Identifier
Values
[1,1] => [1] => 10 => 11 => 2
[2,1] => [1] => 10 => 11 => 2
[1,1,1] => [1,1] => 110 => 111 => 3
[3,1] => [1] => 10 => 11 => 2
[2,2] => [2] => 100 => 011 => 2
[2,1,1] => [1,1] => 110 => 111 => 3
[1,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[4,1] => [1] => 10 => 11 => 2
[3,2] => [2] => 100 => 011 => 2
[3,1,1] => [1,1] => 110 => 111 => 3
[2,2,1] => [2,1] => 1010 => 1101 => 3
[2,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[1,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[5,1] => [1] => 10 => 11 => 2
[4,2] => [2] => 100 => 011 => 2
[4,1,1] => [1,1] => 110 => 111 => 3
[3,3] => [3] => 1000 => 0011 => 2
[3,2,1] => [2,1] => 1010 => 1101 => 3
[3,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[2,2,2] => [2,2] => 1100 => 0111 => 3
[2,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[2,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[6,1] => [1] => 10 => 11 => 2
[5,2] => [2] => 100 => 011 => 2
[5,1,1] => [1,1] => 110 => 111 => 3
[4,3] => [3] => 1000 => 0011 => 2
[4,2,1] => [2,1] => 1010 => 1101 => 3
[4,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[3,3,1] => [3,1] => 10010 => 01101 => 3
[3,2,2] => [2,2] => 1100 => 0111 => 3
[3,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[3,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[2,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[2,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[7,1] => [1] => 10 => 11 => 2
[6,2] => [2] => 100 => 011 => 2
[6,1,1] => [1,1] => 110 => 111 => 3
[5,3] => [3] => 1000 => 0011 => 2
[5,2,1] => [2,1] => 1010 => 1101 => 3
[5,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[4,4] => [4] => 10000 => 00011 => 2
[4,3,1] => [3,1] => 10010 => 01101 => 3
[4,2,2] => [2,2] => 1100 => 0111 => 3
[4,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[4,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[3,3,2] => [3,2] => 10100 => 11001 => 3
[3,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[3,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[3,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[3,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[2,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[2,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[8,1] => [1] => 10 => 11 => 2
[7,2] => [2] => 100 => 011 => 2
[7,1,1] => [1,1] => 110 => 111 => 3
[6,3] => [3] => 1000 => 0011 => 2
[6,2,1] => [2,1] => 1010 => 1101 => 3
[6,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[5,4] => [4] => 10000 => 00011 => 2
[5,3,1] => [3,1] => 10010 => 01101 => 3
[5,2,2] => [2,2] => 1100 => 0111 => 3
[5,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[5,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[4,4,1] => [4,1] => 100010 => 001101 => 3
[4,3,2] => [3,2] => 10100 => 11001 => 3
[4,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[4,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[4,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[4,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[3,3,3] => [3,3] => 11000 => 00111 => 3
[3,3,2,1] => [3,2,1] => 101010 => 110101 => 4
[3,3,1,1,1] => [3,1,1,1] => 1001110 => 0110111 => 5
[3,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[3,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[3,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[2,2,2,2,1] => [2,2,2,1] => 111010 => 111101 => 5
[2,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 1110111 => 6
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 11011111 => 7
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 111111111 => 9
[9,1] => [1] => 10 => 11 => 2
[8,2] => [2] => 100 => 011 => 2
[8,1,1] => [1,1] => 110 => 111 => 3
[7,3] => [3] => 1000 => 0011 => 2
[7,2,1] => [2,1] => 1010 => 1101 => 3
[7,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[6,4] => [4] => 10000 => 00011 => 2
[6,3,1] => [3,1] => 10010 => 01101 => 3
[6,2,2] => [2,2] => 1100 => 0111 => 3
[6,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[6,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[5,5] => [5] => 100000 => 000011 => 2
[5,4,1] => [4,1] => 100010 => 001101 => 3
[5,3,2] => [3,2] => 10100 => 11001 => 3
>>> Load all 843 entries. <<<
[5,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[5,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[5,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[5,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[4,4,2] => [4,2] => 100100 => 011001 => 3
