[1,3,4,6,7],[2,5]] => 100100 => 001001 => 2
[[1,2,4,6,7],[3,5]] => 010100 => 001010 => 2
[[1,2,3,6,7],[4,5]] => 001000 => 000100 => 1
[[1,3,4,5,7],[2,6]] => 100010 => 010001 => 2
[[1,2,4,5,7],[3,6]] => 010010 => 010010 => 2
[[1,2,3,5,7],[4,6]] => 001010 => 010100 => 2
[[1,2,3,4,7],[5,6]] => 000100 => 001000 => 1
[[1,3,4,5,6],[2,7]] => 100001 => 100001 => 2
[[1,2,4,5,6],[3,7]] => 010001 => 100010 => 2
[[1,2,3,5,6],[4,7]] => 001001 => 100100 => 2
[[1,2,3,4,6],[5,7]] => 000101 => 101000 => 2
[[1,2,3,4,5],[6,7]] => 000010 => 010000 => 1
[[1,4,5,6,7],[2],[3]] => 110000 => 000011 => 2
[[1,3,5,6,7],[2],[4]] => 101000 => 000101 => 2
[[1,2,5,6,7],[3],[4]] => 011000 => 000110 => 2
[[1,3,4,6,7],[2],[5]] => 100100 => 001001 => 2
[[1,2,4,6,7],[3],[5]] => 010100 => 001010 => 2
[[1,2,3,6,7],[4],[5]] => 001100 => 001100 => 2
[[1,3,4,5,7],[2],[6]] => 100010 => 010001 => 2
[[1,2,4,5,7],[3],[6]] => 010010 => 010010 => 2
[[1,2,3,5,7],[4],[6]] => 001010 => 010100 => 2
[[1,2,3,4,7],[5],[6]] => 000110 => 011000 => 2
[[1,3,4,5,6],[2],[7]] => 100001 => 100001 => 2
[[1,2,4,5,6],[3],[7]] => 010001 => 100010 => 2
[[1,2,3,5,6],[4],[7]] => 001001 => 100100 => 2
[[1,2,3,4,6],[5],[7]] => 000101 => 101000 => 2
[[1,2,3,4,5],[6],[7]] => 000011 => 110000 => 2
[[1,3,5,7],[2,4,6]] => 101010 => 010101 => 3
[[1,2,5,7],[3,4,6]] => 010010 => 010010 => 2
[[1,3,4,7],[2,5,6]] => 100100 => 001001 => 2
[[1,2,4,7],[3,5,6]] => 010100 => 001010 => 2
[[1,2,3,7],[4,5,6]] => 001000 => 000100 => 1
[[1,3,5,6],[2,4,7]] => 101001 => 100101 => 3
[[1,2,5,6],[3,4,7]] => 010001 => 100010 => 2
[[1,3,4,6],[2,5,7]] => 100101 => 101001 => 3
[[1,2,4,6],[3,5,7]] => 010101 => 101010 => 3
[[1,2,3,6],[4,5,7]] => 001001 => 100100 => 2
[[1,3,4,5],[2,6,7]] => 100010 => 010001 => 2
[[1,2,4,5],[3,6,7]] => 010010 => 010010 => 2
[[1,2,3,5],[4,6,7]] => 001010 => 010100 => 2
[[1,2,3,4],[5,6,7]] => 000100 => 001000 => 1
[[1,4,6,7],[2,5],[3]] => 110100 => 001011 => 3
[[1,3,6,7],[2,5],[4]] => 101000 => 000101 => 2
[[1,2,6,7],[3,5],[4]] => 011000 => 000110 => 2
[[1,3,6,7],[2,4],[5]] => 101100 => 001101 => 3
[[1,2,6,7],[3,4],[5]] => 010100 => 001010 => 2
[[1,4,5,7],[2,6],[3]] => 110010 => 010011 => 3
[[1,3,5,7],[2,6],[4]] => 101010 => 010101 => 3
[[1,2,5,7],[3,6],[4]] => 011010 => 010110 => 3
[[1,3,4,7],[2,6],[5]] => 100100 => 001001 => 2
[[1,2,4,7],[3,6],[5]] => 010100 => 001010 => 2
[[1,2,3,7],[4,6],[5]] => 001100 => 001100 => 2
[[1,3,5,7],[2,4],[6]] => 101010 => 010101 => 3
[[1,2,5,7],[3,4],[6]] => 010010 => 010010 => 2
[[1,3,4,7],[2,5],[6]] => 100110 => 011001 => 3
[[1,2,4,7],[3,5],[6]] => 010110 => 011010 => 3
[[1,2,3,7],[4,5],[6]] => 001010 => 010100 => 2
[[1,4,5,6],[2,7],[3]] => 110001 => 100011 => 3
[[1,3,5,6],[2,7],[4]] => 101001 => 100101 => 3
[[1,2,5,6],[3,7],[4]] => 011001 => 100110 => 3
[[1,3,4,6],[2,7],[5]] => 100101 => 101001 => 3
[[1,2,4,6],[3,7],[5]] => 010101 => 101010 => 3
[[1,2,3,6],[4,7],[5]] => 001101 => 101100 => 3
[[1,3,4,5],[2,7],[6]] => 100010 => 010001 => 2
[[1,2,4,5],[3,7],[6]] => 010010 => 010010 => 2
[[1,2,3,5],[4,7],[6]] => 001010 => 010100 => 2
[[1,2,3,4],[5,7],[6]] => 000110 => 011000 => 2
[[1,3,5,6],[2,4],[7]] => 101001 => 100101 => 3
[[1,2,5,6],[3,4],[7]] => 010001 => 100010 => 2
[[1,3,4,6],[2,5],[7]] => 100101 => 101001 => 3
[[1,2,4,6],[3,5],[7]] => 010101 => 101010 => 3
[[1,2,3,6],[4,5],[7]] => 001001 => 100100 => 2
[[1,3,4,5],[2,6],[7]] => 100011 => 110001 => 3
[[1,2,4,5],[3,6],[7]] => 010011 => 110010 => 3
[[1,2,3,5],[4,6],[7]] => 001011 => 110100 => 3
[[1,2,3,4],[5,6],[7]] => 000101 => 101000 => 2
[[1,5,6,7],[2],[3],[4]] => 111000 => 000111 => 3
[[1,4,6,7],[2],[3],[5]] => 110100 => 001011 => 3
[[1,3,6,7],[2],[4],[5]] => 101100 => 001101 => 3
[[1,2,6,7],[3],[4],[5]] => 011100 => 001110 => 3
[[1,4,5,7],[2],[3],[6]] => 110010 => 010011 => 3
[[1,3,5,7],[2],[4],[6]] => 101010 => 010101 => 3
[[1,2,5,7],[3],[4],[6]] => 011010 => 010110 => 3
[[1,3,4,7],[2],[5],[6]] => 100110 => 011001 => 3
[[1,2,4,7],[3],[5],[6]] => 010110 => 011010 => 3
[[1,2,3,7],[4],[5],[6]] => 001110 => 011100 => 3
[[1,4,5,6],[2],[3],[7]] => 110001 => 100011 => 3
[[1,3,5,6],[2],[4],[7]] => 101001 => 100101 => 3
[[1,2,5,6],[3],[4],[7]] => 011001 => 100110 => 3
[[1,3,4,6],[2],[5],[7]] => 100101 => 101001 => 3
[[1,2,4,6],[3],[5],[7]] => 010101 => 101010 => 3
[[1,2,3,6],[4],[5],[7]] => 001101 => 101100 => 3
[[1,3,4,5],[2],[6],[7]] => 100011 => 110001 => 3
[[1,2,4,5],[3],[6],[7]] => 010011 => 110010 => 3
[[1,2,3,5],[4],[6],[7]] => 001011 => 110100 => 3
[[1,2,3,4],[5],[6],[7]] => 000111 => 111000 => 3
[[1,4,6],[2,5,7],[3]] => 110101 => 101011 => 4
[[1,3,6],[2,5,7],[4]] => 101001 => 100101 => 3
[[1,2,6],[3,5,7],[4]] => 011001 => 100110 => 3
[[1,3,6],[2,4,7],[5]] => 101101 => 101101 => 4
[[1,2,6],[3,4,7],[5]] => 010101 => 101010 => 3
[[1,4,5],[2,6,7],[3]] => 110010 => 010011 => 3
[[1,3,5],[2,6,7],[4]] => 101010 => 010101 => 3
[[1,2,5],[3,6,7],[4]] => 011010 => 010110 => 3
[[1,3,4],[2,6,7],[5]] => 100100 => 001001 => 2
[[1,2,4],[3,6,7],[5]] => 010100 => 001010 => 2
[[1,2,3],[4,6,7],[5]] => 001100 => 001100 => 2
[[1,3,5],[2,4,7],[6]] => 101010 => 010101 => 3
[[1,2,5],[3,4,7],[6]] => 010010 => 010010 => 2
[[1,3,4],[2,5,7],[6]] => 100110 => 011001 => 3
[[1,2,4],[3,5,7],[6]] => 010110 => 011010 => 3
[[1,2,3],[4,5,7],[6]] => 001010 => 010100 => 2
[[1,3,5],[2,4,6],[7]] => 101011 => 110101 => 4
[[1,2,5],[3,4,6],[7]] => 010011 => 110010 => 3
[[1,3,4],[2,5,6],[7]] => 100101 => 101001 => 3
[[1,2,4],[3,5,6],[7]] => 010101 => 101010 => 3
[[1,2,3],[4,5,6],[7]] => 001001 => 100100 => 2
[[1,4,7],[2,5],[3,6]] => 110110 => 011011 => 4
[[1,3,7],[2,5],[4,6]] => 101010 => 010101 => 3
[[1,2,7],[3,5],[4,6]] => 011010 => 010110 => 3
[[1,3,7],[2,4],[5,6]] => 101100 => 001101 => 3
[[1,2,7],[3,4],[5,6]] => 010100 => 001010 => 2
[[1,4,6],[2,5],[3,7]] => 110101 => 101011 => 4
[[1,3,6],[2,5],[4,7]] => 101001 => 100101 => 3
[[1,2,6],[3,5],[4,7]] => 011001 => 100110 => 3
[[1,3,6],[2,4],[5,7]] => 101101 => 101101 => 4
[[1,2,6],[3,4],[5,7]] => 010101 => 101010 => 3
[[1,4,5],[2,6],[3,7]] => 110011 => 110011 => 4
[[1,3,5],[2,6],[4,7]] => 101011 => 110101 => 4
[[1,2,5],[3,6],[4,7]] => 011011 => 110110 => 4
[[1,3,4],[2,6],[5,7]] => 100101 => 101001 => 3
[[1,2,4],[3,6],[5,7]] => 010101 => 101010 => 3
[[1,2,3],[4,6],[5,7]] => 001101 => 101100 => 3
[[1,3,5],[2,4],[6,7]] => 101010 => 010101 => 3
[[1,2,5],[3,4],[6,7]] => 010010 => 010010 => 2
[[1,3,4],[2,5],[6,7]] => 100110 => 011001 => 3
[[1,2,4],[3,5],[6,7]] => 010110 => 011010 => 3
[[1,2,3],[4,5],[6,7]] => 001010 => 010100 => 2
[[1,5,7],[2,6],[3],[4]] => 111010 => 010111 => 4
[[1,4,7],[2,6],[3],[5]] => 110100 => 001011 => 3
[[1,3,7],[2,6],[4],[5]] => 101100 => 001101 => 3
[[1,2,7],[3,6],[4],[5]] => 011100 => 001110 => 3
[[1,4,7],[2,5],[3],[6]] => 110110 => 011011 => 4
[[1,3,7],[2,5],[4],[6]] => 101010 => 010101 => 3
[[1,2,7],[3,5],[4],[6]] => 011010 => 010110 => 3
[[1,3,7],[2,4],[5],[6]] => 101110 => 011101 => 4
[[1,2,7],[3,4],[5],[6]] => 010110 => 011010 => 3
[[1,5,6],[2,7],[3],[4]] => 111001 => 100111 => 4
[[1,4,6],[2,7],[3],[5]] => 110101 => 101011 => 4
[[1,3,6],[2,7],[4],[5]] => 101101 => 101101 => 4
[[1,2,6],[3,7],[4],[5]] => 011101 => 101110 => 4
[[1,4,5],[2,7],[3],[6]] => 110010 => 010011 => 3
[[1,3,5],[2,7],[4],[6]] => 101010 => 010101 => 3
[[1,2,5],[3,7],[4],[6]] => 011010 => 010110 => 3
[[1,3,4],[2,7],[5],[6]] => 100110 => 011001 => 3
[[1,2,4],[3,7],[5],[6]] => 010110 => 011010 => 3
[[1,2,3],[4,7],[5],[6]] => 001110 => 011100 => 3
[[1,4,6],[2,5],[3],[7]] => 110101 => 101011 => 4
[[1,3,6],[2,5],[4],[7]] => 101001 => 100101 => 3
[[1,2,6],[3,5],[4],[7]] => 011001 => 100110 => 3
[[1,3,6],[2,4],[5],[7]] => 101101 => 101101 => 4
[[1,2,6],[3,4],[5],[7]] => 010101 => 101010 => 3
[[1,4,5],[2,6],[3],[7]] => 110011 => 110011 => 4
[[1,3,5],[2,6],[4],[7]] => 101011 => 110101 => 4
[[1,2,5],[3,6],[4],[7]] => 011011 => 110110 => 4
[[1,3,4],[2,6],[5],[7]] => 100101 => 101001 => 3
[[1,2,4],[3,6],[5],[7]] => 010101 => 101010 => 3
[[1,2,3],[4,6],[5],[7]] => 001101 => 101100 => 3
[[1,3,5],[2,4],[6],[7]] => 101011 => 110101 => 4
[[1,2,5],[3,4],[6],[7]] => 010011 => 110010 => 3
[[1,3,4],[2,5],[6],[7]] => 100111 => 111001 => 4
[[1,2,4],[3,5],[6],[7]] => 010111 => 111010 => 4
[[1,2,3],[4,5],[6],[7]] => 001011 => 110100 => 3
[[1,6,7],[2],[3],[4],[5]] => 111100 => 001111 => 4
[[1,5,7],[2],[3],[4],[6]] => 111010 => 010111 => 4
[[1,4,7],[2],[3],[5],[6]] => 110110 => 011011 => 4
[[1,3,7],[2],[4],[5],[6]] => 101110 => 011101 => 4
[[1,2,7],[3],[4],[5],[6]] => 011110 => 011110 => 4
[[1,5,6],[2],[3],[4],[7]] => 111001 => 100111 => 4
[[1,4,6],[2],[3],[5],[7]] => 110101 => 101011 => 4
[[1,3,6],[2],[4],[5],[7]] => 101101 => 101101 => 4
[[1,2,6],[3],[4],[5],[7]] => 011101 => 101110 => 4
[[1,4,5],[2],[3],[6],[7]] => 110011 => 110011 => 4
[[1,3,5],[2],[4],[6],[7]] => 101011 => 110101 => 4
[[1,2,5],[3],[4],[6],[7]] => 011011 => 110110 => 4
[[1,3,4],[2],[5],[6],[7]] => 100111 => 111001 => 4
[[1,2,4],[3],[5],[6],[7]] => 010111 => 111010 => 4
[[1,2,3],[4],[5],[6],[7]] => 001111 => 111100 => 4
[[1,5],[2,6],[3,7],[4]] => 111011 => 110111 => 5
[[1,4],[2,6],[3,7],[5]] => 110101 => 101011 => 4
[[1,3],[2,6],[4,7],[5]] => 101101 => 101101 => 4
[[1,2],[3,6],[4,7],[5]] => 011101 => 101110 => 4
[[1,4],[2,5],[3,7],[6]] => 110110 => 011011 => 4
[[1,3],[2,5],[4,7],[6]] => 101010 => 010101 => 3
[[1,2],[3,5],[4,7],[6]] => 011010 => 010110 => 3
[[1,3],[2,4],[5,7],[6]] => 101110 => 011101 => 4
[[1,2],[3,4],[5,7],[6]] => 010110 => 011010 => 3
[[1,4],[2,5],[3,6],[7]] => 110111 => 111011 => 5
[[1,3],[2,5],[4,6],[7]] => 101011 => 110101 => 4
[[1,2],[3,5],[4,6],[7]] => 011011 => 110110 => 4
[[1,3],[2,4],[5,6],[7]] => 101101 => 101101 => 4
[[1,2],[3,4],[5,6],[7]] => 010101 => 101010 => 3
[[1,6],[2,7],[3],[4],[5]] => 111101 => 101111 => 5
[[1,5],[2,7],[3],[4],[6]] => 111010 => 010111 => 4
[[1,4],[2,7],[3],[5],[6]] => 110110 => 011011 => 4
[[1,3],[2,7],[4],[5],[6]] => 101110 => 011101 => 4
[[1,2],[3,7],[4],[5],[6]] => 011110 => 011110 => 4
[[1,5],[2,6],[3],[4],[7]] => 111011 => 110111 => 5
[[1,4],[2,6],[3],[5],[7]] => 110101 => 101011 => 4
[[1,3],[2,6],[4],[5],[7]] => 101101 => 101101 => 4
[[1,2],[3,6],[4],[5],[7]] => 011101 => 101110 => 4
[[1,4],[2,5],[3],[6],[7]] => 110111 => 111011 => 5
[[1,3],[2,5],[4],[6],[7]] => 101011 => 110101 => 4
[[1,2],[3,5],[4],[6],[7]] => 011011 => 110110 => 4
[[1,3],[2,4],[5],[6],[7]] => 101111 => 111101 => 5
[[1,2],[3,4],[5],[6],[7]] => 010111 => 111010 => 4
[[1,7],[2],[3],[4],[5],[6]] => 111110 => 011111 => 5
[[1,6],[2],[3],[4],[5],[7]] => 111101 => 101111 => 5
[[1,5],[2],[3],[4],[6],[7]] => 111011 => 110111 => 5
[[1,4],[2],[3],[5],[6],[7]] => 110111 => 111011 => 5
[[1,3],[2],[4],[5],[6],[7]] => 101111 => 111101 => 5
[[1,2],[3],[4],[5],[6],[7]] => 011111 => 111110 => 5
[[1],[2],[3],[4],[5],[6],[7]] => 111111 => 111111 => 6
[[1,2,3,4,5,6,7,8]] => 0000000 => 0000000 => 0
[[1,3,4,5,6,7,8],[2]] => 1000000 => 0000001 => 1
[[1,2,4,5,6,7,8],[3]] => 0100000 => 0000010 => 1
[[1,2,3,5,6,7,8],[4]] => 0010000 => 0000100 => 1
[[1,2,3,4,6,7,8],[5]] => 0001000 => 0001000 => 1
[[1,2,3,4,5,7,8],[6]] => 0000100 => 0010000 => 1
[[1,2,3,4,5,6,8],[7]] => 0000010 => 0100000 => 1
[[1,2,3,4,5,6,7],[8]] => 0000001 => 1000000 => 1
[[1,3,5,6,7,8],[2,4]] => 1010000 => 0000101 => 2
[[1,2,5,6,7,8],[3,4]] => 0100000 => 0000010 => 1
[[1,3,4,6,7,8],[2,5]] => 1001000 => 0001001 => 2
[[1,2,4,6,7,8],[3,5]] => 0101000 => 0001010 => 2
[[1,2,3,6,7,8],[4,5]] => 0010000 => 0000100 => 1
[[1,3,4,5,7,8],[2,6]] => 1000100 => 0010001 => 2
[[1,2,4,5,7,8],[3,6]] => 0100100 => 0010010 => 2
[[1,2,3,5,7,8],[4,6]] => 0010100 => 0010100 => 2
[[1,2,3,4,7,8],[5,6]] => 0001000 => 0001000 => 1
[[1,3,4,5,6,8],[2,7]] => 1000010 => 0100001 => 2
[[1,2,4,5,6,8],[3,7]] => 0100010 => 0100010 => 2
[[1,2,3,5,6,8],[4,7]] => 0010010 => 0100100 => 2
[[1,2,3,4,6,8],[5,7]] => 0001010 => 0101000 => 2
[[1,2,3,4,5,8],[6,7]] => 0000100 => 0010000 => 1
[[1,3,4,5,6,7],[2,8]] => 1000001 => 1000001 => 2
[[1,2,4,5,6,7],[3,8]] => 0100001 => 1000010 => 2
[[1,2,3,5,6,7],[4,8]] => 0010001 => 1000100 => 2
[[1,2,3,4,6,7],[5,8]] => 0001001 => 1001000 => 2
[[1,2,3,4,5,7],[6,8]] => 0000101 => 1010000 => 2
[[1,2,3,4,5,6],[7,8]] => 0000010 => 0100000 => 1
[[1,4,5,6,7,8],[2],[3]] => 1100000 => 0000011 => 2
[[1,3,5,6,7,8],[2],[4]] => 1010000 => 0000101 => 2
[[1,2,5,6,7,8],[3],[4]] => 0110000 => 0000110 => 2
[[1,3,4,6,7,8],[2],[5]] => 1001000 => 0001001 => 2
[[1,2,4,6,7,8],[3],[5]] => 0101000 => 0001010 => 2
[[1,2,3,6,7,8],[4],[5]] => 0011000 => 0001100 => 2
[[1,3,4,5,7,8],[2],[6]] => 1000100 => 0010001 => 2
[[1,2,4,5,7,8],[3],[6]] => 0100100 => 0010010 => 2
[[1,2,3,5,7,8],[4],[6]] => 0010100 => 0010100 => 2
[[1,2,3,4,7,8],[5],[6]] => 0001100 => 0011000 => 2
[[1,3,4,5,6,8],[2],[7]] => 1000010 => 0100001 => 2
[[1,2,4,5,6,8],[3],[7]] => 0100010 => 0100010 => 2
[[1,2,3,5,6,8],[4],[7]] => 0010010 => 0100100 => 2
[[1,2,3,4,6,8],[5],[7]] => 0001010 => 0101000 => 2
[[1,2,3,4,5,8],[6],[7]] => 0000110 => 0110000 => 2
[[1,3,4,5,6,7],[2],[8]] => 1000001 => 1000001 => 2
[[1,2,4,5,6,7],[3],[8]] => 0100001 => 1000010 => 2
[[1,2,3,5,6,7],[4],[8]] => 0010001 => 1000100 => 2
[[1,2,3,4,6,7],[5],[8]] => 0001001 => 1001000 => 2
[[1,2,3,4,5,7],[6],[8]] => 0000101 => 1010000 => 2
[[1,2,3,4,5,6],[7],[8]] => 0000011 => 1100000 => 2
[[1,3,5,7,8],[2,4,6]] => 1010100 => 0010101 => 3
[[1,2,5,7,8],[3,4,6]] => 0100100 => 0010010 => 2
[[1,3,4,7,8],[2,5,6]] => 1001000 => 0001001 => 2
[[1,2,4,7,8],[3,5,6]] => 0101000 => 0001010 => 2
[[1,2,3,7,8],[4,5,6]] => 0010000 => 0000100 => 1
[[1,3,5,6,8],[2,4,7]] => 1010010 => 0100101 => 3
[[1,2,5,6,8],[3,4,7]] => 0100010 => 0100010 => 2
[[1,3,4,6,8],[2,5,7]] => 1001010 => 0101001 => 3
[[1,2,4,6,8],[3,5,7]] => 0101010 => 0101010 => 3
[[1,2,3,6,8],[4,5,7]] => 0010010 => 0100100 => 2
[[1,3,4,5,8],[2,6,7]] => 1000100 => 0010001 => 2
[[1,2,4,5,8],[3,6,7]] => 0100100 => 0010010 => 2
[[1,2,3,5,8],[4,6,7]] => 0010100 => 0010100 => 2
[[1,2,3,4,8],[5,6,7]] => 0001000 => 0001000 => 1
[[1,3,5,6,7],[2,4,8]] => 1010001 => 1000101 => 3
[[1,2,5,6,7],[3,4,8]] => 0100001 => 1000010 => 2
[[1,3,4,6,7],[2,5,8]] => 1001001 => 1001001 => 3
[[1,2,4,6,7],[3,5,8]] => 0101001 => 1001010 => 3
[[1,2,3,6,7],[4,5,8]] => 0010001 => 1000100 => 2
[[1,3,4,5,7],[2,6,8]] => 1000101 => 1010001 => 3
[[1,2,4,5,7],[3,6,8]] => 0100101 => 1010010 => 3
[[1,2,3,5,7],[4,6,8]] => 0010101 => 1010100 => 3
[[1,2,3,4,7],[5,6,8]] => 0001001 => 1001000 => 2
[[1,3,4,5,6],[2,7,8]] => 1000010 => 0100001 => 2
[[1,2,4,5,6],[3,7,8]] => 0100010 => 0100010 => 2
[[1,2,3,5,6],[4,7,8]] => 0010010 => 0100100 => 2
[[1,2,3,4,6],[5,7,8]] => 0001010 => 0101000 => 2
[[1,2,3,4,5],[6,7,8]] => 0000100 => 0010000 => 1
[[1,4,6,7,8],[2,5],[3]] => 1101000 => 0001011 => 3
[[1,3,6,7,8],[2,5],[4]] => 1010000 => 0000101 => 2
[[1,2,6,7,8],[3,5],[4]] => 0110000 => 0000110 => 2
[[1,3,6,7,8],[2,4],[5]] => 1011000 => 0001101 => 3
[[1,2,6,7,8],[3,4],[5]] => 0101000 => 0001010 => 2
[[1,4,5,7,8],[2,6],[3]] => 1100100 => 0010011 => 3
[[1,3,5,7,8],[2,6],[4]] => 1010100 => 0010101 => 3
[[1,2,5,7,8],[3,6],[4]] => 0110100 => 0010110 => 3
[[1,3,4,7,8],[2,6],[5]] => 1001000 => 0001001 => 2
[[1,2,4,7,8],[3,6],[5]] => 0101000 => 0001010 => 2
[[1,2,3,7,8],[4,6],[5]] => 0011000 => 0001100 => 2
[[1,3,5,7,8],[2,4],[6]] => 1010100 => 0010101 => 3
[[1,2,5,7,8],[3,4],[6]] => 0100100 => 0010010 => 2
[[1,3,4,7,8],[2,5],[6]] => 1001100 => 0011001 => 3
[[1,2,4,7,8],[3,5],[6]] => 0101100 => 0011010 => 3