[4,4,1,1] => [4,1,1] => 1000110 => 0011011 => 4
[4,3,3] => [3,3] => 11000 => 00111 => 3
[4,3,2,1] => [3,2,1] => 101010 => 110101 => 4
[4,3,1,1,1] => [3,1,1,1] => 1001110 => 0110111 => 5
[4,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[4,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[4,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[3,3,3,1] => [3,3,1] => 110010 => 011101 => 4
[3,3,2,2] => [3,2,2] => 101100 => 110011 => 4
[3,3,2,1,1] => [3,2,1,1] => 1010110 => 1101011 => 5
[3,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01101111 => 6
[3,2,2,2,1] => [2,2,2,1] => 111010 => 111101 => 5
[3,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 1110111 => 6
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 11011111 => 7
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[2,2,2,2,2] => [2,2,2,2] => 111100 => 011111 => 5
[2,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 1111011 => 6
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 11101111 => 7
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 111111111 => 9
[10,1] => [1] => 10 => 11 => 2
[9,2] => [2] => 100 => 011 => 2
[9,1,1] => [1,1] => 110 => 111 => 3
[8,3] => [3] => 1000 => 0011 => 2
[8,2,1] => [2,1] => 1010 => 1101 => 3
[8,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[7,4] => [4] => 10000 => 00011 => 2
[7,3,1] => [3,1] => 10010 => 01101 => 3
[7,2,2] => [2,2] => 1100 => 0111 => 3
[7,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[7,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[6,5] => [5] => 100000 => 000011 => 2
[6,4,1] => [4,1] => 100010 => 001101 => 3
[6,3,2] => [3,2] => 10100 => 11001 => 3
[6,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[6,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[6,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[6,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[5,5,1] => [5,1] => 1000010 => 0001101 => 3
[5,4,2] => [4,2] => 100100 => 011001 => 3
[5,4,1,1] => [4,1,1] => 1000110 => 0011011 => 4
[5,3,3] => [3,3] => 11000 => 00111 => 3
[5,3,2,1] => [3,2,1] => 101010 => 110101 => 4
[5,3,1,1,1] => [3,1,1,1] => 1001110 => 0110111 => 5
[5,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[5,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[5,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[4,4,3] => [4,3] => 101000 => 110001 => 3
[4,4,2,1] => [4,2,1] => 1001010 => 0110101 => 4
[4,4,1,1,1] => [4,1,1,1] => 10001110 => 00110111 => 5
[4,3,3,1] => [3,3,1] => 110010 => 011101 => 4
[4,3,2,2] => [3,2,2] => 101100 => 110011 => 4
[4,3,2,1,1] => [3,2,1,1] => 1010110 => 1101011 => 5
[4,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01101111 => 6
[4,2,2,2,1] => [2,2,2,1] => 111010 => 111101 => 5
[4,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 1110111 => 6
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 11011111 => 7
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[3,3,3,2] => [3,3,2] => 110100 => 111001 => 4
[3,3,3,1,1] => [3,3,1,1] => 1100110 => 0111011 => 5
[3,3,2,2,1] => [3,2,2,1] => 1011010 => 1101101 => 5
[3,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 11010111 => 6
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011011111 => 7
[3,2,2,2,2] => [2,2,2,2] => 111100 => 011111 => 5
[3,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 1111011 => 6
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 11101111 => 7
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 111111111 => 9
[2,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 1111101 => 6
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 11110111 => 7
[11,1] => [1] => 10 => 11 => 2
[10,2] => [2] => 100 => 011 => 2
[10,1,1] => [1,1] => 110 => 111 => 3
[9,3] => [3] => 1000 => 0011 => 2
[9,2,1] => [2,1] => 1010 => 1101 => 3
[9,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[8,4] => [4] => 10000 => 00011 => 2
[8,3,1] => [3,1] => 10010 => 01101 => 3
[8,2,2] => [2,2] => 1100 => 0111 => 3
[8,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[8,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[7,5] => [5] => 100000 => 000011 => 2
[7,4,1] => [4,1] => 100010 => 001101 => 3
[7,3,2] => [3,2] => 10100 => 11001 => 3
[7,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[7,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[7,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[7,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[6,6] => [6] => 1000000 => 0000011 => 2
[6,5,1] => [5,1] => 1000010 => 0001101 => 3
[6,4,2] => [4,2] => 100100 => 011001 => 3
[6,4,1,1] => [4,1,1] => 1000110 => 0011011 => 4
[6,3,3] => [3,3] => 11000 => 00111 => 3
[6,3,2,1] => [3,2,1] => 101010 => 110101 => 4
[6,3,1,1,1] => [3,1,1,1] => 1001110 => 0110111 => 5
[6,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[6,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[6,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[5,5,2] => [5,2] => 1000100 => 0011001 => 3
[5,5,1,1] => [5,1,1] => 10000110 => 00011011 => 4
[5,4,3] => [4,3] => 101000 => 110001 => 3
[5,4,2,1] => [4,2,1] => 1001010 => 0110101 => 4
[5,4,1,1,1] => [4,1,1,1] => 10001110 => 00110111 => 5
[5,3,3,1] => [3,3,1] => 110010 => 011101 => 4
[5,3,2,2] => [3,2,2] => 101100 => 110011 => 4
[5,3,2,1,1] => [3,2,1,1] => 1010110 => 1101011 => 5
[5,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01101111 => 6
[5,2,2,2,1] => [2,2,2,1] => 111010 => 111101 => 5
[5,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 1110111 => 6
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 11011111 => 7
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[4,4,4] => [4,4] => 110000 => 000111 => 3
[4,4,3,1] => [4,3,1] => 1010010 => 1100101 => 4
[4,4,2,2] => [4,2,2] => 1001100 => 0110011 => 4
[4,4,2,1,1] => [4,2,1,1] => 10010110 => 01101011 => 5
[4,3,3,2] => [3,3,2] => 110100 => 111001 => 4
[4,3,3,1,1] => [3,3,1,1] => 1100110 => 0111011 => 5
[4,3,2,2,1] => [3,2,2,1] => 1011010 => 1101101 => 5
[4,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 11010111 => 6
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011011111 => 7
[4,2,2,2,2] => [2,2,2,2] => 111100 => 011111 => 5
[4,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 1111011 => 6
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 11101111 => 7
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 111111111 => 9
[3,3,3,3] => [3,3,3] => 111000 => 001111 => 4
[3,3,3,2,1] => [3,3,2,1] => 1101010 => 1110101 => 5
[3,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 01110111 => 6
[3,3,2,2,2] => [3,2,2,2] => 1011100 => 1100111 => 5
[3,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 11011011 => 6
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110111111 => 8
[3,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 1111101 => 6
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 11110111 => 7
[2,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0111111 => 6
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 11111011 => 7
[12,1] => [1] => 10 => 11 => 2
[11,2] => [2] => 100 => 011 => 2
[11,1,1] => [1,1] => 110 => 111 => 3
[10,3] => [3] => 1000 => 0011 => 2
[10,2,1] => [2,1] => 1010 => 1101 => 3
[10,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[9,4] => [4] => 10000 => 00011 => 2
[9,3,1] => [3,1] => 10010 => 01101 => 3
[9,2,2] => [2,2] => 1100 => 0111 => 3
[9,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[9,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[8,5] => [5] => 100000 => 000011 => 2
[8,4,1] => [4,1] => 100010 => 001101 => 3
[8,3,2] => [3,2] => 10100 => 11001 => 3
[8,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[8,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[8,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[8,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[7,6] => [6] => 1000000 => 0000011 => 2
[7,5,1] => [5,1] => 1000010 => 0001101 => 3
[7,4,2] => [4,2] => 100100 => 011001 => 3
[7,4,1,1] => [4,1,1] => 1000110 => 0011011 => 4
[7,3,3] => [3,3] => 11000 => 00111 => 3
[7,3,2,1] => [3,2,1] => 101010 => 110101 => 4
[7,3,1,1,1] => [3,1,1,1] => 1001110 => 0110111 => 5
[7,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[7,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[7,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[6,6,1] => [6,1] => 10000010 => 00001101 => 3
[6,5,2] => [5,2] => 1000100 => 0011001 => 3
[6,5,1,1] => [5,1,1] => 10000110 => 00011011 => 4
[6,4,3] => [4,3] => 101000 => 110001 => 3
[6,4,2,1] => [4,2,1] => 1001010 => 0110101 => 4
[6,4,1,1,1] => [4,1,1,1] => 10001110 => 00110111 => 5
[6,3,3,1] => [3,3,1] => 110010 => 011101 => 4
[6,3,2,2] => [3,2,2] => 101100 => 110011 => 4
[6,3,2,1,1] => [3,2,1,1] => 1010110 => 1101011 => 5
[6,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01101111 => 6