[[1,2,3,7,8],[4,5],[6]] => 0010100 => 0010100 => 2
[[1,4,5,6,8],[2,7],[3]] => 1100010 => 0100011 => 3
[[1,3,5,6,8],[2,7],[4]] => 1010010 => 0100101 => 3
[[1,2,5,6,8],[3,7],[4]] => 0110010 => 0100110 => 3
[[1,3,4,6,8],[2,7],[5]] => 1001010 => 0101001 => 3
[[1,2,4,6,8],[3,7],[5]] => 0101010 => 0101010 => 3
[[1,2,3,6,8],[4,7],[5]] => 0011010 => 0101100 => 3
[[1,3,4,5,8],[2,7],[6]] => 1000100 => 0010001 => 2
[[1,2,4,5,8],[3,7],[6]] => 0100100 => 0010010 => 2
[[1,2,3,5,8],[4,7],[6]] => 0010100 => 0010100 => 2
[[1,2,3,4,8],[5,7],[6]] => 0001100 => 0011000 => 2
[[1,3,5,6,8],[2,4],[7]] => 1010010 => 0100101 => 3
[[1,2,5,6,8],[3,4],[7]] => 0100010 => 0100010 => 2
[[1,3,4,6,8],[2,5],[7]] => 1001010 => 0101001 => 3
[[1,2,4,6,8],[3,5],[7]] => 0101010 => 0101010 => 3
[[1,2,3,6,8],[4,5],[7]] => 0010010 => 0100100 => 2
[[1,3,4,5,8],[2,6],[7]] => 1000110 => 0110001 => 3
[[1,2,4,5,8],[3,6],[7]] => 0100110 => 0110010 => 3
[[1,2,3,5,8],[4,6],[7]] => 0010110 => 0110100 => 3
[[1,2,3,4,8],[5,6],[7]] => 0001010 => 0101000 => 2
[[1,4,5,6,7],[2,8],[3]] => 1100001 => 1000011 => 3
[[1,3,5,6,7],[2,8],[4]] => 1010001 => 1000101 => 3
[[1,2,5,6,7],[3,8],[4]] => 0110001 => 1000110 => 3
[[1,3,4,6,7],[2,8],[5]] => 1001001 => 1001001 => 3
[[1,2,4,6,7],[3,8],[5]] => 0101001 => 1001010 => 3
[[1,2,3,6,7],[4,8],[5]] => 0011001 => 1001100 => 3
[[1,3,4,5,7],[2,8],[6]] => 1000101 => 1010001 => 3
[[1,2,4,5,7],[3,8],[6]] => 0100101 => 1010010 => 3
[[1,2,3,5,7],[4,8],[6]] => 0010101 => 1010100 => 3
[[1,2,3,4,7],[5,8],[6]] => 0001101 => 1011000 => 3
[[1,3,4,5,6],[2,8],[7]] => 1000010 => 0100001 => 2
[[1,2,4,5,6],[3,8],[7]] => 0100010 => 0100010 => 2
[[1,2,3,5,6],[4,8],[7]] => 0010010 => 0100100 => 2
[[1,2,3,4,6],[5,8],[7]] => 0001010 => 0101000 => 2
[[1,2,3,4,5],[6,8],[7]] => 0000110 => 0110000 => 2
[[1,3,5,6,7],[2,4],[8]] => 1010001 => 1000101 => 3
[[1,2,5,6,7],[3,4],[8]] => 0100001 => 1000010 => 2
[[1,3,4,6,7],[2,5],[8]] => 1001001 => 1001001 => 3
[[1,2,4,6,7],[3,5],[8]] => 0101001 => 1001010 => 3
[[1,2,3,6,7],[4,5],[8]] => 0010001 => 1000100 => 2
[[1,3,4,5,7],[2,6],[8]] => 1000101 => 1010001 => 3
[[1,2,4,5,7],[3,6],[8]] => 0100101 => 1010010 => 3
[[1,2,3,5,7],[4,6],[8]] => 0010101 => 1010100 => 3
[[1,2,3,4,7],[5,6],[8]] => 0001001 => 1001000 => 2
[[1,3,4,5,6],[2,7],[8]] => 1000011 => 1100001 => 3
[[1,2,4,5,6],[3,7],[8]] => 0100011 => 1100010 => 3
[[1,2,3,5,6],[4,7],[8]] => 0010011 => 1100100 => 3
[[1,2,3,4,6],[5,7],[8]] => 0001011 => 1101000 => 3
[[1,2,3,4,5],[6,7],[8]] => 0000101 => 1010000 => 2
[[1,5,6,7,8],[2],[3],[4]] => 1110000 => 0000111 => 3
[[1,4,6,7,8],[2],[3],[5]] => 1101000 => 0001011 => 3
[[1,3,6,7,8],[2],[4],[5]] => 1011000 => 0001101 => 3
[[1,2,6,7,8],[3],[4],[5]] => 0111000 => 0001110 => 3
[[1,4,5,7,8],[2],[3],[6]] => 1100100 => 0010011 => 3
[[1,3,5,7,8],[2],[4],[6]] => 1010100 => 0010101 => 3
[[1,2,5,7,8],[3],[4],[6]] => 0110100 => 0010110 => 3
[[1,3,4,7,8],[2],[5],[6]] => 1001100 => 0011001 => 3
[[1,2,4,7,8],[3],[5],[6]] => 0101100 => 0011010 => 3
[[1,2,3,7,8],[4],[5],[6]] => 0011100 => 0011100 => 3
[[1,4,5,6,8],[2],[3],[7]] => 1100010 => 0100011 => 3
[[1,3,5,6,8],[2],[4],[7]] => 1010010 => 0100101 => 3
[[1,2,5,6,8],[3],[4],[7]] => 0110010 => 0100110 => 3
[[1,3,4,6,8],[2],[5],[7]] => 1001010 => 0101001 => 3
[[1,2,4,6,8],[3],[5],[7]] => 0101010 => 0101010 => 3
[[1,2,3,6,8],[4],[5],[7]] => 0011010 => 0101100 => 3
[[1,3,4,5,8],[2],[6],[7]] => 1000110 => 0110001 => 3
[[1,2,4,5,8],[3],[6],[7]] => 0100110 => 0110010 => 3
[[1,2,3,5,8],[4],[6],[7]] => 0010110 => 0110100 => 3
[[1,2,3,4,8],[5],[6],[7]] => 0001110 => 0111000 => 3
[[1,4,5,6,7],[2],[3],[8]] => 1100001 => 1000011 => 3
[[1,3,5,6,7],[2],[4],[8]] => 1010001 => 1000101 => 3
[[1,2,5,6,7],[3],[4],[8]] => 0110001 => 1000110 => 3
[[1,3,4,6,7],[2],[5],[8]] => 1001001 => 1001001 => 3
[[1,2,4,6,7],[3],[5],[8]] => 0101001 => 1001010 => 3
[[1,2,3,6,7],[4],[5],[8]] => 0011001 => 1001100 => 3
[[1,3,4,5,7],[2],[6],[8]] => 1000101 => 1010001 => 3
[[1,2,4,5,7],[3],[6],[8]] => 0100101 => 1010010 => 3
[[1,2,3,5,7],[4],[6],[8]] => 0010101 => 1010100 => 3
[[1,2,3,4,7],[5],[6],[8]] => 0001101 => 1011000 => 3
[[1,3,4,5,6],[2],[7],[8]] => 1000011 => 1100001 => 3
[[1,2,4,5,6],[3],[7],[8]] => 0100011 => 1100010 => 3
[[1,2,3,5,6],[4],[7],[8]] => 0010011 => 1100100 => 3
[[1,2,3,4,6],[5],[7],[8]] => 0001011 => 1101000 => 3
[[1,2,3,4,5],[6],[7],[8]] => 0000111 => 1110000 => 3
[[1,3,5,7],[2,4,6,8]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3,4,6,8]] => 0100101 => 1010010 => 3
[[1,3,4,7],[2,5,6,8]] => 1001001 => 1001001 => 3
[[1,2,4,7],[3,5,6,8]] => 0101001 => 1001010 => 3
[[1,2,3,7],[4,5,6,8]] => 0010001 => 1000100 => 2
[[1,3,5,6],[2,4,7,8]] => 1010010 => 0100101 => 3
[[1,2,5,6],[3,4,7,8]] => 0100010 => 0100010 => 2
[[1,3,4,6],[2,5,7,8]] => 1001010 => 0101001 => 3
[[1,2,4,6],[3,5,7,8]] => 0101010 => 0101010 => 3
[[1,2,3,6],[4,5,7,8]] => 0010010 => 0100100 => 2
[[1,3,4,5],[2,6,7,8]] => 1000100 => 0010001 => 2
[[1,2,4,5],[3,6,7,8]] => 0100100 => 0010010 => 2
[[1,2,3,5],[4,6,7,8]] => 0010100 => 0010100 => 2
[[1,2,3,4],[5,6,7,8]] => 0001000 => 0001000 => 1
[[1,4,6,8],[2,5,7],[3]] => 1101010 => 0101011 => 4
[[1,3,6,8],[2,5,7],[4]] => 1010010 => 0100101 => 3
[[1,2,6,8],[3,5,7],[4]] => 0110010 => 0100110 => 3
[[1,3,6,8],[2,4,7],[5]] => 1011010 => 0101101 => 4
[[1,2,6,8],[3,4,7],[5]] => 0101010 => 0101010 => 3
[[1,4,5,8],[2,6,7],[3]] => 1100100 => 0010011 => 3
[[1,3,5,8],[2,6,7],[4]] => 1010100 => 0010101 => 3
[[1,2,5,8],[3,6,7],[4]] => 0110100 => 0010110 => 3
[[1,3,4,8],[2,6,7],[5]] => 1001000 => 0001001 => 2
[[1,2,4,8],[3,6,7],[5]] => 0101000 => 0001010 => 2
[[1,2,3,8],[4,6,7],[5]] => 0011000 => 0001100 => 2
[[1,3,5,8],[2,4,7],[6]] => 1010100 => 0010101 => 3
[[1,2,5,8],[3,4,7],[6]] => 0100100 => 0010010 => 2
[[1,3,4,8],[2,5,7],[6]] => 1001100 => 0011001 => 3
[[1,2,4,8],[3,5,7],[6]] => 0101100 => 0011010 => 3
[[1,2,3,8],[4,5,7],[6]] => 0010100 => 0010100 => 2
[[1,3,5,8],[2,4,6],[7]] => 1010110 => 0110101 => 4
[[1,2,5,8],[3,4,6],[7]] => 0100110 => 0110010 => 3
[[1,3,4,8],[2,5,6],[7]] => 1001010 => 0101001 => 3
[[1,2,4,8],[3,5,6],[7]] => 0101010 => 0101010 => 3
[[1,2,3,8],[4,5,6],[7]] => 0010010 => 0100100 => 2
[[1,4,6,7],[2,5,8],[3]] => 1101001 => 1001011 => 4
[[1,3,6,7],[2,5,8],[4]] => 1010001 => 1000101 => 3
[[1,2,6,7],[3,5,8],[4]] => 0110001 => 1000110 => 3
[[1,3,6,7],[2,4,8],[5]] => 1011001 => 1001101 => 4
[[1,2,6,7],[3,4,8],[5]] => 0101001 => 1001010 => 3
[[1,4,5,7],[2,6,8],[3]] => 1100101 => 1010011 => 4
[[1,3,5,7],[2,6,8],[4]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3,6,8],[4]] => 0110101 => 1010110 => 4
[[1,3,4,7],[2,6,8],[5]] => 1001001 => 1001001 => 3
[[1,2,4,7],[3,6,8],[5]] => 0101001 => 1001010 => 3
[[1,2,3,7],[4,6,8],[5]] => 0011001 => 1001100 => 3
[[1,3,5,7],[2,4,8],[6]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3,4,8],[6]] => 0100101 => 1010010 => 3
[[1,3,4,7],[2,5,8],[6]] => 1001101 => 1011001 => 4
[[1,2,4,7],[3,5,8],[6]] => 0101101 => 1011010 => 4
[[1,2,3,7],[4,5,8],[6]] => 0010101 => 1010100 => 3
[[1,4,5,6],[2,7,8],[3]] => 1100010 => 0100011 => 3
[[1,3,5,6],[2,7,8],[4]] => 1010010 => 0100101 => 3
[[1,2,5,6],[3,7,8],[4]] => 0110010 => 0100110 => 3
[[1,3,4,6],[2,7,8],[5]] => 1001010 => 0101001 => 3
[[1,2,4,6],[3,7,8],[5]] => 0101010 => 0101010 => 3
[[1,2,3,6],[4,7,8],[5]] => 0011010 => 0101100 => 3
[[1,3,4,5],[2,7,8],[6]] => 1000100 => 0010001 => 2
[[1,2,4,5],[3,7,8],[6]] => 0100100 => 0010010 => 2
[[1,2,3,5],[4,7,8],[6]] => 0010100 => 0010100 => 2
[[1,2,3,4],[5,7,8],[6]] => 0001100 => 0011000 => 2
[[1,3,5,6],[2,4,8],[7]] => 1010010 => 0100101 => 3
[[1,2,5,6],[3,4,8],[7]] => 0100010 => 0100010 => 2
[[1,3,4,6],[2,5,8],[7]] => 1001010 => 0101001 => 3
[[1,2,4,6],[3,5,8],[7]] => 0101010 => 0101010 => 3
[[1,2,3,6],[4,5,8],[7]] => 0010010 => 0100100 => 2
[[1,3,4,5],[2,6,8],[7]] => 1000110 => 0110001 => 3
[[1,2,4,5],[3,6,8],[7]] => 0100110 => 0110010 => 3
[[1,2,3,5],[4,6,8],[7]] => 0010110 => 0110100 => 3
[[1,2,3,4],[5,6,8],[7]] => 0001010 => 0101000 => 2
[[1,3,5,7],[2,4,6],[8]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3,4,6],[8]] => 0100101 => 1010010 => 3
[[1,3,4,7],[2,5,6],[8]] => 1001001 => 1001001 => 3
[[1,2,4,7],[3,5,6],[8]] => 0101001 => 1001010 => 3
[[1,2,3,7],[4,5,6],[8]] => 0010001 => 1000100 => 2
[[1,3,5,6],[2,4,7],[8]] => 1010011 => 1100101 => 4
[[1,2,5,6],[3,4,7],[8]] => 0100011 => 1100010 => 3
[[1,3,4,6],[2,5,7],[8]] => 1001011 => 1101001 => 4
[[1,2,4,6],[3,5,7],[8]] => 0101011 => 1101010 => 4
[[1,2,3,6],[4,5,7],[8]] => 0010011 => 1100100 => 3
[[1,3,4,5],[2,6,7],[8]] => 1000101 => 1010001 => 3
[[1,2,4,5],[3,6,7],[8]] => 0100101 => 1010010 => 3
[[1,2,3,5],[4,6,7],[8]] => 0010101 => 1010100 => 3
[[1,2,3,4],[5,6,7],[8]] => 0001001 => 1001000 => 2
[[1,4,7,8],[2,5],[3,6]] => 1101100 => 0011011 => 4
[[1,3,7,8],[2,5],[4,6]] => 1010100 => 0010101 => 3
[[1,2,7,8],[3,5],[4,6]] => 0110100 => 0010110 => 3
[[1,3,7,8],[2,4],[5,6]] => 1011000 => 0001101 => 3
[[1,2,7,8],[3,4],[5,6]] => 0101000 => 0001010 => 2
[[1,4,6,8],[2,5],[3,7]] => 1101010 => 0101011 => 4
[[1,3,6,8],[2,5],[4,7]] => 1010010 => 0100101 => 3
[[1,2,6,8],[3,5],[4,7]] => 0110010 => 0100110 => 3
[[1,3,6,8],[2,4],[5,7]] => 1011010 => 0101101 => 4
[[1,2,6,8],[3,4],[5,7]] => 0101010 => 0101010 => 3
[[1,4,5,8],[2,6],[3,7]] => 1100110 => 0110011 => 4
[[1,3,5,8],[2,6],[4,7]] => 1010110 => 0110101 => 4
[[1,2,5,8],[3,6],[4,7]] => 0110110 => 0110110 => 4
[[1,3,4,8],[2,6],[5,7]] => 1001010 => 0101001 => 3
[[1,2,4,8],[3,6],[5,7]] => 0101010 => 0101010 => 3
[[1,2,3,8],[4,6],[5,7]] => 0011010 => 0101100 => 3
[[1,3,5,8],[2,4],[6,7]] => 1010100 => 0010101 => 3
[[1,2,5,8],[3,4],[6,7]] => 0100100 => 0010010 => 2
[[1,3,4,8],[2,5],[6,7]] => 1001100 => 0011001 => 3
[[1,2,4,8],[3,5],[6,7]] => 0101100 => 0011010 => 3
[[1,2,3,8],[4,5],[6,7]] => 0010100 => 0010100 => 2
[[1,4,6,7],[2,5],[3,8]] => 1101001 => 1001011 => 4
[[1,3,6,7],[2,5],[4,8]] => 1010001 => 1000101 => 3
[[1,2,6,7],[3,5],[4,8]] => 0110001 => 1000110 => 3
[[1,3,6,7],[2,4],[5,8]] => 1011001 => 1001101 => 4
[[1,2,6,7],[3,4],[5,8]] => 0101001 => 1001010 => 3
[[1,4,5,7],[2,6],[3,8]] => 1100101 => 1010011 => 4
[[1,3,5,7],[2,6],[4,8]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3,6],[4,8]] => 0110101 => 1010110 => 4
[[1,3,4,7],[2,6],[5,8]] => 1001001 => 1001001 => 3
[[1,2,4,7],[3,6],[5,8]] => 0101001 => 1001010 => 3
[[1,2,3,7],[4,6],[5,8]] => 0011001 => 1001100 => 3
[[1,3,5,7],[2,4],[6,8]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3,4],[6,8]] => 0100101 => 1010010 => 3
[[1,3,4,7],[2,5],[6,8]] => 1001101 => 1011001 => 4
[[1,2,4,7],[3,5],[6,8]] => 0101101 => 1011010 => 4
[[1,2,3,7],[4,5],[6,8]] => 0010101 => 1010100 => 3
[[1,4,5,6],[2,7],[3,8]] => 1100011 => 1100011 => 4
[[1,3,5,6],[2,7],[4,8]] => 1010011 => 1100101 => 4
[[1,2,5,6],[3,7],[4,8]] => 0110011 => 1100110 => 4
[[1,3,4,6],[2,7],[5,8]] => 1001011 => 1101001 => 4
[[1,2,4,6],[3,7],[5,8]] => 0101011 => 1101010 => 4
[[1,2,3,6],[4,7],[5,8]] => 0011011 => 1101100 => 4
[[1,3,4,5],[2,7],[6,8]] => 1000101 => 1010001 => 3
[[1,2,4,5],[3,7],[6,8]] => 0100101 => 1010010 => 3
[[1,2,3,5],[4,7],[6,8]] => 0010101 => 1010100 => 3
[[1,2,3,4],[5,7],[6,8]] => 0001101 => 1011000 => 3
[[1,3,5,6],[2,4],[7,8]] => 1010010 => 0100101 => 3
[[1,2,5,6],[3,4],[7,8]] => 0100010 => 0100010 => 2
[[1,3,4,6],[2,5],[7,8]] => 1001010 => 0101001 => 3
[[1,2,4,6],[3,5],[7,8]] => 0101010 => 0101010 => 3
[[1,2,3,6],[4,5],[7,8]] => 0010010 => 0100100 => 2
[[1,3,4,5],[2,6],[7,8]] => 1000110 => 0110001 => 3
[[1,2,4,5],[3,6],[7,8]] => 0100110 => 0110010 => 3
[[1,2,3,5],[4,6],[7,8]] => 0010110 => 0110100 => 3
[[1,2,3,4],[5,6],[7,8]] => 0001010 => 0101000 => 2
[[1,5,7,8],[2,6],[3],[4]] => 1110100 => 0010111 => 4
[[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0001011 => 3
[[1,3,7,8],[2,6],[4],[5]] => 1011000 => 0001101 => 3
[[1,2,7,8],[3,6],[4],[5]] => 0111000 => 0001110 => 3
[[1,4,7,8],[2,5],[3],[6]] => 1101100 => 0011011 => 4
[[1,3,7,8],[2,5],[4],[6]] => 1010100 => 0010101 => 3
[[1,2,7,8],[3,5],[4],[6]] => 0110100 => 0010110 => 3
[[1,3,7,8],[2,4],[5],[6]] => 1011100 => 0011101 => 4
[[1,2,7,8],[3,4],[5],[6]] => 0101100 => 0011010 => 3
[[1,5,6,8],[2,7],[3],[4]] => 1110010 => 0100111 => 4
[[1,4,6,8],[2,7],[3],[5]] => 1101010 => 0101011 => 4
[[1,3,6,8],[2,7],[4],[5]] => 1011010 => 0101101 => 4
[[1,2,6,8],[3,7],[4],[5]] => 0111010 => 0101110 => 4
[[1,4,5,8],[2,7],[3],[6]] => 1100100 => 0010011 => 3
[[1,3,5,8],[2,7],[4],[6]] => 1010100 => 0010101 => 3
[[1,2,5,8],[3,7],[4],[6]] => 0110100 => 0010110 => 3
[[1,3,4,8],[2,7],[5],[6]] => 1001100 => 0011001 => 3
[[1,2,4,8],[3,7],[5],[6]] => 0101100 => 0011010 => 3
[[1,2,3,8],[4,7],[5],[6]] => 0011100 => 0011100 => 3
[[1,4,6,8],[2,5],[3],[7]] => 1101010 => 0101011 => 4
[[1,3,6,8],[2,5],[4],[7]] => 1010010 => 0100101 => 3
[[1,2,6,8],[3,5],[4],[7]] => 0110010 => 0100110 => 3
[[1,3,6,8],[2,4],[5],[7]] => 1011010 => 0101101 => 4
[[1,2,6,8],[3,4],[5],[7]] => 0101010 => 0101010 => 3
[[1,4,5,8],[2,6],[3],[7]] => 1100110 => 0110011 => 4
[[1,3,5,8],[2,6],[4],[7]] => 1010110 => 0110101 => 4
[[1,2,5,8],[3,6],[4],[7]] => 0110110 => 0110110 => 4
[[1,3,4,8],[2,6],[5],[7]] => 1001010 => 0101001 => 3
[[1,2,4,8],[3,6],[5],[7]] => 0101010 => 0101010 => 3
[[1,2,3,8],[4,6],[5],[7]] => 0011010 => 0101100 => 3
[[1,3,5,8],[2,4],[6],[7]] => 1010110 => 0110101 => 4
[[1,2,5,8],[3,4],[6],[7]] => 0100110 => 0110010 => 3
[[1,3,4,8],[2,5],[6],[7]] => 1001110 => 0111001 => 4
[[1,2,4,8],[3,5],[6],[7]] => 0101110 => 0111010 => 4
[[1,2,3,8],[4,5],[6],[7]] => 0010110 => 0110100 => 3
[[1,5,6,7],[2,8],[3],[4]] => 1110001 => 1000111 => 4
[[1,4,6,7],[2,8],[3],[5]] => 1101001 => 1001011 => 4
[[1,3,6,7],[2,8],[4],[5]] => 1011001 => 1001101 => 4
[[1,2,6,7],[3,8],[4],[5]] => 0111001 => 1001110 => 4
[[1,4,5,7],[2,8],[3],[6]] => 1100101 => 1010011 => 4
[[1,3,5,7],[2,8],[4],[6]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3,8],[4],[6]] => 0110101 => 1010110 => 4
[[1,3,4,7],[2,8],[5],[6]] => 1001101 => 1011001 => 4
[[1,2,4,7],[3,8],[5],[6]] => 0101101 => 1011010 => 4
[[1,2,3,7],[4,8],[5],[6]] => 0011101 => 1011100 => 4
[[1,4,5,6],[2,8],[3],[7]] => 1100010 => 0100011 => 3
[[1,3,5,6],[2,8],[4],[7]] => 1010010 => 0100101 => 3
[[1,2,5,6],[3,8],[4],[7]] => 0110010 => 0100110 => 3
[[1,3,4,6],[2,8],[5],[7]] => 1001010 => 0101001 => 3
[[1,2,4,6],[3,8],[5],[7]] => 0101010 => 0101010 => 3
[[1,2,3,6],[4,8],[5],[7]] => 0011010 => 0101100 => 3
[[1,3,4,5],[2,8],[6],[7]] => 1000110 => 0110001 => 3
[[1,2,4,5],[3,8],[6],[7]] => 0100110 => 0110010 => 3
[[1,2,3,5],[4,8],[6],[7]] => 0010110 => 0110100 => 3
[[1,2,3,4],[5,8],[6],[7]] => 0001110 => 0111000 => 3
[[1,4,6,7],[2,5],[3],[8]] => 1101001 => 1001011 => 4
[[1,3,6,7],[2,5],[4],[8]] => 1010001 => 1000101 => 3
[[1,2,6,7],[3,5],[4],[8]] => 0110001 => 1000110 => 3
[[1,3,6,7],[2,4],[5],[8]] => 1011001 => 1001101 => 4
[[1,2,6,7],[3,4],[5],[8]] => 0101001 => 1001010 => 3
[[1,4,5,7],[2,6],[3],[8]] => 1100101 => 1010011 => 4
[[1,3,5,7],[2,6],[4],[8]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3,6],[4],[8]] => 0110101 => 1010110 => 4
[[1,3,4,7],[2,6],[5],[8]] => 1001001 => 1001001 => 3
[[1,2,4,7],[3,6],[5],[8]] => 0101001 => 1001010 => 3
[[1,2,3,7],[4,6],[5],[8]] => 0011001 => 1001100 => 3
[[1,3,5,7],[2,4],[6],[8]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3,4],[6],[8]] => 0100101 => 1010010 => 3
[[1,3,4,7],[2,5],[6],[8]] => 1001101 => 1011001 => 4
[[1,2,4,7],[3,5],[6],[8]] => 0101101 => 1011010 => 4
[[1,2,3,7],[4,5],[6],[8]] => 0010101 => 1010100 => 3