[6,2,2,2,1] => [2,2,2,1] => 111010 => 111101 => 5
[6,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 1110111 => 6
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 11011111 => 7
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[5,5,3] => [5,3] => 1001000 => 0110001 => 3
[5,5,2,1] => [5,2,1] => 10001010 => 00110101 => 4
[5,4,4] => [4,4] => 110000 => 000111 => 3
[5,4,3,1] => [4,3,1] => 1010010 => 1100101 => 4
[5,4,2,2] => [4,2,2] => 1001100 => 0110011 => 4
[5,4,2,1,1] => [4,2,1,1] => 10010110 => 01101011 => 5
[5,3,3,2] => [3,3,2] => 110100 => 111001 => 4
[5,3,3,1,1] => [3,3,1,1] => 1100110 => 0111011 => 5
[5,3,2,2,1] => [3,2,2,1] => 1011010 => 1101101 => 5
[5,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 11010111 => 6
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011011111 => 7
[5,2,2,2,2] => [2,2,2,2] => 111100 => 011111 => 5
[5,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 1111011 => 6
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 11101111 => 7
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 111111111 => 9
[4,4,4,1] => [4,4,1] => 1100010 => 0011101 => 4
[4,4,3,2] => [4,3,2] => 1010100 => 1101001 => 4
[4,4,3,1,1] => [4,3,1,1] => 10100110 => 11001011 => 5
[4,4,2,2,1] => [4,2,2,1] => 10011010 => 01101101 => 5
[4,3,3,3] => [3,3,3] => 111000 => 001111 => 4
[4,3,3,2,1] => [3,3,2,1] => 1101010 => 1110101 => 5
[4,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 01110111 => 6
[4,3,2,2,2] => [3,2,2,2] => 1011100 => 1100111 => 5
[4,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 11011011 => 6
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110111111 => 8
[4,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 1111101 => 6
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 11110111 => 7
[3,3,3,3,1] => [3,3,3,1] => 1110010 => 0111101 => 5
[3,3,3,2,2] => [3,3,2,2] => 1101100 => 1110011 => 5
[3,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 11101011 => 6
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 011101111 => 7
[3,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 11011101 => 6
[3,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0111111 => 6
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 11111011 => 7
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 11111101 => 7
[13,1] => [1] => 10 => 11 => 2
[12,2] => [2] => 100 => 011 => 2
[12,1,1] => [1,1] => 110 => 111 => 3
[11,3] => [3] => 1000 => 0011 => 2
[11,2,1] => [2,1] => 1010 => 1101 => 3
[11,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[10,4] => [4] => 10000 => 00011 => 2
[10,3,1] => [3,1] => 10010 => 01101 => 3
[10,2,2] => [2,2] => 1100 => 0111 => 3
[10,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[10,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[9,5] => [5] => 100000 => 000011 => 2
[9,4,1] => [4,1] => 100010 => 001101 => 3
[9,3,2] => [3,2] => 10100 => 11001 => 3
[9,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[9,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[9,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[9,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[8,6] => [6] => 1000000 => 0000011 => 2
[8,5,1] => [5,1] => 1000010 => 0001101 => 3
[8,4,2] => [4,2] => 100100 => 011001 => 3
[8,4,1,1] => [4,1,1] => 1000110 => 0011011 => 4
[8,3,3] => [3,3] => 11000 => 00111 => 3
[8,3,2,1] => [3,2,1] => 101010 => 110101 => 4
[8,3,1,1,1] => [3,1,1,1] => 1001110 => 0110111 => 5
[8,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[8,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[8,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[7,7] => [7] => 10000000 => 00000011 => 2
[7,6,1] => [6,1] => 10000010 => 00001101 => 3
[7,5,2] => [5,2] => 1000100 => 0011001 => 3
[7,5,1,1] => [5,1,1] => 10000110 => 00011011 => 4
[7,4,3] => [4,3] => 101000 => 110001 => 3
[7,4,2,1] => [4,2,1] => 1001010 => 0110101 => 4
[7,4,1,1,1] => [4,1,1,1] => 10001110 => 00110111 => 5
[7,3,3,1] => [3,3,1] => 110010 => 011101 => 4
[7,3,2,2] => [3,2,2] => 101100 => 110011 => 4
[7,3,2,1,1] => [3,2,1,1] => 1010110 => 1101011 => 5
[7,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01101111 => 6
[7,2,2,2,1] => [2,2,2,1] => 111010 => 111101 => 5
[7,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 1110111 => 6
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 11011111 => 7
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[6,6,2] => [6,2] => 10000100 => 00011001 => 3