[[1,4,5,6],[2,7],[3],[8]] => 1100011 => 1100011 => 4
[[1,3,5,6],[2,7],[4],[8]] => 1010011 => 1100101 => 4
[[1,2,5,6],[3,7],[4],[8]] => 0110011 => 1100110 => 4
[[1,3,4,6],[2,7],[5],[8]] => 1001011 => 1101001 => 4
[[1,2,4,6],[3,7],[5],[8]] => 0101011 => 1101010 => 4
[[1,2,3,6],[4,7],[5],[8]] => 0011011 => 1101100 => 4
[[1,3,4,5],[2,7],[6],[8]] => 1000101 => 1010001 => 3
[[1,2,4,5],[3,7],[6],[8]] => 0100101 => 1010010 => 3
[[1,2,3,5],[4,7],[6],[8]] => 0010101 => 1010100 => 3
[[1,2,3,4],[5,7],[6],[8]] => 0001101 => 1011000 => 3
[[1,3,5,6],[2,4],[7],[8]] => 1010011 => 1100101 => 4
[[1,2,5,6],[3,4],[7],[8]] => 0100011 => 1100010 => 3
[[1,3,4,6],[2,5],[7],[8]] => 1001011 => 1101001 => 4
[[1,2,4,6],[3,5],[7],[8]] => 0101011 => 1101010 => 4
[[1,2,3,6],[4,5],[7],[8]] => 0010011 => 1100100 => 3
[[1,3,4,5],[2,6],[7],[8]] => 1000111 => 1110001 => 4
[[1,2,4,5],[3,6],[7],[8]] => 0100111 => 1110010 => 4
[[1,2,3,5],[4,6],[7],[8]] => 0010111 => 1110100 => 4
[[1,2,3,4],[5,6],[7],[8]] => 0001011 => 1101000 => 3
[[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 0001111 => 4
[[1,5,7,8],[2],[3],[4],[6]] => 1110100 => 0010111 => 4
[[1,4,7,8],[2],[3],[5],[6]] => 1101100 => 0011011 => 4
[[1,3,7,8],[2],[4],[5],[6]] => 1011100 => 0011101 => 4
[[1,2,7,8],[3],[4],[5],[6]] => 0111100 => 0011110 => 4
[[1,5,6,8],[2],[3],[4],[7]] => 1110010 => 0100111 => 4
[[1,4,6,8],[2],[3],[5],[7]] => 1101010 => 0101011 => 4
[[1,3,6,8],[2],[4],[5],[7]] => 1011010 => 0101101 => 4
[[1,2,6,8],[3],[4],[5],[7]] => 0111010 => 0101110 => 4
[[1,4,5,8],[2],[3],[6],[7]] => 1100110 => 0110011 => 4
[[1,3,5,8],[2],[4],[6],[7]] => 1010110 => 0110101 => 4
[[1,2,5,8],[3],[4],[6],[7]] => 0110110 => 0110110 => 4
[[1,3,4,8],[2],[5],[6],[7]] => 1001110 => 0111001 => 4
[[1,2,4,8],[3],[5],[6],[7]] => 0101110 => 0111010 => 4
[[1,2,3,8],[4],[5],[6],[7]] => 0011110 => 0111100 => 4
[[1,5,6,7],[2],[3],[4],[8]] => 1110001 => 1000111 => 4
[[1,4,6,7],[2],[3],[5],[8]] => 1101001 => 1001011 => 4
[[1,3,6,7],[2],[4],[5],[8]] => 1011001 => 1001101 => 4
[[1,2,6,7],[3],[4],[5],[8]] => 0111001 => 1001110 => 4
[[1,4,5,7],[2],[3],[6],[8]] => 1100101 => 1010011 => 4
[[1,3,5,7],[2],[4],[6],[8]] => 1010101 => 1010101 => 4
[[1,2,5,7],[3],[4],[6],[8]] => 0110101 => 1010110 => 4
[[1,3,4,7],[2],[5],[6],[8]] => 1001101 => 1011001 => 4
[[1,2,4,7],[3],[5],[6],[8]] => 0101101 => 1011010 => 4
[[1,2,3,7],[4],[5],[6],[8]] => 0011101 => 1011100 => 4
[[1,4,5,6],[2],[3],[7],[8]] => 1100011 => 1100011 => 4
[[1,3,5,6],[2],[4],[7],[8]] => 1010011 => 1100101 => 4
[[1,2,5,6],[3],[4],[7],[8]] => 0110011 => 1100110 => 4
[[1,3,4,6],[2],[5],[7],[8]] => 1001011 => 1101001 => 4
[[1,2,4,6],[3],[5],[7],[8]] => 0101011 => 1101010 => 4
[[1,2,3,6],[4],[5],[7],[8]] => 0011011 => 1101100 => 4
[[1,3,4,5],[2],[6],[7],[8]] => 1000111 => 1110001 => 4
[[1,2,4,5],[3],[6],[7],[8]] => 0100111 => 1110010 => 4
[[1,2,3,5],[4],[6],[7],[8]] => 0010111 => 1110100 => 4
[[1,2,3,4],[5],[6],[7],[8]] => 0001111 => 1111000 => 4
[[1,4,7],[2,5,8],[3,6]] => 1101101 => 1011011 => 5
[[1,3,7],[2,5,8],[4,6]] => 1010101 => 1010101 => 4
[[1,2,7],[3,5,8],[4,6]] => 0110101 => 1010110 => 4
[[1,3,7],[2,4,8],[5,6]] => 1011001 => 1001101 => 4
[[1,2,7],[3,4,8],[5,6]] => 0101001 => 1001010 => 3
[[1,4,6],[2,5,8],[3,7]] => 1101010 => 0101011 => 4
[[1,3,6],[2,5,8],[4,7]] => 1010010 => 0100101 => 3
[[1,2,6],[3,5,8],[4,7]] => 0110010 => 0100110 => 3
[[1,3,6],[2,4,8],[5,7]] => 1011010 => 0101101 => 4
[[1,2,6],[3,4,8],[5,7]] => 0101010 => 0101010 => 3
[[1,4,5],[2,6,8],[3,7]] => 1100110 => 0110011 => 4
[[1,3,5],[2,6,8],[4,7]] => 1010110 => 0110101 => 4
[[1,2,5],[3,6,8],[4,7]] => 0110110 => 0110110 => 4
[[1,3,4],[2,6,8],[5,7]] => 1001010 => 0101001 => 3
[[1,2,4],[3,6,8],[5,7]] => 0101010 => 0101010 => 3
[[1,2,3],[4,6,8],[5,7]] => 0011010 => 0101100 => 3
[[1,3,5],[2,4,8],[6,7]] => 1010100 => 0010101 => 3
[[1,2,5],[3,4,8],[6,7]] => 0100100 => 0010010 => 2
[[1,3,4],[2,5,8],[6,7]] => 1001100 => 0011001 => 3
[[1,2,4],[3,5,8],[6,7]] => 0101100 => 0011010 => 3
[[1,2,3],[4,5,8],[6,7]] => 0010100 => 0010100 => 2
[[1,4,6],[2,5,7],[3,8]] => 1101011 => 1101011 => 5
[[1,3,6],[2,5,7],[4,8]] => 1010011 => 1100101 => 4
[[1,2,6],[3,5,7],[4,8]] => 0110011 => 1100110 => 4
[[1,3,6],[2,4,7],[5,8]] => 1011011 => 1101101 => 5
[[1,2,6],[3,4,7],[5,8]] => 0101011 => 1101010 => 4
[[1,4,5],[2,6,7],[3,8]] => 1100101 => 1010011 => 4
[[1,3,5],[2,6,7],[4,8]] => 1010101 => 1010101 => 4
[[1,2,5],[3,6,7],[4,8]] => 0110101 => 1010110 => 4
[[1,3,4],[2,6,7],[5,8]] => 1001001 => 1001001 => 3
[[1,2,4],[3,6,7],[5,8]] => 0101001 => 1001010 => 3
[[1,2,3],[4,6,7],[5,8]] => 0011001 => 1001100 => 3
[[1,3,5],[2,4,7],[6,8]] => 1010101 => 1010101 => 4
[[1,2,5],[3,4,7],[6,8]] => 0100101 => 1010010 => 3
[[1,3,4],[2,5,7],[6,8]] => 1001101 => 1011001 => 4
[[1,2,4],[3,5,7],[6,8]] => 0101101 => 1011010 => 4
[[1,2,3],[4,5,7],[6,8]] => 0010101 => 1010100 => 3
[[1,3,5],[2,4,6],[7,8]] => 1010110 => 0110101 => 4
[[1,2,5],[3,4,6],[7,8]] => 0100110 => 0110010 => 3
[[1,3,4],[2,5,6],[7,8]] => 1001010 => 0101001 => 3
[[1,2,4],[3,5,6],[7,8]] => 0101010 => 0101010 => 3
[[1,2,3],[4,5,6],[7,8]] => 0010010 => 0100100 => 2
[[1,5,7],[2,6,8],[3],[4]] => 1110101 => 1010111 => 5
[[1,4,7],[2,6,8],[3],[5]] => 1101001 => 1001011 => 4
[[1,3,7],[2,6,8],[4],[5]] => 1011001 => 1001101 => 4
[[1,2,7],[3,6,8],[4],[5]] => 0111001 => 1001110 => 4
[[1,4,7],[2,5,8],[3],[6]] => 1101101 => 1011011 => 5
[[1,3,7],[2,5,8],[4],[6]] => 1010101 => 1010101 => 4
[[1,2,7],[3,5,8],[4],[6]] => 0110101 => 1010110 => 4
[[1,3,7],[2,4,8],[5],[6]] => 1011101 => 1011101 => 5
[[1,2,7],[3,4,8],[5],[6]] => 0101101 => 1011010 => 4
[[1,5,6],[2,7,8],[3],[4]] => 1110010 => 0100111 => 4
[[1,4,6],[2,7,8],[3],[5]] => 1101010 => 0101011 => 4
[[1,3,6],[2,7,8],[4],[5]] => 1011010 => 0101101 => 4
[[1,2,6],[3,7,8],[4],[5]] => 0111010 => 0101110 => 4
[[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0010011 => 3
[[1,3,5],[2,7,8],[4],[6]] => 1010100 => 0010101 => 3
[[1,2,5],[3,7,8],[4],[6]] => 0110100 => 0010110 => 3
[[1,3,4],[2,7,8],[5],[6]] => 1001100 => 0011001 => 3
[[1,2,4],[3,7,8],[5],[6]] => 0101100 => 0011010 => 3
[[1,2,3],[4,7,8],[5],[6]] => 0011100 => 0011100 => 3
[[1,4,6],[2,5,8],[3],[7]] => 1101010 => 0101011 => 4
[[1,3,6],[2,5,8],[4],[7]] => 1010010 => 0100101 => 3
[[1,2,6],[3,5,8],[4],[7]] => 0110010 => 0100110 => 3
[[1,3,6],[2,4,8],[5],[7]] => 1011010 => 0101101 => 4
[[1,2,6],[3,4,8],[5],[7]] => 0101010 => 0101010 => 3
[[1,4,5],[2,6,8],[3],[7]] => 1100110 => 0110011 => 4
[[1,3,5],[2,6,8],[4],[7]] => 1010110 => 0110101 => 4
[[1,2,5],[3,6,8],[4],[7]] => 0110110 => 0110110 => 4
[[1,3,4],[2,6,8],[5],[7]] => 1001010 => 0101001 => 3
[[1,2,4],[3,6,8],[5],[7]] => 0101010 => 0101010 => 3
[[1,2,3],[4,6,8],[5],[7]] => 0011010 => 0101100 => 3
[[1,3,5],[2,4,8],[6],[7]] => 1010110 => 0110101 => 4
[[1,2,5],[3,4,8],[6],[7]] => 0100110 => 0110010 => 3
[[1,3,4],[2,5,8],[6],[7]] => 1001110 => 0111001 => 4
[[1,2,4],[3,5,8],[6],[7]] => 0101110 => 0111010 => 4
[[1,2,3],[4,5,8],[6],[7]] => 0010110 => 0110100 => 3
[[1,4,6],[2,5,7],[3],[8]] => 1101011 => 1101011 => 5
[[1,3,6],[2,5,7],[4],[8]] => 1010011 => 1100101 => 4
[[1,2,6],[3,5,7],[4],[8]] => 0110011 => 1100110 => 4
[[1,3,6],[2,4,7],[5],[8]] => 1011011 => 1101101 => 5
[[1,2,6],[3,4,7],[5],[8]] => 0101011 => 1101010 => 4
[[1,4,5],[2,6,7],[3],[8]] => 1100101 => 1010011 => 4
[[1,3,5],[2,6,7],[4],[8]] => 1010101 => 1010101 => 4
[[1,2,5],[3,6,7],[4],[8]] => 0110101 => 1010110 => 4
[[1,3,4],[2,6,7],[5],[8]] => 1001001 => 1001001 => 3
[[1,2,4],[3,6,7],[5],[8]] => 0101001 => 1001010 => 3
[[1,2,3],[4,6,7],[5],[8]] => 0011001 => 1001100 => 3
[[1,3,5],[2,4,7],[6],[8]] => 1010101 => 1010101 => 4
[[1,2,5],[3,4,7],[6],[8]] => 0100101 => 1010010 => 3
[[1,3,4],[2,5,7],[6],[8]] => 1001101 => 1011001 => 4
[[1,2,4],[3,5,7],[6],[8]] => 0101101 => 1011010 => 4
[[1,2,3],[4,5,7],[6],[8]] => 0010101 => 1010100 => 3
[[1,3,5],[2,4,6],[7],[8]] => 1010111 => 1110101 => 5
[[1,2,5],[3,4,6],[7],[8]] => 0100111 => 1110010 => 4
[[1,3,4],[2,5,6],[7],[8]] => 1001011 => 1101001 => 4
[[1,2,4],[3,5,6],[7],[8]] => 0101011 => 1101010 => 4
[[1,2,3],[4,5,6],[7],[8]] => 0010011 => 1100100 => 3
[[1,5,8],[2,6],[3,7],[4]] => 1110110 => 0110111 => 5
[[1,4,8],[2,6],[3,7],[5]] => 1101010 => 0101011 => 4
[[1,3,8],[2,6],[4,7],[5]] => 1011010 => 0101101 => 4
[[1,2,8],[3,6],[4,7],[5]] => 0111010 => 0101110 => 4
[[1,4,8],[2,5],[3,7],[6]] => 1101100 => 0011011 => 4
[[1,3,8],[2,5],[4,7],[6]] => 1010100 => 0010101 => 3
[[1,2,8],[3,5],[4,7],[6]] => 0110100 => 0010110 => 3
[[1,3,8],[2,4],[5,7],[6]] => 1011100 => 0011101 => 4
[[1,2,8],[3,4],[5,7],[6]] => 0101100 => 0011010 => 3
[[1,4,8],[2,5],[3,6],[7]] => 1101110 => 0111011 => 5
[[1,3,8],[2,5],[4,6],[7]] => 1010110 => 0110101 => 4
[[1,2,8],[3,5],[4,6],[7]] => 0110110 => 0110110 => 4
[[1,3,8],[2,4],[5,6],[7]] => 1011010 => 0101101 => 4
[[1,2,8],[3,4],[5,6],[7]] => 0101010 => 0101010 => 3
[[1,5,7],[2,6],[3,8],[4]] => 1110101 => 1010111 => 5
[[1,4,7],[2,6],[3,8],[5]] => 1101001 => 1001011 => 4
[[1,3,7],[2,6],[4,8],[5]] => 1011001 => 1001101 => 4
[[1,2,7],[3,6],[4,8],[5]] => 0111001 => 1001110 => 4
[[1,4,7],[2,5],[3,8],[6]] => 1101101 => 1011011 => 5
[[1,3,7],[2,5],[4,8],[6]] => 1010101 => 1010101 => 4
[[1,2,7],[3,5],[4,8],[6]] => 0110101 => 1010110 => 4
[[1,3,7],[2,4],[5,8],[6]] => 1011101 => 1011101 => 5
[[1,2,7],[3,4],[5,8],[6]] => 0101101 => 1011010 => 4
[[1,5,6],[2,7],[3,8],[4]] => 1110011 => 1100111 => 5
[[1,4,6],[2,7],[3,8],[5]] => 1101011 => 1101011 => 5
[[1,3,6],[2,7],[4,8],[5]] => 1011011 => 1101101 => 5
[[1,2,6],[3,7],[4,8],[5]] => 0111011 => 1101110 => 5
[[1,4,5],[2,7],[3,8],[6]] => 1100101 => 1010011 => 4
[[1,3,5],[2,7],[4,8],[6]] => 1010101 => 1010101 => 4
[[1,2,5],[3,7],[4,8],[6]] => 0110101 => 1010110 => 4
[[1,3,4],[2,7],[5,8],[6]] => 1001101 => 1011001 => 4
[[1,2,4],[3,7],[5,8],[6]] => 0101101 => 1011010 => 4
[[1,2,3],[4,7],[5,8],[6]] => 0011101 => 1011100 => 4
[[1,4,6],[2,5],[3,8],[7]] => 1101010 => 0101011 => 4
[[1,3,6],[2,5],[4,8],[7]] => 1010010 => 0100101 => 3
[[1,2,6],[3,5],[4,8],[7]] => 0110010 => 0100110 => 3
[[1,3,6],[2,4],[5,8],[7]] => 1011010 => 0101101 => 4
[[1,2,6],[3,4],[5,8],[7]] => 0101010 => 0101010 => 3
[[1,4,5],[2,6],[3,8],[7]] => 1100110 => 0110011 => 4
[[1,3,5],[2,6],[4,8],[7]] => 1010110 => 0110101 => 4
[[1,2,5],[3,6],[4,8],[7]] => 0110110 => 0110110 => 4
[[1,3,4],[2,6],[5,8],[7]] => 1001010 => 0101001 => 3
[[1,2,4],[3,6],[5,8],[7]] => 0101010 => 0101010 => 3
[[1,2,3],[4,6],[5,8],[7]] => 0011010 => 0101100 => 3
[[1,3,5],[2,4],[6,8],[7]] => 1010110 => 0110101 => 4
[[1,2,5],[3,4],[6,8],[7]] => 0100110 => 0110010 => 3
[[1,3,4],[2,5],[6,8],[7]] => 1001110 => 0111001 => 4
[[1,2,4],[3,5],[6,8],[7]] => 0101110 => 0111010 => 4
[[1,2,3],[4,5],[6,8],[7]] => 0010110 => 0110100 => 3
[[1,4,7],[2,5],[3,6],[8]] => 1101101 => 1011011 => 5
[[1,3,7],[2,5],[4,6],[8]] => 1010101 => 1010101 => 4
[[1,2,7],[3,5],[4,6],[8]] => 0110101 => 1010110 => 4
[[1,3,7],[2,4],[5,6],[8]] => 1011001 => 1001101 => 4
[[1,2,7],[3,4],[5,6],[8]] => 0101001 => 1001010 => 3
[[1,4,6],[2,5],[3,7],[8]] => 1101011 => 1101011 => 5
[[1,3,6],[2,5],[4,7],[8]] => 1010011 => 1100101 => 4
[[1,2,6],[3,5],[4,7],[8]] => 0110011 => 1100110 => 4
[[1,3,6],[2,4],[5,7],[8]] => 1011011 => 1101101 => 5
[[1,2,6],[3,4],[5,7],[8]] => 0101011 => 1101010 => 4
[[1,4,5],[2,6],[3,7],[8]] => 1100111 => 1110011 => 5
[[1,3,5],[2,6],[4,7],[8]] => 1010111 => 1110101 => 5
[[1,2,5],[3,6],[4,7],[8]] => 0110111 => 1110110 => 5
[[1,3,4],[2,6],[5,7],[8]] => 1001011 => 1101001 => 4
[[1,2,4],[3,6],[5,7],[8]] => 0101011 => 1101010 => 4
[[1,2,3],[4,6],[5,7],[8]] => 0011011 => 1101100 => 4
[[1,3,5],[2,4],[6,7],[8]] => 1010101 => 1010101 => 4
[[1,2,5],[3,4],[6,7],[8]] => 0100101 => 1010010 => 3
[[1,3,4],[2,5],[6,7],[8]] => 1001101 => 1011001 => 4
[[1,2,4],[3,5],[6,7],[8]] => 0101101 => 1011010 => 4
[[1,2,3],[4,5],[6,7],[8]] => 0010101 => 1010100 => 3
[[1,6,8],[2,7],[3],[4],[5]] => 1111010 => 0101111 => 5
[[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 0010111 => 4
[[1,4,8],[2,7],[3],[5],[6]] => 1101100 => 0011011 => 4
[[1,3,8],[2,7],[4],[5],[6]] => 1011100 => 0011101 => 4
[[1,2,8],[3,7],[4],[5],[6]] => 0111100 => 0011110 => 4
[[1,5,8],[2,6],[3],[4],[7]] => 1110110 => 0110111 => 5
[[1,4,8],[2,6],[3],[5],[7]] => 1101010 => 0101011 => 4
[[1,3,8],[2,6],[4],[5],[7]] => 1011010 => 0101101 => 4
[[1,2,8],[3,6],[4],[5],[7]] => 0111010 => 0101110 => 4
[[1,4,8],[2,5],[3],[6],[7]] => 1101110 => 0111011 => 5
[[1,3,8],[2,5],[4],[6],[7]] => 1010110 => 0110101 => 4
[[1,2,8],[3,5],[4],[6],[7]] => 0110110 => 0110110 => 4
[[1,3,8],[2,4],[5],[6],[7]] => 1011110 => 0111101 => 5
[[1,2,8],[3,4],[5],[6],[7]] => 0101110 => 0111010 => 4
[[1,6,7],[2,8],[3],[4],[5]] => 1111001 => 1001111 => 5
[[1,5,7],[2,8],[3],[4],[6]] => 1110101 => 1010111 => 5
[[1,4,7],[2,8],[3],[5],[6]] => 1101101 => 1011011 => 5
[[1,3,7],[2,8],[4],[5],[6]] => 1011101 => 1011101 => 5
[[1,2,7],[3,8],[4],[5],[6]] => 0111101 => 1011110 => 5
[[1,5,6],[2,8],[3],[4],[7]] => 1110010 => 0100111 => 4
[[1,4,6],[2,8],[3],[5],[7]] => 1101010 => 0101011 => 4
[[1,3,6],[2,8],[4],[5],[7]] => 1011010 => 0101101 => 4
[[1,2,6],[3,8],[4],[5],[7]] => 0111010 => 0101110 => 4
[[1,4,5],[2,8],[3],[6],[7]] => 1100110 => 0110011 => 4
[[1,3,5],[2,8],[4],[6],[7]] => 1010110 => 0110101 => 4
[[1,2,5],[3,8],[4],[6],[7]] => 0110110 => 0110110 => 4
[[1,3,4],[2,8],[5],[6],[7]] => 1001110 => 0111001 => 4
[[1,2,4],[3,8],[5],[6],[7]] => 0101110 => 0111010 => 4
[[1,2,3],[4,8],[5],[6],[7]] => 0011110 => 0111100 => 4
[[1,5,7],[2,6],[3],[4],[8]] => 1110101 => 1010111 => 5
[[1,4,7],[2,6],[3],[5],[8]] => 1101001 => 1001011 => 4
[[1,3,7],[2,6],[4],[5],[8]] => 1011001 => 1001101 => 4
[[1,2,7],[3,6],[4],[5],[8]] => 0111001 => 1001110 => 4
[[1,4,7],[2,5],[3],[6],[8]] => 1101101 => 1011011 => 5
[[1,3,7],[2,5],[4],[6],[8]] => 1010101 => 1010101 => 4
[[1,2,7],[3,5],[4],[6],[8]] => 0110101 => 1010110 => 4
[[1,3,7],[2,4],[5],[6],[8]] => 1011101 => 1011101 => 5
[[1,2,7],[3,4],[5],[6],[8]] => 0101101 => 1011010 => 4
[[1,5,6],[2,7],[3],[4],[8]] => 1110011 => 1100111 => 5
[[1,4,6],[2,7],[3],[5],[8]] => 1101011 => 1101011 => 5
[[1,3,6],[2,7],[4],[5],[8]] => 1011011 => 1101101 => 5
[[1,2,6],[3,7],[4],[5],[8]] => 0111011 => 1101110 => 5
[[1,4,5],[2,7],[3],[6],[8]] => 1100101 => 1010011 => 4
[[1,3,5],[2,7],[4],[6],[8]] => 1010101 => 1010101 => 4
[[1,2,5],[3,7],[4],[6],[8]] => 0110101 => 1010110 => 4
[[1,3,4],[2,7],[5],[6],[8]] => 1001101 => 1011001 => 4
[[1,2,4],[3,7],[5],[6],[8]] => 0101101 => 1011010 => 4
[[1,2,3],[4,7],[5],[6],[8]] => 0011101 => 1011100 => 4
[[1,4,6],[2,5],[3],[7],[8]] => 1101011 => 1101011 => 5
[[1,3,6],[2,5],[4],[7],[8]] => 1010011 => 1100101 => 4
[[1,2,6],[3,5],[4],[7],[8]] => 0110011 => 1100110 => 4
[[1,3,6],[2,4],[5],[7],[8]] => 1011011 => 1101101 => 5
[[1,2,6],[3,4],[5],[7],[8]] => 0101011 => 1101010 => 4
[[1,4,5],[2,6],[3],[7],[8]] => 1100111 => 1110011 => 5
[[1,3,5],[2,6],[4],[7],[8]] => 1010111 => 1110101 => 5
[[1,2,5],[3,6],[4],[7],[8]] => 0110111 => 1110110 => 5
[[1,3,4],[2,6],[5],[7],[8]] => 1001011 => 1101001 => 4
[[1,2,4],[3,6],[5],[7],[8]] => 0101011 => 1101010 => 4
[[1,2,3],[4,6],[5],[7],[8]] => 0011011 => 1101100 => 4
[[1,3,5],[2,4],[6],[7],[8]] => 1010111 => 1110101 => 5
[[1,2,5],[3,4],[6],[7],[8]] => 0100111 => 1110010 => 4
[[1,3,4],[2,5],[6],[7],[8]] => 1001111 => 1111001 => 5
[[1,2,4],[3,5],[6],[7],[8]] => 0101111 => 1111010 => 5
[[1,2,3],[4,5],[6],[7],[8]] => 0010111 => 1110100 => 4
[[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 0011111 => 5
[[1,6,8],[2],[3],[4],[5],[7]] => 1111010 => 0101111 => 5
[[1,5,8],[2],[3],[4],[6],[7]] => 1110110 => 0110111 => 5
[[1,4,8],[2],[3],[5],[6],[7]] => 1101110 => 0111011 => 5
[[1,3,8],[2],[4],[5],[6],[7]] => 1011110 => 0111101 => 5
[[1,2,8],[3],[4],[5],[6],[7]] => 0111110 => 0111110 => 5
[[1,6,7],[2],[3],[4],[5],[8]] => 1111001 => 1001111 => 5
[[1,5,7],[2],[3],[4],[6],[8]] => 1110101 => 1010111 => 5
[[1,4,7],[2],[3],[5],[6],[8]] => 1101101 => 1011011 => 5
[[1,3,7],[2],[4],[5],[6],[8]] => 1011101 => 1011101 => 5
[[1,2,7],[3],[4],[5],[6],[8]] => 0111101 => 1011110 => 5
[[1,5,6],[2],[3],[4],[7],[8]] => 1110011 => 1100111 => 5
[[1,4,6],[2],[3],[5],[7],[8]] => 1101011 => 1101011 => 5
[[1,3,6],[2],[4],[5],[7],[8]] => 1011011 => 1101101 => 5
[[1,2,6],[3],[4],[5],[7],[8]] => 0111011 => 1101110 => 5
[[1,4,5],[2],[3],[6],[7],[8]] => 1100111 => 1110011 => 5
[[1,3,5],[2],[4],[6],[7],[8]] => 1010111 => 1110101 => 5
[[1,2,5],[3],[4],[6],[7],[8]] => 0110111 => 1110110 => 5
[[1,3,4],[2],[5],[6],[7],[8]] => 1001111 => 1111001 => 5
[[1,2,4],[3],[5],[6],[7],[8]] => 0101111 => 1111010 => 5
[[1,2,3],[4],[5],[6],[7],[8]] => 0011111 => 1111100 => 5
[[1,5],[2,6],[3,7],[4,8]] => 1110111 => 1110111 => 6
[[1,4],[2,6],[3,7],[5,8]] => 1101011 => 1101011 => 5
[[1,3],[2,6],[4,7],[5,8]] => 1011011 => 1101101 => 5
[[1,2],[3,6],[4,7],[5,8]] => 0111011 => 1101110 => 5
[[1,4],[2,5],[3,7],[6,8]] => 1101101 => 1011011 => 5
[[1,3],[2,5],[4,7],[6,8]] => 1010101 => 1010101 => 4
[[1,2],[3,5],[4,7],[6,8]] => 0110101 => 1010110 => 4
[[1,3],[2,4],[5,7],[6,8]] => 1011101 => 1011101 => 5
[[1,2],[3,4],[5,7],[6,8]] => 0101101 => 1011010 => 4
[[1,4],[2,5],[3,6],[7,8]] => 1101110 => 0111011 => 5
[[1,3],[2,5],[4,6],[7,8]] => 1010110 => 0110101 => 4
[[1,2],[3,5],[4,6],[7,8]] => 0110110 => 0110110 => 4
[[1,3],[2,4],[5,6],[7,8]] => 1011010 => 0101101 => 4
[[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0101010 => 3
[[1,6],[2,7],[3,8],[4],[5]] => 1111011 => 1101111 => 6
[[1,5],[2,7],[3,8],[4],[6]] => 1110101 => 1010111 => 5
[[1,4],[2,7],[3,8],[5],[6]] => 1101101 => 1011011 => 5
[[1,3],[2,7],[4,8],[5],[6]] => 1011101 => 1011101 => 5
[[1,2],[3,7],[4,8],[5],[6]] => 0111101 => 1011110 => 5
[[1,5],[2,6],[3,8],[4],[7]] => 1110110 => 0110111 => 5
[[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0101011 => 4
[[1,3],[2,6],[4,8],[5],[7]] => 1011010 => 0101101 => 4
[[1,2],[3,6],[4,8],[5],[7]] => 0111010 => 0101110 => 4
[[1,4],[2,5],[3,8],[6],[7]] => 1101110 => 0111011 => 5
[[1,3],[2,5],[4,8],[6],[7]] => 1010110 => 0110101 => 4
[[1,2],[3,5],[4,8],[6],[7]] => 0110110 => 0110110 => 4
[[1,3],[2,4],[5,8],[6],[7]] => 1011110 => 0111101 => 5
[[1,2],[3,4],[5,8],[6],[7]] => 0101110 => 0111010 => 4
[[1,5],[2,6],[3,7],[4],[8]] => 1110111 => 1110111 => 6
[[1,4],[2,6],[3,7],[5],[8]] => 1101011 => 1101011 => 5
[[1,3],[2,6],[4,7],[5],[8]] => 1011011 => 1101101 => 5
[[1,2],[3,6],[4,7],[5],[8]] => 0111011 => 1101110 => 5
[[1,4],[2,5],[3,7],[6],[8]] => 1101101 => 1011011 => 5
[[1,3],[2,5],[4,7],[6],[8]] => 1010101 => 1010101 => 4
[[1,2],[3,5],[4,7],[6],[8]] => 0110101 => 1010110 => 4
[[1,3],[2,4],[5,7],[6],[8]] => 1011101 => 1011101 => 5
[[1,2],[3,4],[5,7],[6],[8]] => 0101101 => 1011010 => 4
[[1,4],[2,5],[3,6],[7],[8]] => 1101111 => 1111011 => 6
[[1,3],[2,5],[4,6],[7],[8]] => 1010111 => 1110101 => 5
[[1,2],[3,5],[4,6],[7],[8]] => 0110111 => 1110110 => 5
[[1,3],[2,4],[5,6],[7],[8]] => 1011011 => 1101101 => 5
[[1,2],[3,4],[5,6],[7],[8]] => 0101011 => 1101010 => 4
[[1,7],[2,8],[3],[4],[5],[6]] => 1111101 => 1011111 => 6
[[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 0101111 => 5
[[1,5],[2,8],[3],[4],[6],[7]] => 1110110 => 0110111 => 5
[[1,4],[2,8],[3],[5],[6],[7]] => 1101110 => 0111011 => 5
[[1,3],[2,8],[4],[5],[6],[7]] => 1011110 => 0111101 => 5
[[1,2],[3,8],[4],[5],[6],[7]] => 0111110 => 0111110 => 5
[[1,6],[2,7],[3],[4],[5],[8]] => 1111011 => 1101111 => 6
[[1,5],[2,7],[3],[4],[6],[8]] => 1110101 => 1010111 => 5
[[1,4],[2,7],[3],[5],[6],[8]] => 1101101 => 1011011 => 5
[[1,3],[2,7],[4],[5],[6],[8]] => 1011101 => 1011101 => 5
[[1,2],[3,7],[4],[5],[6],[8]] => 0111101 => 1011110 => 5
[[1,5],[2,6],[3],[4],[7],[8]] => 1110111 => 1110111 => 6
[[1,4],[2,6],[3],[5],[7],[8]] => 1101011 => 1101011 => 5
[[1,3],[2,6],[4],[5],[7],[8]] => 1011011 => 1101101 => 5
[[1,2],[3,6],[4],[5],[7],[8]] => 0111011 => 1101110 => 5
[[1,4],[2,5],[3],[6],[7],[8]] => 1101111 => 1111011 => 6
[[1,3],[2,5],[4],[6],[7],[8]] => 1010111 => 1110101 => 5
[[1,2],[3,5],[4],[6],[7],[8]] => 0110111 => 1110110 => 5
[[1,3],[2,4],[5],[6],[7],[8]] => 1011111 => 1111101 => 6
[[1,2],[3,4],[5],[6],[7],[8]] => 0101111 => 1111010 => 5
[[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 0111111 => 6
[[1,7],[2],[3],[4],[5],[6],[8]] => 1111101 => 1011111 => 6
[[1,6],[2],[3],[4],[5],[7],[8]] => 1111011 => 1101111 => 6
[[1,5],[2],[3],[4],[6],[7],[8]] => 1110111 => 1110111 => 6
[[1,4],[2],[3],[5],[6],[7],[8]] => 1101111 => 1111011 => 6
[[1,3],[2],[4],[5],[6],[7],[8]] => 1011111 => 1111101 => 6
[[1,2],[3],[4],[5],[6],[7],[8]] => 0111111 => 1111110 => 6
[[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 1111111 => 7
[[1,3,5,7,9],[2,4,6,8,10]] => 101010101 => 101010101 => 5
[[1,3,5,7,8],[2,4,6,9,10]] => 101010010 => 010010101 => 4
[[1,3,5,6,9],[2,4,7,8,10]] => 101001001 => 100100101 => 4
[[1,3,5,6,8],[2,4,7,9,10]] => 101001010 => 010100101 => 4
[[1,3,5,6,7],[2,4,8,9,10]] => 101000100 => 001000101 => 3
[[1,3,4,7,9],[2,5,6,8,10]] => 100100101 => 101001001 => 4
[[1,3,4,7,8],[2,5,6,9,10]] => 100100010 => 010001001 => 3
[[1,3,4,6,9],[2,5,7,8,10]] => 100101001 => 100101001 => 4
[[1,3,4,6,8],[2,5,7,9,10]] => 100101010 => 010101001 => 4
[[1,3,4,6,7],[2,5,8,9,10]] => 100100100 => 001001001 => 3
[[1,3,4,5,9],[2,6,7,8,10]] => 100010001 => 100010001 => 3
[[1,3,4,5,8],[2,6,7,9,10]] => 100010010 => 010010001 => 3
[[1,3,4,5,7],[2,6,8,9,10]] => 100010100 => 001010001 => 3
[[1,3,4,5,6],[2,7,8,9,10]] => 100001000 => 000100001 => 2
[[1,2,5,7,9],[3,4,6,8,10]] => 010010101 => 101010010 => 4
[[1,2,5,7,8],[3,4,6,9,10]] => 010010010 => 010010010 => 3
[[1,2,5,6,9],[3,4,7,8,10]] => 010001001 => 100100010 => 3
[[1,2,5,6,8],[3,4,7,9,10]] => 010001010 => 010100010 => 3
[[1,2,5,6,7],[3,4,8,9,10]] => 010000100 => 001000010 => 2
[[1,2,4,7,9],[3,5,6,8,10]] => 010100101 => 101001010 => 4
[[1,2,4,7,8],[3,5,6,9,10]] => 010100010 => 010001010 => 3
[[1,2,4,6,9],[3,5,7,8,10]] => 010101001 => 100101010 => 4
[[1,2,4,6,8],[3,5,7,9,10]] => 010101010 => 010101010 => 4
[[1,2,4,6,7],[3,5,8,9,10]] => 010100100 => 001001010 => 3
[[1,2,4,5,9],[3,6,7,8,10]] => 010010001 => 100010010 => 3
[[1,2,4,5,8],[3,6,7,9,10]] => 010010010 => 010010010 => 3
[[1,2,4,5,7],[3,6,8,9,10]] => 010010100 => 001010010 => 3
[[1,2,4,5,6],[3,7,8,9,10]] => 010001000 => 000100010 => 2
[[1,2,3,7,9],[4,5,6,8,10]] => 001000101 => 101000100 => 3
[[1,2,3,7,8],[4,5,6,9,10]] => 001000010 => 010000100 => 2
[[1,2,3,6,9],[4,5,7,8,10]] => 001001001 => 100100100 => 3
[[1,2,3,6,8],[4,5,7,9,10]] => 001001010 => 010100100 => 3
[[1,2,3,6,7],[4,5,8,9,10]] => 001000100 => 001000100 => 2
[[1,2,3,5,9],[4,6,7,8,10]] => 001010001 => 100010100 => 3
[[1,2,3,5,8],[4,6,7,9,10]] => 001010010 => 010010100 => 3
[[1,2,3,5,7],[4,6,8,9,10]] => 001010100 => 001010100 => 3
[[1,2,3,5,6],[4,7,8,9,10]] => 001001000 => 000100100 => 2
[[1,2,3,4,9],[5,6,7,8,10]] => 000100001 => 100001000 => 2
[[1,2,3,4,8],[5,6,7,9,10]] => 000100010 => 010001000 => 2
[[1,2,3,4,7],[5,6,8,9,10]] => 000100100 => 001001000 => 2
[[1,2,3,4,6],[5,7,8,9,10]] => 000101000 => 000101000 => 2
[[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 000010000 => 1
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => 10101010101 => 10101010101 => 6
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => 10101010010 => 01001010101 => 5
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => 10101001001 => 10010010101 => 5
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => 10101001010 => 01010010101 => 5
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => 10101000100 => 00100010101 => 4
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => 10100100101 => 10100100101 => 5
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => 10100100010 => 01000100101 => 4
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => 10100101001 => 10010100101 => 5
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => 10100101010 => 01010100101 => 5
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => 10100100100 => 00100100101 => 4
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => 10100010001 => 10001000101 => 4
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => 10100010010 => 01001000101 => 4
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => 10100010100 => 00101000101 => 4
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => 10100001000 => 00010000101 => 3
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => 10010010101 => 10101001001 => 5
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => 10010010010 => 01001001001 => 4
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => 10010001001 => 10010001001 => 4
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => 10010001010 => 01010001001 => 4
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => 10010000100 => 00100001001 => 3
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => 10010100101 => 10100101001 => 5
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => 10010100010 => 01000101001 => 4
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => 10010101001 => 10010101001 => 5
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => 10010101010 => 01010101001 => 5
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => 10010100100 => 00100101001 => 4
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => 10010010001 => 10001001001 => 4
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => 10010010010 => 01001001001 => 4
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => 10010010100 => 00101001001 => 4
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => 10010001000 => 00010001001 => 3
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => 10001000101 => 10100010001 => 4
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => 10001000010 => 01000010001 => 3
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => 10001001001 => 10010010001 => 4
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => 10001001010 => 01010010001 => 4
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => 10001000100 => 00100010001 => 3
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => 10001010001 => 10001010001 => 4
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => 10001010010 => 01001010001 => 4
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => 10001010100 => 00101010001 => 4
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => 10001001000 => 00010010001 => 3
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => 10000100001 => 10000100001 => 3
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => 10000100010 => 01000100001 => 3
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => 10000100100 => 00100100001 => 3
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => 10000101000 => 00010100001 => 3
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => 10000010000 => 00001000001 => 2
[[1,2,5,7,9,11],[3,4,6,8,10,12]] => 01001010101 => 10101010010 => 5
[[1,2,5,7,9,10],[3,4,6,8,11,12]] => 01001010010 => 01001010010 => 4
[[1,2,5,7,8,11],[3,4,6,9,10,12]] => 01001001001 => 10010010010 => 4
[[1,2,5,7,8,10],[3,4,6,9,11,12]] => 01001001010 => 01010010010 => 4
[[1,2,5,7,8,9],[3,4,6,10,11,12]] => 01001000100 => 00100010010 => 3
[[1,2,5,6,9,11],[3,4,7,8,10,12]] => 01000100101 => 10100100010 => 4
[[1,2,5,6,9,10],[3,4,7,8,11,12]] => 01000100010 => 01000100010 => 3
[[1,2,5,6,8,11],[3,4,7,9,10,12]] => 01000101001 => 10010100010 => 4
[[1,2,5,6,8,10],[3,4,7,9,11,12]] => 01000101010 => 01010100010 => 4
[[1,2,5,6,8,9],[3,4,7,10,11,12]] => 01000100100 => 00100100010 => 3
[[1,2,5,6,7,11],[3,4,8,9,10,12]] => 01000010001 => 10001000010 => 3
[[1,2,5,6,7,10],[3,4,8,9,11,12]] => 01000010010 => 01001000010 => 3
[[1,2,5,6,7,9],[3,4,8,10,11,12]] => 01000010100 => 00101000010 => 3
[[1,2,5,6,7,8],[3,4,9,10,11,12]] => 01000001000 => 00010000010 => 2
[[1,2,4,7,9,11],[3,5,6,8,10,12]] => 01010010101 => 10101001010 => 5
[[1,2,4,7,9,10],[3,5,6,8,11,12]] => 01010010010 => 01001001010 => 4
[[1,2,4,7,8,11],[3,5,6,9,10,12]] => 01010001001 => 10010001010 => 4
[[1,2,4,7,8,10],[3,5,6,9,11,12]] => 01010001010 => 01010001010 => 4
[[1,2,4,7,8,9],[3,5,6,10,11,12]] => 01010000100 => 00100001010 => 3
[[1,2,4,6,9,11],[3,5,7,8,10,12]] => 01010100101 => 10100101010 => 5
[[1,2,4,6,9,10],[3,5,7,8,11,12]] => 01010100010 => 01000101010 => 4
[[1,2,4,6,8,11],[3,5,7,9,10,12]] => 01010101001 => 10010101010 => 5
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => 01010101010 => 01010101010 => 5
[[1,2,4,6,8,9],[3,5,7,10,11,12]] => 01010100100 => 00100101010 => 4
[[1,2,4,6,7,11],[3,5,8,9,10,12]] => 01010010001 => 10001001010 => 4
[[1,2,4,6,7,10],[3,5,8,9,11,12]] => 01010010010 => 01001001010 => 4
[[1,2,4,6,7,9],[3,5,8,10,11,12]] => 01010010100 => 00101001010 => 4
[[1,2,4,6,7,8],[3,5,9,10,11,12]] => 01010001000 => 00010001010 => 3
[[1,2,4,5,9,11],[3,6,7,8,10,12]] => 01001000101 => 10100010010 => 4
[[1,2,4,5,9,10],[3,6,7,8,11,12]] => 01001000010 => 01000010010 => 3
[[1,2,4,5,8,11],[3,6,7,9,10,12]] => 01001001001 => 10010010010 => 4
[[1,2,4,5,8,10],[3,6,7,9,11,12]] => 01001001010 => 01010010010 => 4
[[1,2,4,5,8,9],[3,6,7,10,11,12]] => 01001000100 => 00100010010 => 3
[[1,2,4,5,7,11],[3,6,8,9,10,12]] => 01001010001 => 10001010010 => 4
[[1,2,4,5,7,10],[3,6,8,9,11,12]] => 01001010010 => 01001010010 => 4
[[1,2,4,5,7,9],[3,6,8,10,11,12]] => 01001010100 => 00101010010 => 4
[[1,2,4,5,7,8],[3,6,9,10,11,12]] => 01001001000 => 00010010010 => 3
[[1,2,4,5,6,11],[3,7,8,9,10,12]] => 01000100001 => 10000100010 => 3
[[1,2,4,5,6,10],[3,7,8,9,11,12]] => 01000100010 => 01000100010 => 3
[[1,2,4,5,6,9],[3,7,8,10,11,12]] => 01000100100 => 00100100010 => 3
[[1,2,4,5,6,8],[3,7,9,10,11,12]] => 01000101000 => 00010100010 => 3
[[1,2,4,5,6,7],[3,8,9,10,11,12]] => 01000010000 => 00001000010 => 2
[[1,2,3,7,9,11],[4,5,6,8,10,12]] => 00100010101 => 10101000100 => 4
[[1,2,3,7,9,10],[4,5,6,8,11,12]] => 00100010010 => 01001000100 => 3
[[1,2,3,7,8,11],[4,5,6,9,10,12]] => 00100001001 => 10010000100 => 3
[[1,2,3,7,8,10],[4,5,6,9,11,12]] => 00100001010 => 01010000100 => 3
[[1,2,3,7,8,9],[4,5,6,10,11,12]] => 00100000100 => 00100000100 => 2
[[1,2,3,6,9,11],[4,5,7,8,10,12]] => 00100100101 => 10100100100 => 4
[[1,2,3,6,9,10],[4,5,7,8,11,12]] => 00100100010 => 01000100100 => 3
[[1,2,3,6,8,11],[4,5,7,9,10,12]] => 00100101001 => 10010100100 => 4
[[1,2,3,6,8,10],[4,5,7,9,11,12]] => 00100101010 => 01010100100 => 4
[[1,2,3,6,8,9],[4,5,7,10,11,12]] => 00100100100 => 00100100100 => 3
[[1,2,3,6,7,11],[4,5,8,9,10,12]] => 00100010001 => 10001000100 => 3
[[1,2,3,6,7,10],[4,5,8,9,11,12]] => 00100010010 => 01001000100 => 3
[[1,2,3,6,7,9],[4,5,8,10,11,12]] => 00100010100 => 00101000100 => 3
[[1,2,3,6,7,8],[4,5,9,10,11,12]] => 00100001000 => 00010000100 => 2
[[1,2,3,5,9,11],[4,6,7,8,10,12]] => 00101000101 => 10100010100 => 4
[[1,2,3,5,9,10],[4,6,7,8,11,12]] => 00101000010 => 01000010100 => 3
[[1,2,3,5,8,11],[4,6,7,9,10,12]] => 00101001001 => 10010010100 => 4
[[1,2,3,5,8,10],[4,6,7,9,11,12]] => 00101001010 => 01010010100 => 4
[[1,2,3,5,8,9],[4,6,7,10,11,12]] => 00101000100 => 00100010100 => 3
[[1,2,3,5,7,11],[4,6,8,9,10,12]] => 00101010001 => 10001010100 => 4
[[1,2,3,5,7,10],[4,6,8,9,11,12]] => 00101010010 => 01001010100 => 4
[[1,2,3,5,7,9],[4,6,8,10,11,12]] => 00101010100 => 00101010100 => 4
[[1,2,3,5,7,8],[4,6,9,10,11,12]] => 00101001000 => 00010010100 => 3
[[1,2,3,5,6,11],[4,7,8,9,10,12]] => 00100100001 => 10000100100 => 3
[[1,2,3,5,6,10],[4,7,8,9,11,12]] => 00100100010 => 01000100100 => 3
[[1,2,3,5,6,9],[4,7,8,10,11,12]] => 00100100100 => 00100100100 => 3
[[1,2,3,5,6,8],[4,7,9,10,11,12]] => 00100101000 => 00010100100 => 3
[[1,2,3,5,6,7],[4,8,9,10,11,12]] => 00100010000 => 00001000100 => 2
[[1,2,3,4,9,11],[5,6,7,8,10,12]] => 00010000101 => 10100001000 => 3
[[1,2,3,4,9,10],[5,6,7,8,11,12]] => 00010000010 => 01000001000 => 2
[[1,2,3,4,8,11],[5,6,7,9,10,12]] => 00010001001 => 10010001000 => 3
[[1,2,3,4,8,10],[5,6,7,9,11,12]] => 00010001010 => 01010001000 => 3
[[1,2,3,4,8,9],[5,6,7,10,11,12]] => 00010000100 => 00100001000 => 2
[[1,2,3,4,7,11],[5,6,8,9,10,12]] => 00010010001 => 10001001000 => 3
[[1,2,3,4,7,10],[5,6,8,9,11,12]] => 00010010010 => 01001001000 => 3
[[1,2,3,4,7,9],[5,6,8,10,11,12]] => 00010010100 => 00101001000 => 3
[[1,2,3,4,7,8],[5,6,9,10,11,12]] => 00010001000 => 00010001000 => 2
[[1,2,3,4,6,11],[5,7,8,9,10,12]] => 00010100001 => 10000101000 => 3
[[1,2,3,4,6,10],[5,7,8,9,11,12]] => 00010100010 => 01000101000 => 3
[[1,2,3,4,6,9],[5,7,8,10,11,12]] => 00010100100 => 00100101000 => 3
[[1,2,3,4,6,8],[5,7,9,10,11,12]] => 00010101000 => 00010101000 => 3
[[1,2,3,4,6,7],[5,8,9,10,11,12]] => 00010010000 => 00001001000 => 2
[[1,2,3,4,5,11],[6,7,8,9,10,12]] => 00001000001 => 10000010000 => 2
[[1,2,3,4,5,10],[6,7,8,9,11,12]] => 00001000010 => 01000010000 => 2
[[1,2,3,4,5,9],[6,7,8,10,11,12]] => 00001000100 => 00100010000 => 2
[[1,2,3,4,5,8],[6,7,9,10,11,12]] => 00001001000 => 00010010000 => 2
[[1,2,3,4,5,7],[6,8,9,10,11,12]] => 00001010000 => 00001010000 => 2
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000 => 00000100000 => 1
[[1,2,3,4,5,6,7,8,9]] => 00000000 => 00000000 => 0
[[1,2,3,4,5,6,7,8],[9]] => 00000001 => 10000000 => 1
[[1,2,3,4,5,6,7],[8,9]] => 00000010 => 01000000 => 1
[[1,2,3,4,5,6,7],[8],[9]] => 00000011 => 11000000 => 2
[[1,2,3,4,5,6],[7,8,9]] => 00000100 => 00100000 => 1
[[1,2,3,4,5,6],[7,8],[9]] => 00000101 => 10100000 => 2
[[1,2,3,4,5,6],[7],[8],[9]] => 00000111 => 11100000 => 3
[[1,2,3,4,5],[6,7,8,9]] => 00001000 => 00010000 => 1
[[1,2,3,4,5],[6,7,8],[9]] => 00001001 => 10010000 => 2
[[1,2,3,4,5],[6,7],[8,9]] => 00001010 => 01010000 => 2
[[1,2,3,4,5],[6,7],[8],[9]] => 00001011 => 11010000 => 3
[[1,2,3,4,5],[6],[7],[8],[9]] => 00001111 => 11110000 => 4
[[1,2,3,4],[5,6,7,8],[9]] => 00010001 => 10001000 => 2
[[1,2,3,4],[5,6,7],[8,9]] => 00010010 => 01001000 => 2
[[1,2,3,4],[5,6,7],[8],[9]] => 00010011 => 11001000 => 3
[[1,2,3,4],[5,6],[7,8],[9]] => 00010101 => 10101000 => 3
[[1,2,3,4],[5,6],[7],[8],[9]] => 00010111 => 11101000 => 4
[[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111 => 11111000 => 5
[[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 00100100 => 2
[[1,2,3],[4,5,6],[7,8],[9]] => 00100101 => 10100100 => 3
[[1,2,3],[4,5,6],[7],[8],[9]] => 00100111 => 11100100 => 4
[[1,2,3],[4,5],[6,7],[8,9]] => 00101010 => 01010100 => 3
[[1,2,3],[4,5],[6,7],[8],[9]] => 00101011 => 11010100 => 4
[[1,2,3],[4,5],[6],[7],[8],[9]] => 00101111 => 11110100 => 5
[[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111 => 11111100 => 6
[[1,2],[3,4],[5,6],[7,8],[9]] => 01010101 => 10101010 => 4
[[1,2],[3,4],[5,6],[7],[8],[9]] => 01010111 => 11101010 => 5
[[1,2],[3,4],[5],[6],[7],[8],[9]] => 01011111 => 11111010 => 6
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111 => 11111110 => 7
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 11111111 => 8
[[1,2,3,4,5,6,7,8,9,10]] => 000000000 => 000000000 => 0
[[1,2,3,4,5,6,7,8,9],[10]] => 000000001 => 100000000 => 1
[[1,2,3,4,5,6,7,8],[9,10]] => 000000010 => 010000000 => 1
[[1,2,3,4,5,6,7,8],[9],[10]] => 000000011 => 110000000 => 2
[[1,2,3,4,5,6,7],[8,9,10]] => 000000100 => 001000000 => 1
[[1,2,3,4,5,6,7],[8,9],[10]] => 000000101 => 101000000 => 2
[[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111 => 111000000 => 3
[[1,2,3,4,5,6],[7,8,9,10]] => 000001000 => 000100000 => 1
[[1,2,3,4,5,6],[7,8,9],[10]] => 000001001 => 100100000 => 2
[[1,2,3,4,5,6],[7,8],[9,10]] => 000001010 => 010100000 => 2
[[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011 => 110100000 => 3
[[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111 => 111100000 => 4
[[1,2,3,4,5],[6,7,8,9],[10]] => 000010001 => 100010000 => 2
[[1,2,3,4,5],[6,7,8],[9,10]] => 000010010 => 010010000 => 2
[[1,2,3,4,5],[6,7,8],[9],[10]] => 000010011 => 110010000 => 3
[[1,2,3,4,5],[6,7],[8,9],[10]] => 000010101 => 101010000 => 3
[[1,2,3,4,5],[6,7],[8],[9],[10]] => 000010111 => 111010000 => 4
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111 => 111110000 => 5
[[1,2,3,4],[5,6,7,8],[9,10]] => 000100010 => 010001000 => 2
[[1,2,3,4],[5,6,7,8],[9],[10]] => 000100011 => 110001000 => 3
[[1,2,3,4],[5,6,7],[8,9,10]] => 000100100 => 001001000 => 2
[[1,2,3,4],[5,6,7],[8,9],[10]] => 000100101 => 101001000 => 3
[[1,2,3,4],[5,6,7],[8],[9],[10]] => 000100111 => 111001000 => 4
[[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010 => 010101000 => 3
[[1,2,3,4],[5,6],[7,8],[9],[10]] => 000101011 => 110101000 => 4
[[1,2,3,4],[5,6],[7],[8],[9],[10]] => 000101111 => 111101000 => 5
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111 => 111111000 => 6
[[1,2,3],[4,5,6],[7,8,9],[10]] => 001001001 => 100100100 => 3
[[1,2,3],[4,5,6],[7,8],[9,10]] => 001001010 => 010100100 => 3
[[1,2,3],[4,5,6],[7,8],[9],[10]] => 001001011 => 110100100 => 4
[[1,2,3],[4,5,6],[7],[8],[9],[10]] => 001001111 => 111100100 => 5
[[1,2,3],[4,5],[6,7],[8,9],[10]] => 001010101 => 101010100 => 4
[[1,2,3],[4,5],[6,7],[8],[9],[10]] => 001010111 => 111010100 => 5
[[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 001011111 => 111110100 => 6
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111 => 111111100 => 7
[[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 010101010 => 4
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => 010101011 => 110101010 => 5
[[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 010101111 => 111101010 => 6
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 010111111 => 111111010 => 7
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111 => 111111110 => 8
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 111111111 => 9
[[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 00001000100 => 00100010000 => 2
[[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 00010001001 => 10010001000 => 3
[[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 00010001010 => 01010001000 => 3
[[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 00010010010 => 01001001000 => 3
[[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 00100100101 => 10100100100 => 4
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010 => 01010101010 => 5
[[1,3,4,5,6,7,8,9],[2]] => 10000000 => 00000001 => 1
[[1,2,5,6,7,8,9],[3,4]] => 01000000 => 00000010 => 1
[[1,4,5,6,7,8,9],[2],[3]] => 11000000 => 00000011 => 2
[[1,2,3,7,8,9],[4,5,6]] => 00100000 => 00000100 => 1
[[1,3,6,7,8,9],[2,5],[4]] => 10100000 => 00000101 => 2
[[1,5,6,7,8,9],[2],[3],[4]] => 11100000 => 00000111 => 3
[[1,2,3,4,9],[5,6,7,8]] => 00010000 => 00001000 => 1
[[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 00001001 => 2
[[1,2,7,8,9],[3,4],[5,6]] => 01010000 => 00001010 => 2
[[1,4,7,8,9],[2,6],[3],[5]] => 11010000 => 00001011 => 3
[[1,6,7,8,9],[2],[3],[4],[5]] => 11110000 => 00001111 => 4
[[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 00010001 => 2
[[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 00010010 => 2
[[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 00010011 => 3
[[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 00010101 => 3
[[1,5,8,9],[2,7],[3],[4],[6]] => 11101000 => 00010111 => 4
[[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 00011111 => 5
[[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 00100101 => 3
[[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 00100111 => 4
[[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 00101010 => 3
[[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 00101011 => 4
[[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 00101111 => 5
[[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100 => 00111111 => 6
[[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 01010101 => 4
[[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 01010111 => 5
[[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 01011111 => 6
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 01111111 => 7
[[1,3,4,5,6,7,8,9,10],[2]] => 100000000 => 000000001 => 1
[[1,2,5,6,7,8,9,10],[3,4]] => 010000000 => 000000010 => 1
[[1,4,5,6,7,8,9,10],[2],[3]] => 110000000 => 000000011 => 2
[[1,2,3,7,8,9,10],[4,5,6]] => 001000000 => 000000100 => 1
[[1,3,6,7,8,9,10],[2,5],[4]] => 101000000 => 000000101 => 2
[[1,5,6,7,8,9,10],[2],[3],[4]] => 111000000 => 000000111 => 3
[[1,2,3,4,9,10],[5,6,7,8]] => 000100000 => 000001000 => 1
[[1,3,4,8,9,10],[2,6,7],[5]] => 100100000 => 000001001 => 2
[[1,2,7,8,9,10],[3,4],[5,6]] => 010100000 => 000001010 => 2
[[1,4,7,8,9,10],[2,6],[3],[5]] => 110100000 => 000001011 => 3
[[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000 => 000001111 => 4
[[1,3,4,5,10],[2,7,8,9],[6]] => 100010000 => 000010001 => 2
[[1,2,5,9,10],[3,4,8],[6,7]] => 010010000 => 000010010 => 2
[[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000 => 000010011 => 3
[[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000 => 000010101 => 3
[[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000 => 000010111 => 4
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000 => 000011111 => 5
[[1,2,5,6],[3,4,9,10],[7,8]] => 010001000 => 000100010 => 2
[[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000 => 000100011 => 3
[[1,2,3,10],[4,5,6],[7,8,9]] => 001001000 => 000100100 => 2
[[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 000100101 => 3
[[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000 => 000100111 => 4
[[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000 => 000101010 => 3
[[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000 => 000101011 => 4
[[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000 => 000101111 => 5
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000 => 000111111 => 6
[[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 001001001 => 3
[[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 001001010 => 3
[[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100 => 001001011 => 4
[[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100 => 001001111 => 5
[[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 001010101 => 4
[[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100 => 001010111 => 5
[[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100 => 001011111 => 6
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100 => 001111111 => 7
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 010101011 => 5
[[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010 => 010101111 => 6
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010 => 010111111 => 7
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110 => 011111111 => 8
[[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 00100010000 => 00001000100 => 2
[[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 10010001000 => 00010001001 => 3
[[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000 => 00010001010 => 3
[[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 01001001000 => 00010010010 => 3
[[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 10100100100 => 00100100101 => 4
[[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101 => 10111111 => 7
[[1,7],[2,8],[3,9],[4],[5],[6]] => 11111011 => 11011111 => 7
[[1,7,9],[2,8],[3],[4],[5],[6]] => 11111010 => 01011111 => 6
[[1,6],[2,7],[3,8],[4,9],[5]] => 11110111 => 11101111 => 7
[[1,6,9],[2,7],[3,8],[4],[5]] => 11110110 => 01101111 => 6
[[1,6,8],[2,7,9],[3],[4],[5]] => 11110101 => 10101111 => 6
[[1,6,8,9],[2,7],[3],[4],[5]] => 11110100 => 00101111 => 5
[[1,5,9],[2,6],[3,7],[4,8]] => 11101110 => 01110111 => 6
[[1,5,8],[2,6,9],[3,7],[4]] => 11101101 => 10110111 => 6
[[1,5,8,9],[2,6],[3,7],[4]] => 11101100 => 00110111 => 5
[[1,5,7,9],[2,6,8],[3],[4]] => 11101010 => 01010111 => 5
[[1,5,7,8,9],[2,6],[3],[4]] => 11101000 => 00010111 => 4
[[1,4,7],[2,5,8],[3,6,9]] => 11011011 => 11011011 => 6
[[1,4,7,9],[2,5,8],[3,6]] => 11011010 => 01011011 => 5
[[1,4,7,8,9],[2,5],[3,6]] => 11011000 => 00011011 => 4
[[1,4,6,8],[2,5,7,9],[3]] => 11010101 => 10101011 => 5
[[1,4,6,8,9],[2,5,7],[3]] => 11010100 => 00101011 => 4
[[1,4,6,7,8,9],[2,5],[3]] => 11010000 => 00001011 => 3
[[1,3,5,7,9],[2,4,6,8]] => 10101010 => 01010101 => 4
[[1,3,5,7,8,9],[2,4,6]] => 10101000 => 00010101 => 3
[[1,3,5,6,7,8,9],[2,4]] => 10100000 => 00000101 => 2
[[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 111111010 => 010111111 => 7
[[1,7,10],[2,8],[3,9],[4],[5],[6]] => 111110110 => 011011111 => 7
[[1,7,9,10],[2,8],[3],[4],[5],[6]] => 111110100 => 001011111 => 6
[[1,6,10],[2,7],[3,8],[4,9],[5]] => 111101110 => 011101111 => 7
[[1,6,8,10],[2,7,9],[3],[4],[5]] => 111101010 => 010101111 => 6
[[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000 => 000101111 => 5
[[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010 => 010110111 => 6
[[1,5,7,9,10],[2,6,8],[3],[4]] => 111010100 => 001010111 => 5
[[1,5,7,8,9,10],[2,6],[3],[4]] => 111010000 => 000010111 => 4
[[1,4,6,8,10],[2,5,7,9],[3]] => 110101010 => 010101011 => 5
[[1,4,6,8,9,10],[2,5,7],[3]] => 110101000 => 000101011 => 4
[[1,4,6,7,8,9,10],[2,5],[3]] => 110100000 => 000001011 => 3
[[1,3,5,7,9,10],[2,4,6,8]] => 101010100 => 001010101 => 4
[[1,3,5,7,8,9,10],[2,4,6]] => 101010000 => 000010101 => 3
[[1,3,5,6,7,8,9,10],[2,4]] => 101000000 => 000000101 => 2
[[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111 => 11111101 => 7
[[1,4],[2,5],[3,6],[7],[8],[9]] => 11011111 => 11111011 => 7
[[1,2,4],[3,5],[6],[7],[8],[9]] => 01011111 => 11111010 => 6
[[1,5],[2,6],[3,7],[4,8],[9]] => 11101111 => 11110111 => 7
[[1,2,5],[3,6],[4,7],[8],[9]] => 01101111 => 11110110 => 6
[[1,3,5],[2,4,6],[7],[8],[9]] => 10101111 => 11110101 => 6
[[1,2,3,5],[4,6],[7],[8],[9]] => 00101111 => 11110100 => 5
[[1,2,6],[3,7],[4,8],[5,9]] => 01110111 => 11101110 => 6
[[1,3,6],[2,4,7],[5,8],[9]] => 10110111 => 11101101 => 6
[[1,2,3,6],[4,7],[5,8],[9]] => 00110111 => 11101100 => 5
[[1,2,4,6],[3,5,7],[8],[9]] => 01010111 => 11101010 => 5
[[1,2,3,4,6],[5,7],[8],[9]] => 00010111 => 11101000 => 4
[[1,2,4,7],[3,5,8],[6,9]] => 01011011 => 11011010 => 5
[[1,2,3,4,7],[5,8],[6,9]] => 00011011 => 11011000 => 4
[[1,3,5,7],[2,4,6,8],[9]] => 10101011 => 11010101 => 5
[[1,2,3,5,7],[4,6,8],[9]] => 00101011 => 11010100 => 4
[[1,2,3,4,5,7],[6,8],[9]] => 00001011 => 11010000 => 3
[[1,2,4,6,8],[3,5,7,9]] => 01010101 => 10101010 => 4
[[1,2,3,4,6,8],[5,7,9]] => 00010101 => 10101000 => 3
[[1,2,3,4,5,6,8],[7,9]] => 00000101 => 10100000 => 2
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111 => 111111101 => 8
[[1,2,4],[3,5],[6],[7],[8],[9],[10]] => 010111111 => 111111010 => 7
[[1,2,3,5],[4,6],[7],[8],[9],[10]] => 001011111 => 111110100 => 6
[[1,2,6],[3,7],[4,8],[5,9],[10]] => 011101111 => 111101110 => 7
[[1,2,4,6],[3,5,7],[8],[9],[10]] => 010101111 => 111101010 => 6
[[1,2,3,4,6],[5,7],[8],[9],[10]] => 000101111 => 111101000 => 5
[[1,2,3,5,7],[4,6,8],[9],[10]] => 001010111 => 111010100 => 5
[[1,2,3,4,5,7],[6,8],[9],[10]] => 000010111 => 111010000 => 4
[[1,2,5,8],[3,6,9],[4,7,10]] => 011011011 => 110110110 => 6
[[1,2,4,6,8],[3,5,7,9],[10]] => 010101011 => 110101010 => 5
[[1,2,3,4,6,8],[5,7,9],[10]] => 000101011 => 110101000 => 4
[[1,2,3,4,5,6,8],[7,9],[10]] => 000001011 => 110100000 => 3
[[1,2,3,5,7,9],[4,6,8,10]] => 001010101 => 101010100 => 4
[[1,2,3,4,5,7,9],[6,8,10]] => 000010101 => 101010000 => 3
[[1,2,3,4,5,6,7,9],[8,10]] => 000000101 => 101000000 => 2
[[1,2],[3,4],[5,6],[7,9],[8,10]] => 010101101 => 101101010 => 5
[[1,2],[3,4],[5,7],[6,9],[8,10]] => 010110101 => 101011010 => 5
[[1,2],[3,5],[4,7],[6,9],[8,10]] => 011010101 => 101010110 => 5
[[1,2],[3,5],[4,8],[6,9],[7,10]] => 011011011 => 110110110 => 6
[[1,2],[3,6],[4,7],[5,9],[8,10]] => 011101101 => 101101110 => 6
[[1,2],[3,7],[4,8],[5,9],[6,10]] => 011110111 => 111011110 => 7
[[1,3],[2,4],[5,7],[6,8],[9,10]] => 101110110 => 011011101 => 6
[[1,3],[2,4],[5,8],[6,9],[7,10]] => 101111011 => 110111101 => 7
[[1,3],[2,5],[4,7],[6,9],[8,10]] => 101010101 => 101010101 => 5
[[1,3],[2,6],[4,7],[5,8],[9,10]] => 101101110 => 011101101 => 6
[[1,5],[2,6],[3,7],[4,8],[9,10]] => 111011110 => 011110111 => 7
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => 10101010101 => 10101010101 => 6
[[1,2,3,4,5,6,7,9],[8]] => 00000010 => 01000000 => 1
[[1,2,3,4,5,6,9],[7,8]] => 00000100 => 00100000 => 1
[[1,2,3,4,5,6,9],[7],[8]] => 00000110 => 01100000 => 2
[[1,2,3,4,5,9],[6,7,8]] => 00001000 => 00010000 => 1
[[1,2,3,4,5,9],[6,7],[8]] => 00001010 => 01010000 => 2
[[1,2,3,4,5,9],[6],[7],[8]] => 00001110 => 01110000 => 3
[[1,2,3,4,9],[5,6,7],[8]] => 00010010 => 01001000 => 2
[[1,2,3,4,9],[5,6],[7,8]] => 00010100 => 00101000 => 2
[[1,2,3,4,9],[5,6],[7],[8]] => 00010110 => 01101000 => 3
[[1,2,3,4,9],[5],[6],[7],[8]] => 00011110 => 01111000 => 4
[[1,2,3,7],[4,5,6,9],[8]] => 00100010 => 01000100 => 2
[[1,2,3,9],[4,5,6],[7,8]] => 00100100 => 00100100 => 2
[[1,2,3,9],[4,5,6],[7],[8]] => 00100110 => 01100100 => 3
[[1,2,3,9],[4,5],[6,7],[8]] => 00101010 => 01010100 => 3
[[1,2,3,9],[4,5],[6],[7],[8]] => 00101110 => 01110100 => 4
[[1,2,3,9],[4],[5],[6],[7],[8]] => 00111110 => 01111100 => 5
[[1,2,5],[3,4,8],[6,7,9]] => 01001001 => 10010010 => 3
[[1,2,5],[3,4,9],[6,7],[8]] => 01001010 => 01010010 => 3
[[1,2,5],[3,4,9],[6],[7],[8]] => 01001110 => 01110010 => 4
[[1,2,9],[3,4],[5,6],[7],[8]] => 01010110 => 01101010 => 4
[[1,2,9],[3,4],[5],[6],[7],[8]] => 01011110 => 01111010 => 5
[[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110 => 01111110 => 6
[[1,3],[2,5],[4,9],[6],[7],[8]] => 10101110 => 01110101 => 5
[[1,3],[2,9],[4],[5],[6],[7],[8]] => 10111110 => 01111101 => 6
[[1,2,3,4,5,6,7,8,10],[9]] => 000000010 => 010000000 => 1
[[1,2,3,4,5,6,7,10],[8,9]] => 000000100 => 001000000 => 1
[[1,2,3,4,5,6,10],[7,8,9]] => 000001000 => 000100000 => 1
[[1,2,3,4,5,6,10],[7,8],[9]] => 000001010 => 010100000 => 2
[[1,2,3,4,5,10],[6,7,8,9]] => 000010000 => 000010000 => 1
[[1,2,3,4,5,10],[6,7,8],[9]] => 000010010 => 010010000 => 2
[[1,2,3,4,10],[5,6,7,8],[9]] => 000100010 => 010001000 => 2
[[1,2,3,4,10],[5,6,7],[8,9]] => 000100100 => 001001000 => 2
[[1,2,3,4,10],[5,6],[7,8],[9]] => 000101010 => 010101000 => 3
[[1,2,3,7],[4,5,6,10],[8,9]] => 001000100 => 001000100 => 2
[[1,2,3,10],[4,5,6],[7,8],[9]] => 001001010 => 010100100 => 3
[[1,2,3,10],[4,5],[6,7],[8,9]] => 001010100 => 001010100 => 3
[[1,2,5],[3,4,8],[6,7,10],[9]] => 010010010 => 010010010 => 3
[[1,2,5],[3,4,10],[6,7],[8,9]] => 010010100 => 001010010 => 3
[[1,2,10],[3,4],[5,6],[7,8],[9]] => 010101010 => 010101010 => 4
[[1,3],[2,5],[4,10],[6],[7],[8],[9]] => 101011110 => 011110101 => 6
[[1,3],[2,10],[4],[5],[6],[7],[8],[9]] => 101111110 => 011111101 => 7
[[1,2,4,5,6,7,8,9],[3]] => 01000000 => 00000010 => 1
[[1,3,4,6,7,8,9],[2,5]] => 10010000 => 00001001 => 2
[[1,3,5,6,7,8,9],[2],[4]] => 10100000 => 00000101 => 2
[[1,3,5,6,8,9],[2,4,7]] => 10100100 => 00100101 => 3
[[1,2,4,7,8,9],[3,5],[6]] => 01011000 => 00011010 => 3
[[1,4,6,7,8,9],[2],[3],[5]] => 11010000 => 00001011 => 3
[[1,3,5,7,8],[2,4,6,9]] => 10101001 => 10010101 => 4
[[1,2,5,7,9],[3,6,8],[4]] => 01101010 => 01010110 => 4
[[1,4,6,8,9],[2,5],[3,7]] => 11010100 => 00101011 => 4
[[1,3,5,8,9],[2,6],[4],[7]] => 10101100 => 00110101 => 4
[[1,5,7,8,9],[2],[3],[4],[6]] => 11101000 => 00010111 => 4
[[1,2,5,6],[3,7,8,9],[4]] => 01100100 => 00100110 => 3
[[1,3,4,7],[2,6,8],[5,9]] => 10010011 => 11001001 => 4
[[1,3,6,8],[2,7,9],[4],[5]] => 10110101 => 10101101 => 5
[[1,2,6,9],[3,4],[5,7],[8]] => 01010110 => 01101010 => 4
[[1,4,6,9],[2,7],[3],[5],[8]] => 11010110 => 01101011 => 5
[[1,6,8,9],[2],[3],[4],[5],[7]] => 11110100 => 00101111 => 5
[[1,2,4],[3,5,7],[6,8],[9]] => 01011011 => 11011010 => 5
[[1,4,7],[2,8,9],[3],[5],[6]] => 11011010 => 01011011 => 5
[[1,5,8],[2,6],[3,7],[4,9]] => 11101101 => 10110111 => 6
[[1,3,7],[2,5],[4,8],[6],[9]] => 10101011 => 11010101 => 5
[[1,5,7],[2,8],[3],[4],[6],[9]] => 11101011 => 11010111 => 6
[[1,7,9],[2],[3],[4],[5],[6],[8]] => 11111010 => 01011111 => 6
[[1,4],[2,6],[3,8],[5],[7],[9]] => 11010101 => 10101011 => 5
[[1,6],[2,8],[3],[4],[5],[7],[9]] => 11110101 => 10101111 => 6
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => 11111101 => 10111111 => 7
[[1,2,4,5,6,7,8,9,10],[3]] => 010000000 => 000000010 => 1
[[1,3,4,6,7,8,9,10],[2,5]] => 100100000 => 000001001 => 2
[[1,3,5,6,7,8,9,10],[2],[4]] => 101000000 => 000000101 => 2
[[1,3,5,6,8,9,10],[2,4,7]] => 101001000 => 000100101 => 3
[[1,4,6,7,8,9,10],[2],[3],[5]] => 110100000 => 000001011 => 3
[[1,3,5,7,8,10],[2,4,6,9]] => 101010010 => 010010101 => 4
[[1,4,6,8,9,10],[2,5],[3,7]] => 110101000 => 000101011 => 4
[[1,3,5,8,9,10],[2,6],[4],[7]] => 101011000 => 000110101 => 4
[[1,5,7,8,9,10],[2],[3],[4],[6]] => 111010000 => 000010111 => 4
[[1,2,5,6,9],[3,7,8,10],[4]] => 011001001 => 100100110 => 4
[[1,3,4,7,10],[2,6,8],[5,9]] => 100100110 => 011001001 => 4
[[1,6,8,9,10],[2],[3],[4],[5],[7]] => 111101000 => 000101111 => 5
[[1,3,4,8],[2,6,9,10],[5,7]] => 100101010 => 010101001 => 4
[[1,3,6,7],[2,8,9,10],[4],[5]] => 101100100 => 001001101 => 4
[[1,5,8,10],[2,6],[3,7],[4,9]] => 111011010 => 010110111 => 6
[[1,7,9,10],[2],[3],[4],[5],[6],[8]] => 111110100 => 001011111 => 6
[[1,5,8],[2,9,10],[3],[4],[6],[7]] => 111011010 => 010110111 => 6
[[1,2,8],[3,4],[5,6],[7,9],[10]] => 010101011 => 110101010 => 5
[[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => 111111010 => 010111111 => 7
[[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101 => 101010101 => 5
[[1,3,4,5,6,7,8],[2,9]] => 10000001 => 10000001 => 2
[[1,3,4,5,6,7,8],[2],[9]] => 10000001 => 10000001 => 2
[[1,3,4,5,6,7],[2,8,9]] => 10000010 => 01000001 => 2
[[1,3,4,5,6,7],[2,9],[8]] => 10000010 => 01000001 => 2
[[1,3,4,5,6,7],[2],[8],[9]] => 10000011 => 11000001 => 3
[[1,3,4,5,6],[2,7,8,9]] => 10000100 => 00100001 => 2
[[1,3,4,5,6],[2,8,9],[7]] => 10000100 => 00100001 => 2
[[1,3,4,5,6],[2,8],[7,9]] => 10000101 => 10100001 => 3
[[1,3,4,5,6],[2,8],[7],[9]] => 10000101 => 10100001 => 3
[[1,3,4,5,6],[2],[7],[8],[9]] => 10000111 => 11100001 => 4
[[1,3,4,5],[2,7,8],[6,9]] => 10001001 => 10010001 => 3
[[1,3,4,5],[2,7,8],[6],[9]] => 10001001 => 10010001 => 3
[[1,3,4,5],[2,7],[6,9],[8]] => 10001010 => 01010001 => 3
[[1,3,4,5],[2,7],[6],[8],[9]] => 10001011 => 11010001 => 4
[[1,3,4,5],[2],[6],[7],[8],[9]] => 10001111 => 11110001 => 5
[[1,3,4],[2,6,7],[5,8,9]] => 10010010 => 01001001 => 3
[[1,3,4],[2,6,7],[5,9],[8]] => 10010010 => 01001001 => 3
[[1,3,4],[2,6,7],[5],[8],[9]] => 10010011 => 11001001 => 4
[[1,3,4],[2,6],[5,8],[7,9]] => 10010101 => 10101001 => 4
[[1,3,4],[2,6],[5,8],[7],[9]] => 10010101 => 10101001 => 4
[[1,3,4],[2,6],[5],[7],[8],[9]] => 10010111 => 11101001 => 5
[[1,3,4],[2],[5],[6],[7],[8],[9]] => 10011111 => 11111001 => 6
[[1,3],[2,5],[4,7],[6],[8],[9]] => 10101011 => 11010101 => 5
[[1,3],[2,5],[4],[6],[7],[8],[9]] => 10101111 => 11110101 => 6
[[1,3],[2],[4],[5],[6],[7],[8],[9]] => 10111111 => 11111101 => 7
[[1,3,4,5,6,7,8],[2,9,10]] => 100000010 => 010000001 => 2
[[1,3,4,5,6,7,8],[2,10],[9]] => 100000010 => 010000001 => 2
[[1,3,4,5,6,7],[2,8,9,10]] => 100000100 => 001000001 => 2
[[1,3,4,5,6,7],[2,9,10],[8]] => 100000100 => 001000001 => 2
[[1,3,4,5,6],[2,8,9,10],[7]] => 100001000 => 000100001 => 2
[[1,3,4,5,6],[2,8],[7,10],[9]] => 100001010 => 010100001 => 3
[[1,3,4,5],[2,7,8,9],[6,10]] => 100010001 => 100010001 => 3
[[1,3,4,5],[2,7,8,9],[6],[10]] => 100010001 => 100010001 => 3
[[1,3,4,5],[2,7,8],[6,9,10]] => 100010010 => 010010001 => 3
[[1,3,4,5],[2,7,8],[6,10],[9]] => 100010010 => 010010001 => 3
[[1,3,4],[2,6,7],[5,9],[8,10]] => 100100101 => 101001001 => 4
[[1,3,4],[2,6,7],[5,9],[8],[10]] => 100100101 => 101001001 => 4
[[1,3,4],[2,6],[5,8],[7,10],[9]] => 100101010 => 010101001 => 4
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => 101111111 => 111111101 => 8
[[1,2,4,6,8,10],[3,5,7,9]] => 010101010 => 010101010 => 4
[[1,2,4,6,8,9,10],[3,5,7]] => 010101000 => 000101010 => 3
[[1,2,4,6,7,8,10],[3,5,9]] => 010100010 => 010001010 => 3
[[1,2,4,6,7,9,10],[3,5,8]] => 010100100 => 001001010 => 3
[[1,2,4,6,7,8,9,10],[3,5]] => 010100000 => 000001010 => 2
[[1,2,4,5,6,8,10],[3,7,9]] => 010001010 => 010100010 => 3
[[1,2,4,5,6,9,10],[3,7,8]] => 010001000 => 000100010 => 2
[[1,2,4,5,7,8,10],[3,6,9]] => 010010010 => 010010010 => 3
[[1,2,4,5,7,9,10],[3,6,8]] => 010010100 => 001010010 => 3
[[1,2,4,5,7,8,9,10],[3,6]] => 010010000 => 000010010 => 2
[[1,2,4,5,6,7,8,10],[3,9]] => 010000010 => 010000010 => 2
[[1,2,4,5,6,7,9,10],[3,8]] => 010000100 => 001000010 => 2
[[1,2,4,5,6,8,9,10],[3,7]] => 010001000 => 000100010 => 2
[[1,2,3,4,6,8,10],[5,7,9]] => 000101010 => 010101000 => 3
[[1,2,3,4,6,9,10],[5,7,8]] => 000101000 => 000101000 => 2
[[1,2,3,4,7,8,10],[5,6,9]] => 000100010 => 010001000 => 2
[[1,2,3,4,7,9,10],[5,6,8]] => 000100100 => 001001000 => 2
[[1,2,3,4,7,8,9,10],[5,6]] => 000100000 => 000001000 => 1
[[1,2,3,5,6,8,10],[4,7,9]] => 001001010 => 010100100 => 3
[[1,2,3,5,6,9,10],[4,7,8]] => 001001000 => 000100100 => 2
[[1,2,3,5,7,8,10],[4,6,9]] => 001010010 => 010010100 => 3
[[1,2,3,5,7,9,10],[4,6,8]] => 001010100 => 001010100 => 3
[[1,2,3,5,6,7,8,10],[4,9]] => 001000010 => 010000100 => 2
[[1,2,3,5,6,7,9,10],[4,8]] => 001000100 => 001000100 => 2
[[1,2,3,5,6,8,9,10],[4,7]] => 001001000 => 000100100 => 2
[[1,2,3,5,6,7,8,9,10],[4]] => 001000000 => 000000100 => 1
[[1,2,3,4,5,6,8,10],[7,9]] => 000001010 => 010100000 => 2
[[1,2,3,4,5,6,9,10],[7,8]] => 000001000 => 000100000 => 1
[[1,2,3,4,5,7,8,10],[6,9]] => 000010010 => 010010000 => 2
[[1,2,3,4,5,8,9,10],[6,7]] => 000010000 => 000010000 => 1
[[1,2,3,4,6,7,8,10],[5,9]] => 000100010 => 010001000 => 2
[[1,2,3,4,6,7,9,10],[5,8]] => 000100100 => 001001000 => 2
[[1,2,3,4,6,8,9,10],[5,7]] => 000101000 => 000101000 => 2
[[1,2,3,4,6,7,8,9,10],[5]] => 000100000 => 000001000 => 1
[[1,2,3,4,5,6,7,9,10],[8]] => 000000100 => 001000000 => 1
[[1,2,3,4,5,6,8,9,10],[7]] => 000001000 => 000100000 => 1
[[1,2,3,4,5,7,8,9,10],[6]] => 000010000 => 000010000 => 1
[[1,2,4,6,8,10,12],[3,5,7,9,11]] => 01010101010 => 01010101010 => 5
[[1,2,4,6,8,9,10,12],[3,5,7,11]] => 01010100010 => 01000101010 => 4
[[1,2,4,6,8,9,11,12],[3,5,7,10]] => 01010100100 => 00100101010 => 4
[[1,2,4,6,7,8,10,12],[3,5,9,11]] => 01010001010 => 01010001010 => 4
[[1,2,4,6,7,8,11,12],[3,5,9,10]] => 01010001000 => 00010001010 => 3
[[1,2,4,6,7,9,10,12],[3,5,8,11]] => 01010010010 => 01001001010 => 4
[[1,2,4,6,7,9,11,12],[3,5,8,10]] => 01010010100 => 00101001010 => 4
[[1,2,4,6,7,8,9,11,12],[3,5,10]] => 01010000100 => 00100001010 => 3
[[1,2,4,6,7,8,10,11,12],[3,5,9]] => 01010001000 => 00010001010 => 3
[[1,2,4,5,6,8,10,12],[3,7,9,11]] => 01000101010 => 01010100010 => 4
[[1,2,4,5,6,8,11,12],[3,7,9,10]] => 01000101000 => 00010100010 => 3
[[1,2,4,5,6,9,10,12],[3,7,8,11]] => 01000100010 => 01000100010 => 3
[[1,2,4,5,6,9,11,12],[3,7,8,10]] => 01000100100 => 00100100010 => 3
[[1,2,4,5,7,8,10,12],[3,6,9,11]] => 01001001010 => 01010010010 => 4
[[1,2,4,5,7,8,11,12],[3,6,9,10]] => 01001001000 => 00010010010 => 3
[[1,2,4,5,7,9,10,12],[3,6,8,11]] => 01001010010 => 01001010010 => 4
[[1,2,4,5,7,9,11,12],[3,6,8,10]] => 01001010100 => 00101010010 => 4
[[1,2,4,5,7,8,9,10,12],[3,6,11]] => 01001000010 => 01000010010 => 3
[[1,2,4,5,7,8,9,11,12],[3,6,10]] => 01001000100 => 00100010010 => 3
[[1,2,4,5,7,8,10,11,12],[3,6,9]] => 01001001000 => 00010010010 => 3
[[1,2,4,5,6,7,8,11,12],[3,9,10]] => 01000001000 => 00010000010 => 2
[[1,2,4,5,6,7,9,10,12],[3,8,11]] => 01000010010 => 01001000010 => 3
[[1,2,4,5,6,7,9,11,12],[3,8,10]] => 01000010100 => 00101000010 => 3
[[1,2,4,5,6,7,10,11,12],[3,8,9]] => 01000010000 => 00001000010 => 2
[[1,2,4,5,6,8,9,10,12],[3,7,11]] => 01000100010 => 01000100010 => 3
[[1,2,4,5,6,8,9,11,12],[3,7,10]] => 01000100100 => 00100100010 => 3
[[1,2,4,5,6,8,10,11,12],[3,7,9]] => 01000101000 => 00010100010 => 3
[[1,2,4,5,6,7,8,10,11,12],[3,9]] => 01000001000 => 00010000010 => 2
[[1,2,4,5,6,7,9,10,11,12],[3,8]] => 01000010000 => 00001000010 => 2
[[1,2,4,5,6,7,8,9,10,11,12],[3]] => 01000000000 => 00000000010 => 1
[[1,2,3,4,6,8,11,12],[5,7,9,10]] => 00010101000 => 00010101000 => 3
[[1,2,3,4,6,9,10,12],[5,7,8,11]] => 00010100010 => 01000101000 => 3
[[1,2,3,4,6,9,11,12],[5,7,8,10]] => 00010100100 => 00100101000 => 3
[[1,2,3,4,7,8,10,12],[5,6,9,11]] => 00010001010 => 01010001000 => 3
[[1,2,3,4,7,8,11,12],[5,6,9,10]] => 00010001000 => 00010001000 => 2
[[1,2,3,4,7,9,10,12],[5,6,8,11]] => 00010010010 => 01001001000 => 3
[[1,2,3,4,7,9,11,12],[5,6,8,10]] => 00010010100 => 00101001000 => 3
[[1,2,3,4,7,9,10,11,12],[5,6,8]] => 00010010000 => 00001001000 => 2
[[1,2,3,4,7,8,9,10,12],[5,6,11]] => 00010000010 => 01000001000 => 2
[[1,2,3,4,7,8,9,11,12],[5,6,10]] => 00010000100 => 00100001000 => 2
[[1,2,3,4,7,8,10,11,12],[5,6,9]] => 00010001000 => 00010001000 => 2
[[1,2,3,5,6,8,10,12],[4,7,9,11]] => 00100101010 => 01010100100 => 4
[[1,2,3,5,6,8,11,12],[4,7,9,10]] => 00100101000 => 00010100100 => 3
[[1,2,3,5,6,9,10,12],[4,7,8,11]] => 00100100010 => 01000100100 => 3
[[1,2,3,5,6,9,11,12],[4,7,8,10]] => 00100100100 => 00100100100 => 3
[[1,2,3,5,7,8,10,12],[4,6,9,11]] => 00101001010 => 01010010100 => 4
[[1,2,3,5,7,8,11,12],[4,6,9,10]] => 00101001000 => 00010010100 => 3
[[1,2,3,5,7,9,10,12],[4,6,8,11]] => 00101010010 => 01001010100 => 4
[[1,2,3,5,7,9,11,12],[4,6,8,10]] => 00101010100 => 00101010100 => 4
[[1,2,3,5,7,8,9,10,12],[4,6,11]] => 00101000010 => 01000010100 => 3
[[1,2,3,5,7,8,9,11,12],[4,6,10]] => 00101000100 => 00100010100 => 3
[[1,2,3,5,7,8,10,11,12],[4,6,9]] => 00101001000 => 00010010100 => 3
[[1,2,3,5,6,7,8,10,12],[4,9,11]] => 00100001010 => 01010000100 => 3
[[1,2,3,5,6,7,8,11,12],[4,9,10]] => 00100001000 => 00010000100 => 2
[[1,2,3,5,6,7,9,10,12],[4,8,11]] => 00100010010 => 01001000100 => 3
[[1,2,3,5,6,7,9,11,12],[4,8,10]] => 00100010100 => 00101000100 => 3
[[1,2,3,5,6,7,10,11,12],[4,8,9]] => 00100010000 => 00001000100 => 2
[[1,2,3,5,6,8,9,10,12],[4,7,11]] => 00100100010 => 01000100100 => 3
[[1,2,3,5,6,8,9,11,12],[4,7,10]] => 00100100100 => 00100100100 => 3
[[1,2,3,5,6,8,10,11,12],[4,7,9]] => 00100101000 => 00010100100 => 3
[[1,2,3,5,6,7,8,9,11,12],[4,10]] => 00100000100 => 00100000100 => 2
[[1,2,3,5,6,7,8,10,11,12],[4,9]] => 00100001000 => 00010000100 => 2
[[1,2,3,5,6,7,9,10,11,12],[4,8]] => 00100010000 => 00001000100 => 2
[[1,2,3,4,5,6,10,11,12],[7,8,9]] => 00000100000 => 00000100000 => 1
[[1,2,3,4,5,7,8,11,12],[6,9,10]] => 00001001000 => 00010010000 => 2
[[1,2,3,4,5,7,10,11,12],[6,8,9]] => 00001010000 => 00001010000 => 2
[[1,2,3,4,5,8,9,10,12],[6,7,11]] => 00001000010 => 01000010000 => 2
[[1,2,3,4,5,8,9,11,12],[6,7,10]] => 00001000100 => 00100010000 => 2
[[1,2,3,4,5,8,10,11,12],[6,7,9]] => 00001001000 => 00010010000 => 2
[[1,2,3,4,6,7,8,10,12],[5,9,11]] => 00010001010 => 01010001000 => 3
[[1,2,3,4,6,7,8,11,12],[5,9,10]] => 00010001000 => 00010001000 => 2
[[1,2,3,4,6,7,9,10,12],[5,8,11]] => 00010010010 => 01001001000 => 3
[[1,2,3,4,6,7,9,11,12],[5,8,10]] => 00010010100 => 00101001000 => 3
[[1,2,3,4,6,7,10,11,12],[5,8,9]] => 00010010000 => 00001001000 => 2
[[1,2,3,4,6,8,9,10,12],[5,7,11]] => 00010100010 => 01000101000 => 3
[[1,2,3,4,6,8,9,11,12],[5,7,10]] => 00010100100 => 00100101000 => 3
[[1,2,3,4,6,8,10,11,12],[5,7,9]] => 00010101000 => 00010101000 => 3
[[1,2,3,4,6,7,8,9,10,12],[5,11]] => 00010000010 => 01000001000 => 2
[[1,2,3,4,6,7,8,9,11,12],[5,10]] => 00010000100 => 00100001000 => 2
[[1,2,3,4,6,7,8,10,11,12],[5,9]] => 00010001000 => 00010001000 => 2
[[1,2,3,4,6,7,9,10,11,12],[5,8]] => 00010010000 => 00001001000 => 2
[[1,2,3,4,5,6,9,10,11,12],[7,8]] => 00000100000 => 00000100000 => 1
[[1,2,3,4,5,7,8,9,10,12],[6,11]] => 00001000010 => 01000010000 => 2
[[1,2,3,4,5,7,8,9,11,12],[6,10]] => 00001000100 => 00100010000 => 2
[[1,2,3,4,5,7,8,10,11,12],[6,9]] => 00001001000 => 00010010000 => 2
[[1,2,3,4,5,7,9,10,11,12],[6,8]] => 00001010000 => 00001010000 => 2
[[1,2,3,4,5,6,7,8,9,10,12],[11]] => 00000000010 => 01000000000 => 1
[[1,2,3,4,5,6,8,9,10,11,12],[7]] => 00000100000 => 00000100000 => 1
[[1,2,5,6,7,8],[3,4,9]] => 01000001 => 10000010 => 2
[[1,2,5,6,7,8],[3,4],[9]] => 01000001 => 10000010 => 2
[[1,4,5,6,7,8],[2],[3],[9]] => 11000001 => 10000011 => 3
[[1,2,3,7,8],[4,5,6,9]] => 00100001 => 10000100 => 2
[[1,2,3,7,8],[4,5,6],[9]] => 00100001 => 10000100 => 2
[[1,3,6,7,8],[2,5],[4,9]] => 10100001 => 10000101 => 3
[[1,3,6,7,8],[2,5],[4],[9]] => 10100001 => 10000101 => 3
[[1,5,6,7,8],[2],[3],[4],[9]] => 11100001 => 10000111 => 4
[[1,3,4,8],[2,6,7],[5,9]] => 10010001 => 10001001 => 3
[[1,3,4,8],[2,6,7],[5],[9]] => 10010001 => 10001001 => 3
[[1,2,7,8],[3,4],[5,6],[9]] => 01010001 => 10001010 => 3
[[1,4,7,8],[2,6],[3],[5],[9]] => 11010001 => 10001011 => 4
[[1,6,7,8],[2],[3],[4],[5],[9]] => 11110001 => 10001111 => 5
[[1,2,5],[3,4,8],[6,7],[9]] => 01001001 => 10010010 => 3
[[1,4,5],[2,7,8],[3],[6],[9]] => 11001001 => 10010011 => 4
[[1,3,8],[2,5],[4,7],[6,9]] => 10101001 => 10010101 => 4
[[1,3,8],[2,5],[4,7],[6],[9]] => 10101001 => 10010101 => 4
[[1,5,8],[2,7],[3],[4],[6],[9]] => 11101001 => 10010111 => 5
[[1,7,8],[2],[3],[4],[5],[6],[9]] => 11111001 => 10011111 => 6
[[1,2,5,6,7,8,9],[3,4,10]] => 010000001 => 100000010 => 2
[[1,2,5,6,7,8,9],[3,4],[10]] => 010000001 => 100000010 => 2
[[1,2,3,7,8,9],[4,5,6,10]] => 001000001 => 100000100 => 2
[[1,2,3,7,8,9],[4,5,6],[10]] => 001000001 => 100000100 => 2
[[1,2,3,4,9],[5,6,7,8],[10]] => 000100001 => 100001000 => 2
[[1,2,7,8,9],[3,4],[5,6],[10]] => 010100001 => 100001010 => 3
[[1,2,5,9],[3,4,8],[6,7,10]] => 010010001 => 100010010 => 3
[[1,2,5,9],[3,4,8],[6,7],[10]] => 010010001 => 100010010 => 3
[[1,3,6],[2,5,9],[4,8],[7,10]] => 101001001 => 100100101 => 4
[[1,3,6],[2,5,9],[4,8],[7],[10]] => 101001001 => 100100101 => 4
[[1,2,9],[3,4],[5,6],[7,8],[10]] => 010101001 => 100101010 => 4
[[1,2,3,6,7,8,9],[4,5]] => 00100000 => 00000100 => 1
[[1,2,5,6,7,8,9],[3],[4]] => 01100000 => 00000110 => 2
[[1,2,3,4,8,9],[5,6,7]] => 00010000 => 00001000 => 1
[[1,2,4,7,8,9],[3,6],[5]] => 01010000 => 00001010 => 2
[[1,2,6,7,8,9],[3],[4],[5]] => 01110000 => 00001110 => 3
[[1,2,4,5,9],[3,7,8],[6]] => 01001000 => 00010010 => 2
[[1,2,3,8,9],[4,5],[6,7]] => 00101000 => 00010100 => 2
[[1,2,5,8,9],[3,7],[4],[6]] => 01101000 => 00010110 => 3
[[1,2,7,8,9],[3],[4],[5],[6]] => 01111000 => 00011110 => 4
[[1,2,5,6],[3,4,8,9],[7]] => 01000100 => 00100010 => 2
[[1,2,3,6],[4,5,9],[7,8]] => 00100100 => 00100100 => 2
[[1,2,5,6],[3,8,9],[4],[7]] => 01100100 => 00100110 => 3
[[1,2,4,9],[3,6],[5,8],[7]] => 01010100 => 00101010 => 3
[[1,2,6,9],[3,8],[4],[5],[7]] => 01110100 => 00101110 => 4
[[1,2,8,9],[3],[4],[5],[6],[7]] => 01111100 => 00111110 => 5
[[1,2,4],[3,6,7],[5,9],[8]] => 01010010 => 01001010 => 3
[[1,2,7],[3,6,9],[4],[5],[8]] => 01110010 => 01001110 => 4
[[1,2,5],[3,7],[4,9],[6],[8]] => 01101010 => 01010110 => 4
[[1,2,7],[3,9],[4],[5],[6],[8]] => 01111010 => 01011110 => 5
[[1,2],[3,6],[4,8],[5],[7],[9]] => 01110101 => 10101110 => 5
[[1,2],[3,8],[4],[5],[6],[7],[9]] => 01111101 => 10111110 => 6
[[1,2,3,6,7,8,9,10],[4,5]] => 001000000 => 000000100 => 1
[[1,2,3,4,8,9,10],[5,6,7]] => 000100000 => 000001000 => 1
[[1,2,4,7,8,9,10],[3,6],[5]] => 010100000 => 000001010 => 2
[[1,2,4,5,9,10],[3,7,8],[6]] => 010010000 => 000010010 => 2
[[1,2,4,5,6],[3,8,9,10],[7]] => 010001000 => 000100010 => 2
[[1,2,3,6,10],[4,5,9],[7,8]] => 001001000 => 000100100 => 2
[[1,2,4,9,10],[3,6],[5,8],[7]] => 010101000 => 000101010 => 3
[[1,2,4,7],[3,6,10],[5,9],[8]] => 010100100 => 001001010 => 3
[[1,2,3],[4,5,8],[6,7],[9,10]] => 001010010 => 010010100 => 3
[[1,2,4],[3,6],[5,8],[7,10],[9]] => 010101010 => 010101010 => 4
[[1,2],[3,5],[4,7],[6,9],[8],[10]] => 011010101 => 101010110 => 5
[[1,2],[3,7],[4,9],[5],[6],[8],[10]] => 011110101 => 101011110 => 6
[[1,2],[3,9],[4],[5],[6],[7],[8],[10]] => 011111101 => 101111110 => 7
[[1,2,3,4,7,8,9],[5,6]] => 00010000 => 00001000 => 1
[[1,2,4,5,8,9],[3,7],[6]] => 01001000 => 00010010 => 2
[[1,2,4,5,6,7],[3,9],[8]] => 01000010 => 01000010 => 2
[[1,2,5,6,9],[3,8],[4],[7]] => 01100100 => 00100110 => 3
[[1,2,3,4,7,8],[5,6],[9]] => 00010001 => 10001000 => 2
[[1,2,5,6,7,8],[3],[4],[9]] => 01100001 => 10000110 => 3
[[1,2,4,5],[3,7],[6,9],[8]] => 01001010 => 01010010 => 3
[[1,2,6,7],[3,9],[4],[5],[8]] => 01110010 => 01001110 => 4
[[1,2,5,6],[3,8],[4],[7],[9]] => 01100101 => 10100110 => 4
[[1,2,7,8],[3],[4],[5],[6],[9]] => 01111001 => 10011110 => 5
[[1,2,4,5,8,9,10],[3,7],[6]] => 010010000 => 000010010 => 2
[[1,2,4,5,6,7],[3,9,10],[8]] => 010000100 => 001000010 => 2
[[1,2,3,4,9,10],[5,6],[7,8]] => 000101000 => 000101000 => 2
[[1,2,4,5,6,7,8,9],[3],[10]] => 010000001 => 100000010 => 2
[[1,2,3,4,7,8],[5,6],[9,10]] => 000100010 => 010001000 => 2
[[1,2,5,6,7,8],[3,10],[4],[9]] => 011000010 => 010000110 => 3
[[1,2,4,5,10],[3,7],[6,9],[8]] => 010010100 => 001010010 => 3
[[1,2,4,5,8,9],[3,7],[6],[10]] => 010010001 => 100010010 => 3
[[1,2,6,7,8,9],[3],[4],[5],[10]] => 011100001 => 100001110 => 4
[[1,2,4,5],[3,7],[6,9],[8],[10]] => 010010101 => 101010010 => 4
[[1,2,6,7],[3,9],[4],[5],[8],[10]] => 011100101 => 101001110 => 5
[[1,2,8,9],[3],[4],[5],[6],[7],[10]] => 011111001 => 100111110 => 6
[[1,3],[2,9],[4],[5],[6],[7],[8],[10]] => 101111101 => 101111101 => 7
[[1,3],[2,8],[4],[5],[6],[7],[9],[10]] => 101111011 => 110111101 => 7
[[1,3],[2,5],[4,7],[6,9],[8,11],[10],[12]] => 10101010101 => 10101010101 => 6
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => 10111111111 => 11111111101 => 10
[[1,2],[3,5],[4],[6],[7],[8],[9]] => 01101111 => 11110110 => 6
[[1,2,4],[3],[5],[6],[7],[8],[9]] => 01011111 => 11111010 => 6
[[1,2],[3,4],[5,7],[6],[8],[9]] => 01011011 => 11011010 => 5
[[1,3,6],[2,5],[4],[7],[8],[9]] => 10100111 => 11100101 => 5
[[1,2,3,5],[4],[6],[7],[8],[9]] => 00101111 => 11110100 => 5
[[1,2],[3,4],[5,6],[7,9],[8]] => 01010110 => 01101010 => 4
[[1,2,3],[4,5,7],[6],[8],[9]] => 00101011 => 11010100 => 4
[[1,2,4,7],[3,6],[5],[8],[9]] => 01010011 => 11001010 => 4
[[1,2,3,4,6],[5],[7],[8],[9]] => 00010111 => 11101000 => 4
[[1,3,4],[2,7],[5,8],[6,9]] => 10011011 => 11011001 => 5
[[1,2,5],[3,6,9],[4,8],[7]] => 01101100 => 00110110 => 4
[[1,3,5,8],[2,4,7],[6],[9]] => 10101001 => 10010101 => 4
[[1,2,3,5,8],[4,7],[6],[9]] => 00101001 => 10010100 => 3
[[1,2,3,4,5,7],[6],[8],[9]] => 00001011 => 11010000 => 3
[[1,3,6,9],[2,5,8],[4,7]] => 10100100 => 00100101 => 3
[[1,2,3,5,6],[4,8],[7,9]] => 00100101 => 10100100 => 3
[[1,2,3,4],[5,6,7,9],[8]] => 00010010 => 01001000 => 2
[[1,2,4,6,9],[3,5,8],[7]] => 01010100 => 00101010 => 3
[[1,2,3,4,6,9],[5,8],[7]] => 00010100 => 00101000 => 2
[[1,2,3,4,5,6,8],[7],[9]] => 00000101 => 10100000 => 2
[[1,2,3,5,7,9],[4,6,8]] => 00101010 => 01010100 => 3
[[1,2,3,4,5,7,9],[6,8]] => 00001010 => 01010000 => 2
[[1,2,4],[3],[5],[6],[7],[8],[9],[10]] => 010111111 => 111111010 => 7
[[1,2,3,5],[4],[6],[7],[8],[9],[10]] => 001011111 => 111110100 => 6
[[1,2],[3,4],[5,6],[7,9],[8],[10]] => 010101101 => 101101010 => 5
[[1,2,3],[4,5,7],[6],[8],[9],[10]] => 001010111 => 111010100 => 5
[[1,2,3,4,6],[5],[7],[8],[9],[10]] => 000101111 => 111101000 => 5
[[1,3,4],[2,7],[5,8],[6,10],[9]] => 100110110 => 011011001 => 5
[[1,2,5],[3,6,9],[4,8],[7],[10]] => 011011001 => 100110110 => 5
[[1,2,3,5,8],[4,7],[6],[9],[10]] => 001010011 => 110010100 => 4
[[1,2,3,4,5,7],[6],[8],[9],[10]] => 000010111 => 111010000 => 4
[[1,2,5],[3,6,7],[4,9],[8,10]] => 011010101 => 101010110 => 5
[[1,2,3],[4,5,6],[7,8,10],[9]] => 001001010 => 010100100 => 3
[[1,2,3,5,6],[4,8],[7,10],[9]] => 001001010 => 010100100 => 3
[[1,2,3,4],[5,6,7,9],[8],[10]] => 000100101 => 101001000 => 3
[[1,2,4,6,9],[3,5,8],[7],[10]] => 010101001 => 100101010 => 4
[[1,2,3,4,5,6,8],[7],[9],[10]] => 000001011 => 110100000 => 3
[[1,2,4,7,10],[3,6,9],[5,8]] => 010100100 => 001001010 => 3
[[1,2,3,4,6,7],[5,9],[8,10]] => 000100101 => 101001000 => 3
[[1,3,5,7,10],[2,4,6,9],[8]] => 101010100 => 001010101 => 4
[[1,2,3,5,7,10],[4,6,9],[8]] => 001010100 => 001010100 => 3
[[1,2,3,4,5,6,7,9],[8],[10]] => 000000101 => 101000000 => 2
[[1,2,8],[3,9],[4],[5],[6],[7]] => 01111101 => 10111110 => 6
[[1,2,7],[3,8],[4,9],[5],[6]] => 01111011 => 11011110 => 6
[[1,2,7,9],[3,8],[4],[5],[6]] => 01111010 => 01011110 => 5
[[1,2,6,9],[3,7],[4,8],[5]] => 01110110 => 01101110 => 5
[[1,2,6,8],[3,7,9],[4],[5]] => 01110101 => 10101110 => 5
[[1,2,6,8,9],[3,7],[4],[5]] => 01110100 => 00101110 => 4
[[1,2,5,8],[3,6,9],[4,7]] => 01101101 => 10110110 => 5
[[1,2,5,8,9],[3,6],[4,7]] => 01101100 => 00110110 => 4
[[1,2,5,7,8,9],[3,6],[4]] => 01101000 => 00010110 => 3
[[1,2,4,6,8,9],[3,5,7]] => 01010100 => 00101010 => 3
[[1,2,4,6,7,8,9],[3,5]] => 01010000 => 00001010 => 2
[[1,2,9],[3,10],[4],[5],[6],[7],[8]] => 011111101 => 101111110 => 7
[[1,2,8],[3,9],[4,10],[5],[6],[7]] => 011111011 => 110111110 => 7
[[1,2,7],[3,8],[4,9],[5,10],[6]] => 011110111 => 111011110 => 7
[[1,2,7,9],[3,8,10],[4],[5],[6]] => 011110101 => 101011110 => 6
[[1,2,6,9],[3,7,10],[4,8],[5]] => 011101101 => 101101110 => 6
[[1,2,5,7,9],[3,6,8,10],[4]] => 011010101 => 101010110 => 5
[[1,2,3,5],[4,7],[6,9],[8,10]] => 001010101 => 101010100 => 4
[[1,2,4,6],[3,5],[7,8],[9,10]] => 010101010 => 010101010 => 4
[[1,2,4,6],[3,5],[7,9],[8,10]] => 010101101 => 101101010 => 5
[[1,2,4,7],[3,5],[6,9],[8,10]] => 010110101 => 101011010 => 5
[[1,2,4,5],[3,7],[6,9],[8,10]] => 010010101 => 101010010 => 4
[[1,2,4,6],[3,7],[5,9],[8,10]] => 010101101 => 101101010 => 5
[[1,2,4,6],[3,8],[5,9],[7,10]] => 010101011 => 110101010 => 5
[[1,2,5,7],[3,6],[4,9],[8,10]] => 011010101 => 101010110 => 5
[[1,2,5,8],[3,6],[4,9],[7,10]] => 011011011 => 110110110 => 6
[[1,2,5,6],[3,7],[4,9],[8,10]] => 011001101 => 101100110 => 5
[[1,2,5,6],[3,8],[4,9],[7,10]] => 011001011 => 110100110 => 5
[[1,2,5,7],[3,8],[4,9],[6,10]] => 011010111 => 111010110 => 6
[[1,2,6,9],[3,7],[4,8],[5,10]] => 011101101 => 101101110 => 6
[[1,2,6,7],[3,8],[4,9],[5,10]] => 011100111 => 111001110 => 6
[[1,2,4,6],[3,5],[7,8],[9,10],[11,12]] => 01010101010 => 01010101010 => 5
[[1,2,4,5],[3,7],[6,9],[8,11],[10,12]] => 01001010101 => 10101010010 => 5
[[1,5],[2,6],[3],[4],[7],[8],[9]] => 11101111 => 11110111 => 7
[[1,3,6],[2,7],[4],[5],[8],[9]] => 10110111 => 11101101 => 6
[[1,3,8],[2,9],[4],[5],[6],[7]] => 10111101 => 10111101 => 6
[[1,5,7],[2,6,8],[3],[4],[9]] => 11101011 => 11010111 => 6
[[1,3,4,7],[2,8],[5],[6],[9]] => 10011011 => 11011001 => 5
[[1,5,9],[2,6],[3],[4],[7],[8]] => 11101110 => 01110111 => 6
[[1,3,4,9],[2],[5],[6],[7],[8]] => 10011110 => 01111001 => 5
[[1,3,4,5,8],[2,9],[6],[7]] => 10001101 => 10110001 => 4
[[1,3,4,7,9],[2,8],[5],[6]] => 10011010 => 01011001 => 4
[[1,3,4,5,6,9],[2],[7],[8]] => 10000110 => 01100001 => 3
[[1,3,8],[2,9],[4,10],[5],[6],[7]] => 101111011 => 110111101 => 7
[[1,3,10],[2],[4],[5],[6],[7],[8],[9]] => 101111110 => 011111101 => 7
[[1,3,6,10],[2,7],[4],[5],[8],[9]] => 101101110 => 011101101 => 6
[[1,3,4,5,10],[2],[6],[7],[8],[9]] => 100011110 => 011110001 => 5
[[1,3,4,5,8,10],[2,9],[6],[7]] => 100011010 => 010110001 => 4
[[1,3,4,5,6,7,10],[2],[8],[9]] => 100000110 => 011000001 => 3
[[1,6],[2,8],[3,9],[4],[5],[7]] => 11110101 => 10101111 => 6
[[1,6,8],[2,9],[3],[4],[5],[7]] => 11110101 => 10101111 => 6
[[1,5],[2,7],[3,8],[4,9],[6]] => 11101011 => 11010111 => 6
[[1,5,8],[2,7],[3,9],[4],[6]] => 11101001 => 10010111 => 5
[[1,5,7],[2,8,9],[3],[4],[6]] => 11101010 => 01010111 => 5
[[1,5,7,9],[2,8],[3],[4],[6]] => 11101010 => 01010111 => 5
[[1,4,8],[2,6],[3,7],[5,9]] => 11010101 => 10101011 => 5
[[1,4,7],[2,6,9],[3,8],[5]] => 11010010 => 01001011 => 4
[[1,4,7,9],[2,6],[3,8],[5]] => 11010010 => 01001011 => 4
[[1,4,6,8],[2,7,9],[3],[5]] => 11010101 => 10101011 => 5
[[1,4,6,8,9],[2,7],[3],[5]] => 11010100 => 00101011 => 4
[[1,3,6],[2,5,8],[4,7,9]] => 10100101 => 10100101 => 4
[[1,3,6,8],[2,5,9],[4,7]] => 10100101 => 10100101 => 4
[[1,3,6,8,9],[2,5],[4,7]] => 10100100 => 00100101 => 3
[[1,3,5,7],[2,6,8,9],[4]] => 10101010 => 01010101 => 4
[[1,3,5,7,9],[2,6,8],[4]] => 10101010 => 01010101 => 4
[[1,3,5,7,8,9],[2,6],[4]] => 10101000 => 00010101 => 3
[[1,6,8],[2,9,10],[3],[4],[5],[7]] => 111101010 => 010101111 => 6
[[1,6,8,10],[2,9],[3],[4],[5],[7]] => 111101010 => 010101111 => 6
[[1,5,8],[2,7,10],[3,9],[4],[6]] => 111010010 => 010010111 => 5
[[1,5,8,10],[2,7],[3,9],[4],[6]] => 111010010 => 010010111 => 5
[[1,5,7,9,10],[2,8],[3],[4],[6]] => 111010100 => 001010111 => 5
[[1,4,8],[2,6,10],[3,7],[5,9]] => 110101010 => 010101011 => 5
[[1,4,8,10],[2,6],[3,7],[5,9]] => 110101010 => 010101011 => 5
[[1,4,7,9,10],[2,6],[3,8],[5]] => 110100100 => 001001011 => 4
[[1,4,6,8],[2,7,9,10],[3],[5]] => 110101010 => 010101011 => 5
[[1,4,6,8,10],[2,7,9],[3],[5]] => 110101010 => 010101011 => 5
[[1,4,6,8,9,10],[2,7],[3],[5]] => 110101000 => 000101011 => 4
[[1,3,6,9],[2,5,8],[4,7,10]] => 101001001 => 100100101 => 4
[[1,3,6,8],[2,5,9,10],[4,7]] => 101001010 => 010100101 => 4
[[1,3,6,8,10],[2,5,9],[4,7]] => 101001010 => 010100101 => 4
[[1,3,6,8,9,10],[2,5],[4,7]] => 101001000 => 000100101 => 3
[[1,3,5,7,9],[2,6,8,10],[4]] => 101010101 => 101010101 => 5
[[1,3,5,7,9,10],[2,6,8],[4]] => 101010100 => 001010101 => 4
[[1,3,5,7,8,9,10],[2,6],[4]] => 101010000 => 000010101 => 3
[[1,7],[2,8],[3],[4],[5],[6],[9]] => 11111011 => 11011111 => 7
[[1,6],[2,7],[3,8],[4],[5],[9]] => 11110111 => 11101111 => 7
[[1,6,8],[2,7],[3],[4],[5],[9]] => 11110101 => 10101111 => 6
[[1,5,8],[2,6],[3,7],[4],[9]] => 11101101 => 10110111 => 6
[[1,5,7,8],[2,6],[3],[4],[9]] => 11101001 => 10010111 => 5
[[1,4,8],[2,5],[3,6],[7,9]] => 11011101 => 10111011 => 6
[[1,4,7],[2,5,8],[3,6],[9]] => 11011011 => 11011011 => 6
[[1,4,7,8],[2,5],[3,6],[9]] => 11011001 => 10011011 => 5
[[1,4,6,8],[2,5,7],[3],[9]] => 11010101 => 10101011 => 5
[[1,4,6,7,8],[2,5],[3],[9]] => 11010001 => 10001011 => 4
[[1,3,6],[2,4,7],[5,8,9]] => 10110110 => 01101101 => 5
[[1,3,6,8],[2,4,7],[5,9]] => 10110101 => 10101101 => 5
[[1,3,6,7,8],[2,4],[5,9]] => 10110001 => 10001101 => 4
[[1,3,5,7,8],[2,4,6],[9]] => 10101001 => 10010101 => 4
[[1,3,5,6,7,8],[2,4],[9]] => 10100001 => 10000101 => 3
[[1,2,4,6,7,8],[3,5,9]] => 01010001 => 10001010 => 3
[[1,2,4,5,6,7,8],[3,9]] => 01000001 => 10000010 => 2
[[1,3,5,7,9],[2,4,6,8],[10]] => 101010101 => 101010101 => 5
[[1,2,4,6,8,9],[3,5,7,10]] => 010101001 => 100101010 => 4
[[1,2,4,6,7,8,9],[3,5,10]] => 010100001 => 100001010 => 3
[[1,2,4,5,6,7,8,9],[3,10]] => 010000001 => 100000010 => 2
[[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110 => 01111110 => 6
[[1,2],[3,8],[4,9],[5],[6],[7]] => 01111101 => 10111110 => 6
[[1,2],[3,7],[4,8],[5,9],[6]] => 01111011 => 11011110 => 6
[[1,2,7],[3,8,9],[4],[5],[6]] => 01111010 => 01011110 => 5
[[1,2,6],[3,7,9],[4,8],[5]] => 01110110 => 01101110 => 5
[[1,2,5],[3,6,8],[4,7,9]] => 01101101 => 10110110 => 5
[[1,2,5,7],[3,6,8,9],[4]] => 01101010 => 01010110 => 4
[[1,2],[3,9],[4,10],[5],[6],[7],[8]] => 011111101 => 101111110 => 7
[[1,2],[3,8],[4,9],[5,10],[6],[7]] => 011111011 => 110111110 => 7
[[1,2,6],[3,7,9],[4,8,10],[5]] => 011101101 => 101101110 => 6
[[1,3],[2,8],[4,9],[5],[6],[7]] => 10111101 => 10111101 => 6
[[1,2,3],[4,9],[5],[6],[7],[8]] => 00111110 => 01111100 => 5
[[1,4],[2,7],[3,8],[5,9],[6]] => 11011011 => 11011011 => 6
[[1,3,9],[2,4],[5,8],[6],[7]] => 10111100 => 00111101 => 5
[[1,2,4],[3,8,9],[5],[6],[7]] => 01011100 => 00111010 => 4
[[1,2,3,4],[5,9],[6],[7],[8]] => 00011110 => 01111000 => 4
[[1,4,9],[2,5],[3,7],[6,8]] => 11011010 => 01011011 => 5
[[1,2,5],[3,4,9],[6,8],[7]] => 01001100 => 00110010 => 3
[[1,4,5,9],[2,7],[3,8],[6]] => 11001010 => 01010011 => 4
[[1,2,3,5],[4,8,9],[6],[7]] => 00101100 => 00110100 => 3
[[1,2,3,4,5],[6,9],[7],[8]] => 00001110 => 01110000 => 3
[[1,4,5,6,9],[2,7],[3,8]] => 11000110 => 01100011 => 4
[[1,2,4,6],[3,5,8,9],[7]] => 01010100 => 00101010 => 3
[[1,2,3,4,6],[5,8,9],[7]] => 00010100 => 00101000 => 2
[[1,2,3,4,5,6],[7,9],[8]] => 00000110 => 01100000 => 2
[[1,2,3,5,7],[4,6,8,9]] => 00101010 => 01010100 => 3
[[1,2,3,4,5,7],[6,8,9]] => 00001010 => 01010000 => 2
[[1,3],[2,9],[4,10],[5],[6],[7],[8]] => 101111101 => 101111101 => 7
[[1,3,10],[2,4],[5,9],[6],[7],[8]] => 101111100 => 001111101 => 6
[[1,2,9],[3,5,10],[4,6],[7,8]] => 011011001 => 100110110 => 5
[[1,3,6],[2,5,9],[4,8,10],[7]] => 101001001 => 100100101 => 4
[[1,3,6,10],[2,4,7],[5,8,9]] => 101101100 => 001101101 => 5
[[1,2,4,7],[3,5,6,10],[8,9]] => 010100100 => 001001010 => 3
[[1,2,3,5,7],[4,6,9,10],[8]] => 001010100 => 001010100 => 3
[[1,2,3,4,6,8],[5,7,9,10]] => 000101010 => 010101000 => 3
[[1,2,3,4,5,6,8],[7,9,10]] => 000001010 => 010100000 => 2
[[1,3],[2,4],[5,9],[6],[7],[8]] => 10111110 => 01111101 => 6
[[1,3,9],[2,4],[5],[6],[7],[8]] => 10111110 => 01111101 => 6
[[1,4],[2,5],[3,6],[7,9],[8]] => 11011110 => 01111011 => 6
[[1,4,9],[2,5],[3,6],[7],[8]] => 11011110 => 01111011 => 6
[[1,2,4],[3,5,9],[6],[7],[8]] => 01011110 => 01111010 => 5
[[1,2,4,9],[3,5],[6],[7],[8]] => 01011110 => 01111010 => 5
[[1,2,5],[3,6,9],[4,7],[8]] => 01101110 => 01110110 => 5
[[1,2,5,9],[3,6],[4,7],[8]] => 01101110 => 01110110 => 5
[[1,3,5,9],[2,4,6],[7],[8]] => 10101110 => 01110101 => 5
[[1,2,3,5,9],[4,6],[7],[8]] => 00101110 => 01110100 => 4
[[1,3,6,9],[2,4,7],[5,8]] => 10110110 => 01101101 => 5
[[1,2,3,6,9],[4,7],[5,8]] => 00110110 => 01101100 => 4
[[1,2,4,6],[3,5,7,9],[8]] => 01010110 => 01101010 => 4
[[1,2,4,6,9],[3,5,7],[8]] => 01010110 => 01101010 => 4
[[1,2,3,4,6,9],[5,7],[8]] => 00010110 => 01101000 => 3
[[1,3],[2,4],[5,10],[6],[7],[8],[9]] => 101111110 => 011111101 => 7
[[1,3,10],[2,4],[5],[6],[7],[8],[9]] => 101111110 => 011111101 => 7
[[1,4],[2,5],[3,6],[7,10],[8],[9]] => 110111110 => 011111011 => 7
[[1,4,10],[2,5],[3,6],[7],[8],[9]] => 110111110 => 011111011 => 7
[[1,5,10],[2,6],[3,7],[4,8],[9]] => 111011110 => 011110111 => 7
[[1,3,5,10],[2,4,6],[7],[8],[9]] => 101011110 => 011110101 => 6
[[1,3,6],[2,4,7],[5,8,10],[9]] => 101101110 => 011101101 => 6
[[1,3,6,10],[2,4,7],[5,8],[9]] => 101101110 => 011101101 => 6
[[1,4],[2,5],[3],[6],[7],[8],[9]] => 11011111 => 11111011 => 7
[[1,5],[2,6],[3,7],[4],[8],[9]] => 11101111 => 11110111 => 7
[[1,3,5],[2,6],[4],[7],[8],[9]] => 10101111 => 11110101 => 6
[[1,3,6],[2,7],[4,8],[5],[9]] => 10110111 => 11101101 => 6
[[1,4,6],[2,5,7],[3],[8],[9]] => 11010111 => 11101011 => 6
[[1,3,4,6],[2,7],[5],[8],[9]] => 10010111 => 11101001 => 5
[[1,3,7],[2,4],[5,8],[6,9]] => 10111011 => 11011101 => 6
[[1,4,7],[2,5,8],[3,9],[6]] => 11011011 => 11011011 => 6
[[1,3,4,7],[2,8],[5,9],[6]] => 10011011 => 11011001 => 5
[[1,3,5,7],[2,6,8],[4],[9]] => 10101011 => 11010101 => 5
[[1,3,4,5,7],[2,8],[6],[9]] => 10001011 => 11010001 => 4
[[1,3,5,8],[2,6,9],[4,7]] => 10101101 => 10110101 => 5
[[1,3,4,5,8],[2,6],[7,9]] => 10001101 => 10110001 => 4
[[1,3,4,6,8],[2,7,9],[5]] => 10010101 => 10101001 => 4
[[1,3,4,5,6,8],[2,9],[7]] => 10000101 => 10100001 => 3
[[1,3,4,5,7,9],[2,6,8]] => 10001010 => 01010001 => 3
[[1,3,4,5,6,7,9],[2,8]] => 10000010 => 01000001 => 2
[[1,3,4,6,8,10],[2,5,7,9]] => 100101010 => 010101001 => 4
[[1,3,4,5,6,8,10],[2,7,9]] => 100001010 => 010100001 => 3
[[1,3,4,5,6,7,8,10],[2,9]] => 100000010 => 010000001 => 2
[[1,2,3,7],[4,8],[5,9],[6]] => 00111011 => 11011100 => 5
[[1,2,3,5,8],[4,6,9],[7]] => 00101101 => 10110100 => 4
[[1,2,3,4,5,8],[6,9],[7]] => 00001101 => 10110000 => 3
[[1,2,4,6,9],[3,5,7,10],[8]] => 010101101 => 101101010 => 5
[[1,2,3,4,5,7],[6,9],[8]] => 00001010 => 01010000 => 2
[[1,2,3,4,6],[5,7,8,9]] => 00010100 => 00101000 => 2
[[1,2,3,4,6],[5,7,9],[8]] => 00010110 => 01101000 => 3
[[1,2,3,4,6],[5,8],[7,9]] => 00010101 => 10101000 => 3
[[1,2,3,4,6],[5,8],[7],[9]] => 00010101 => 10101000 => 3
[[1,2,3,5],[4,6,7,9],[8]] => 00101010 => 01010100 => 3
[[1,2,3,5],[4,6,8],[7,9]] => 00101101 => 10110100 => 4
[[1,2,3,5],[4,6,8],[7],[9]] => 00101101 => 10110100 => 4
[[1,2,3,5],[4,7],[6,9],[8]] => 00101010 => 01010100 => 3
[[1,2,3,5],[4,7],[6],[8],[9]] => 00101011 => 11010100 => 4
[[1,2,4],[3,5,7],[6,8,9]] => 01011010 => 01011010 => 4
[[1,2,4],[3,5,7],[6,9],[8]] => 01011010 => 01011010 => 4
[[1,2,4],[3,5,7],[6],[8],[9]] => 01011011 => 11011010 => 5
[[1,2,4],[3,6],[5,8],[7,9]] => 01010101 => 10101010 => 4
[[1,2,4],[3,6],[5,8],[7],[9]] => 01010101 => 10101010 => 4
[[1,2,4],[3,6],[5],[7],[8],[9]] => 01010111 => 11101010 => 5
[[1,2,3,4,5,6,8],[7,10],[9]] => 000001010 => 010100000 => 2
[[1,2,3,4,5,7],[6,9],[8,10]] => 000010101 => 101010000 => 3
[[1,2,3,4,5,7],[6,9],[8],[10]] => 000010101 => 101010000 => 3
[[1,2,3,4,6],[5,7,8,10],[9]] => 000101010 => 010101000 => 3
[[1,2,3,4,6],[5,8],[7,10],[9]] => 000101010 => 010101000 => 3
[[1,2,3,4,6],[5,8],[7],[9],[10]] => 000101011 => 110101000 => 4
[[1,2,3,5],[4,6,7,9],[8,10]] => 001010101 => 101010100 => 4
[[1,2,3,5],[4,6,7,9],[8],[10]] => 001010101 => 101010100 => 4
[[1,2,3,5],[4,7],[6,9],[8],[10]] => 001010101 => 101010100 => 4
[[1,2,3,5],[4,7],[6],[8],[9],[10]] => 001010111 => 111010100 => 5
[[1,2,4],[3,5,7],[6,9],[8,10]] => 010110101 => 101011010 => 5
[[1,2,4],[3,5,7],[6,9],[8],[10]] => 010110101 => 101011010 => 5
[[1,2,4],[3,6],[5,8],[7],[9],[10]] => 010101011 => 110101010 => 5
[[1,2,4],[3,6],[5],[7],[8],[9],[10]] => 010101111 => 111101010 => 6
[[1,4,5,6],[2,8,9],[3],[7]] => 11000100 => 00100011 => 3
[[1,4,5],[2,7,8],[3,10],[6],[9]] => 110010010 => 010010011 => 4
[[1,2,4,5,6,7],[3,8,9]] => 01000010 => 01000010 => 2
[[1,2,4,5,6,7,8],[3,9,10]] => 010000010 => 010000010 => 2
[[1,3,8],[2,5],[4,7],[6,10],[9]] => 101010010 => 010010101 => 4
[[1,4,7],[2,6],[3,9],[5],[8]] => 11010010 => 01001011 => 4
[[1,6,7],[2,9],[3],[4],[5],[8]] => 11110010 => 01001111 => 5
[[1,3,6,7],[2,5,10],[4,9],[8]] => 101000100 => 001000101 => 3
[[1,5,8],[2,7],[3,10],[4],[6],[9]] => 111010010 => 010010111 => 5
[[1,7,8],[2,10],[3],[4],[5],[6],[9]] => 111110010 => 010011111 => 6
[[1,5,7,8],[2,6,9,10],[3],[4]] => 111010010 => 010010111 => 5
[[1,5,6,8],[2,7,9,10],[3],[4]] => 111001010 => 010100111 => 5
[[1,4,7,8],[2,6,9,10],[3],[5]] => 110100010 => 010001011 => 4
[[1,4,6,7],[2,8,9,10],[3],[5]] => 110100100 => 001001011 => 4
[[1,4,5,8],[2,7,9,10],[3],[6]] => 110010010 => 010010011 => 4
[[1,3,7,9],[2,5,8,10],[4],[6]] => 101010101 => 101010101 => 5
[[1,3,7,8],[2,5,9,10],[4],[6]] => 101010010 => 010010101 => 4
[[1,3,6,9],[2,5,8,10],[4],[7]] => 101001001 => 100100101 => 4
[[1,3,6,8],[2,5,9,10],[4],[7]] => 101001010 => 010100101 => 4
[[1,3,6,7],[2,5,9,10],[4],[8]] => 101000100 => 001000101 => 3
[[1,3,7,8],[2,6,9,10],[4],[5]] => 101100010 => 010001101 => 4
[[1,3,5,8],[2,7,9,10],[4],[6]] => 101010010 => 010010101 => 4
[[1,3,5,7],[2,8,9,10],[4],[6]] => 101010100 => 001010101 => 4
[[1,3,5,6],[2,8,9,10],[4],[7]] => 101001000 => 000100101 => 3
[[1,3,4,9],[2,6,7,10],[5],[8]] => 100100101 => 101001001 => 4
[[1,3,4,8],[2,6,7,10],[5],[9]] => 100100010 => 010001001 => 3
[[1,3,4,9],[2,6,8,10],[5],[7]] => 100101001 => 100101001 => 4
[[1,3,4,8],[2,6,9,10],[5],[7]] => 100101010 => 010101001 => 4
[[1,3,4,7],[2,6,9,10],[5],[8]] => 100100100 => 001001001 => 3
[[1,3,4,5],[2,7,8,10],[6],[9]] => 100010010 => 010010001 => 3
[[1,3,4,5],[2,7,9,10],[6],[8]] => 100010100 => 001010001 => 3
[[1,3,7,9,11],[2,5,8,10,12],[4],[6]] => 10101010101 => 10101010101 => 6
[[1,3,7,9,10],[2,5,8,11,12],[4],[6]] => 10101010010 => 01001010101 => 5
[[1,3,7,8,11],[2,5,9,10,12],[4],[6]] => 10101001001 => 10010010101 => 5
[[1,3,7,8,10],[2,5,9,11,12],[4],[6]] => 10101001010 => 01010010101 => 5
[[1,3,7,8,9],[2,5,10,11,12],[4],[6]] => 10101000100 => 00100010101 => 4
[[1,3,6,9,11],[2,5,8,10,12],[4],[7]] => 10100100101 => 10100100101 => 5
[[1,3,6,9,10],[2,5,8,11,12],[4],[7]] => 10100100010 => 01000100101 => 4
[[1,3,6,8,11],[2,5,9,10,12],[4],[7]] => 10100101001 => 10010100101 => 5
[[1,3,6,8,10],[2,5,9,11,12],[4],[7]] => 10100101010 => 01010100101 => 5
[[1,3,6,8,9],[2,5,10,11,12],[4],[7]] => 10100100100 => 00100100101 => 4
[[1,3,6,7,11],[2,5,9,10,12],[4],[8]] => 10100010001 => 10001000101 => 4
[[1,3,6,7,10],[2,5,9,11,12],[4],[8]] => 10100010010 => 01001000101 => 4
[[1,3,6,7,9],[2,5,10,11,12],[4],[8]] => 10100010100 => 00101000101 => 4
[[1,3,6,7,8],[2,5,10,11,12],[4],[9]] => 10100001000 => 00010000101 => 3
[[1,3,5,8,11],[2,7,9,10,12],[4],[6]] => 10101001001 => 10010010101 => 5
[[1,3,5,8,10],[2,7,9,11,12],[4],[6]] => 10101001010 => 01010010101 => 5
[[1,3,5,8,9],[2,7,10,11,12],[4],[6]] => 10101000100 => 00100010101 => 4
[[1,3,5,7,10],[2,8,9,11,12],[4],[6]] => 10101010010 => 01001010101 => 5
[[1,3,5,6,10],[2,8,9,11,12],[4],[7]] => 10100100010 => 01000100101 => 4
[[1,3,5,6,9],[2,8,10,11,12],[4],[7]] => 10100100100 => 00100100101 => 4
[[1,3,4,9,11],[2,6,7,10,12],[5],[8]] => 10010010101 => 10101001001 => 5
[[1,3,4,9,10],[2,6,7,11,12],[5],[8]] => 10010010010 => 01001001001 => 4
[[1,3,4,8,11],[2,6,7,10,12],[5],[9]] => 10010001001 => 10010001001 => 4
[[1,3,4,8,10],[2,6,7,11,12],[5],[9]] => 10010001010 => 01010001001 => 4
[[1,3,4,8,9],[2,6,7,11,12],[5],[10]] => 10010000100 => 00100001001 => 3
[[1,3,4,9,11],[2,6,8,10,12],[5],[7]] => 10010100101 => 10100101001 => 5
[[1,3,4,9,10],[2,6,8,11,12],[5],[7]] => 10010100010 => 01000101001 => 4
[[1,3,4,8,11],[2,6,9,10,12],[5],[7]] => 10010101001 => 10010101001 => 5
[[1,3,4,8,10],[2,6,9,11,12],[5],[7]] => 10010101010 => 01010101001 => 5
[[1,3,4,8,9],[2,6,10,11,12],[5],[7]] => 10010100100 => 00100101001 => 4
[[1,3,4,7,11],[2,6,9,10,12],[5],[8]] => 10010010001 => 10001001001 => 4
[[1,3,4,7,10],[2,6,9,11,12],[5],[8]] => 10010010010 => 01001001001 => 4
[[1,3,4,7,9],[2,6,10,11,12],[5],[8]] => 10010010100 => 00101001001 => 4
[[1,3,4,7,8],[2,6,10,11,12],[5],[9]] => 10010001000 => 00010001001 => 3
[[1,3,4,6,10],[2,8,9,11,12],[5],[7]] => 10010100010 => 01000101001 => 4
[[1,3,4,6,9],[2,8,10,11,12],[5],[7]] => 10010100100 => 00100101001 => 4
[[1,3,4,5,11],[2,7,8,9,12],[6],[10]] => 10001000101 => 10100010001 => 4
[[1,3,4,5,10],[2,7,8,9,12],[6],[11]] => 10001000010 => 01000010001 => 3
[[1,3,4,5,11],[2,7,8,10,12],[6],[9]] => 10001001001 => 10010010001 => 4
[[1,3,4,5,10],[2,7,8,11,12],[6],[9]] => 10001001010 => 01010010001 => 4
[[1,3,4,5,9],[2,7,8,11,12],[6],[10]] => 10001000100 => 00100010001 => 3
[[1,3,4,5,11],[2,7,9,10,12],[6],[8]] => 10001010001 => 10001010001 => 4
[[1,3,4,5,10],[2,7,9,11,12],[6],[8]] => 10001010010 => 01001010001 => 4
[[1,3,4,5,9],[2,7,10,11,12],[6],[8]] => 10001010100 => 00101010001 => 4
[[1,3,4,5,8],[2,7,10,11,12],[6],[9]] => 10001001000 => 00010010001 => 3
[[1,3,4,5,6],[2,8,9,10,11],[7],[12]] => 10000100001 => 10000100001 => 3
[[1,3,4,5,6],[2,8,9,10,12],[7],[11]] => 10000100010 => 01000100001 => 3
[[1,3,4,5,6],[2,8,9,11,12],[7],[10]] => 10000100100 => 00100100001 => 3
[[1,3,4,5,6],[2,8,10,11,12],[7],[9]] => 10000101000 => 00010100001 => 3
[[1,3,4,5,6,7],[2,9,10,11,12],[8]] => 10000010000 => 00001000001 => 2
[[1,2,3],[4,7,8],[5],[6],[9]] => 00111001 => 10011100 => 4
[[1,4,5,6,7,8],[2,9],[3]] => 11000001 => 10000011 => 3
[[1,2,3,5,6],[4,7,8,9]] => 00100100 => 00100100 => 2
[[1,2,5,6,7],[3,4,8],[9]] => 01000011 => 11000010 => 3
[[1,3,5,6,7],[2,8],[4,9]] => 10100011 => 11000101 => 4
[[1,5,6,7,8],[2,9],[3],[4]] => 11100001 => 10000111 => 4
[[1,2,3,6],[4,5,7,8],[9]] => 00100101 => 10100100 => 3
[[1,3,6,7],[2,4,8],[5,9]] => 10110011 => 11001101 => 5
[[1,2,3,6],[4,7,8],[5],[9]] => 00110101 => 10101100 => 4
[[1,4,6,7],[2,8],[3,9],[5]] => 11010011 => 11001011 => 5
[[1,6,7,8],[2,9],[3],[4],[5]] => 11110001 => 10001111 => 5
[[1,3,7],[2,5],[4,8],[6,9]] => 10101011 => 11010101 => 5
[[1,5,7],[2,8],[3,9],[4],[6]] => 11101011 => 11010111 => 6
[[1,7,8],[2,9],[3],[4],[5],[6]] => 11111001 => 10011111 => 6
[[1,4],[2,6],[3,8],[5,9],[7]] => 11010101 => 10101011 => 5
[[1,2,3,5,6,7],[4,8,9,10]] => 001000100 => 001000100 => 2
[[1,2,3,6,7],[4,5,8,9],[10]] => 001000101 => 101000100 => 3
[[1,2,3,6,7],[4,8,9],[5],[10]] => 001100101 => 101001100 => 4
[[1,3,4,7],[2,5,6,8],[9,10]] => 100100110 => 011001001 => 4
[[1,2,5],[3,4,8],[6,7,9],[10]] => 010010011 => 110010010 => 4
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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 1,2,1 1,4,4,1 1,6,12,6,1 1,9,28,28,9,1 1,12,57,92,57,12,1 1,16,105,260,260,105,16,1
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + q^{2}$
$F_{4} = 1 + 4\ q + 4\ q^{2} + q^{3}$
$F_{5} = 1 + 6\ q + 12\ q^{2} + 6\ q^{3} + q^{4}$
$F_{6} = 1 + 9\ q + 28\ q^{2} + 28\ q^{3} + 9\ q^{4} + q^{5}$
$F_{7} = 1 + 12\ q + 57\ q^{2} + 92\ q^{3} + 57\ q^{4} + 12\ q^{5} + q^{6}$
$F_{8} = 1 + 16\ q + 105\ q^{2} + 260\ q^{3} + 260\ q^{4} + 105\ q^{5} + 16\ q^{6} + q^{7}$
Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
This is also known as the Hamming weight of the word.
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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 $1\leq i < n$.
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 $1\leq i < n$.
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reverse
Description
Return the reversal of a binary word.
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