[6,5,3] => [5,3] => 1001000 => 0110001 => 3
[6,5,2,1] => [5,2,1] => 10001010 => 00110101 => 4
[6,4,4] => [4,4] => 110000 => 000111 => 3
[6,4,3,1] => [4,3,1] => 1010010 => 1100101 => 4
[6,4,2,2] => [4,2,2] => 1001100 => 0110011 => 4
[6,4,2,1,1] => [4,2,1,1] => 10010110 => 01101011 => 5
[6,3,3,2] => [3,3,2] => 110100 => 111001 => 4
[6,3,3,1,1] => [3,3,1,1] => 1100110 => 0111011 => 5
[6,3,2,2,1] => [3,2,2,1] => 1011010 => 1101101 => 5
[6,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 11010111 => 6
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011011111 => 7
[6,2,2,2,2] => [2,2,2,2] => 111100 => 011111 => 5
[6,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 1111011 => 6
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 11101111 => 7
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 111111111 => 9
[5,5,4] => [5,4] => 1010000 => 1100001 => 3
[5,5,3,1] => [5,3,1] => 10010010 => 01100101 => 4
[5,5,2,2] => [5,2,2] => 10001100 => 00110011 => 4
[5,4,4,1] => [4,4,1] => 1100010 => 0011101 => 4
[5,4,3,2] => [4,3,2] => 1010100 => 1101001 => 4
[5,4,3,1,1] => [4,3,1,1] => 10100110 => 11001011 => 5
[5,4,2,2,1] => [4,2,2,1] => 10011010 => 01101101 => 5
[5,3,3,3] => [3,3,3] => 111000 => 001111 => 4
[5,3,3,2,1] => [3,3,2,1] => 1101010 => 1110101 => 5
[5,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 01110111 => 6
[5,3,2,2,2] => [3,2,2,2] => 1011100 => 1100111 => 5
[5,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 11011011 => 6
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110111111 => 8
[5,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 1111101 => 6
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 11110111 => 7
[4,4,4,2] => [4,4,2] => 1100100 => 0111001 => 4
[4,4,4,1,1] => [4,4,1,1] => 11000110 => 00111011 => 5
[4,4,3,3] => [4,3,3] => 1011000 => 1100011 => 4
[4,4,3,2,1] => [4,3,2,1] => 10101010 => 11010101 => 5
[4,4,2,2,2] => [4,2,2,2] => 10011100 => 01100111 => 5
[4,3,3,3,1] => [3,3,3,1] => 1110010 => 0111101 => 5
[4,3,3,2,2] => [3,3,2,2] => 1101100 => 1110011 => 5
[4,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 11101011 => 6
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 011101111 => 7
[4,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 11011101 => 6
[4,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0111111 => 6
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 11111011 => 7
[3,3,3,3,2] => [3,3,3,2] => 1110100 => 1111001 => 5
[3,3,3,3,1,1] => [3,3,3,1,1] => 11100110 => 01111011 => 6
[3,3,3,2,2,1] => [3,3,2,2,1] => 11011010 => 11101101 => 6
[3,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 11001111 => 6
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 11111101 => 7
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 01111111 => 7
[14,1] => [1] => 10 => 11 => 2
[13,2] => [2] => 100 => 011 => 2
[13,1,1] => [1,1] => 110 => 111 => 3
[12,3] => [3] => 1000 => 0011 => 2
[12,2,1] => [2,1] => 1010 => 1101 => 3
[12,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[11,4] => [4] => 10000 => 00011 => 2
[11,3,1] => [3,1] => 10010 => 01101 => 3
[11,2,2] => [2,2] => 1100 => 0111 => 3
[11,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[11,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[10,5] => [5] => 100000 => 000011 => 2
[10,4,1] => [4,1] => 100010 => 001101 => 3
[10,3,2] => [3,2] => 10100 => 11001 => 3
[10,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[10,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[10,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[10,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[9,6] => [6] => 1000000 => 0000011 => 2
[9,5,1] => [5,1] => 1000010 => 0001101 => 3
[9,4,2] => [4,2] => 100100 => 011001 => 3
[9,4,1,1] => [4,1,1] => 1000110 => 0011011 => 4
[9,3,3] => [3,3] => 11000 => 00111 => 3
[9,3,2,1] => [3,2,1] => 101010 => 110101 => 4
[9,3,1,1,1] => [3,1,1,1] => 1001110 => 0110111 => 5
[9,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[9,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[9,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[8,7] => [7] => 10000000 => 00000011 => 2
[8,6,1] => [6,1] => 10000010 => 00001101 => 3
[8,5,2] => [5,2] => 1000100 => 0011001 => 3
[8,5,1,1] => [5,1,1] => 10000110 => 00011011 => 4
[8,4,3] => [4,3] => 101000 => 110001 => 3
[8,4,2,1] => [4,2,1] => 1001010 => 0110101 => 4
[8,4,1,1,1] => [4,1,1,1] => 10001110 => 00110111 => 5
[8,3,3,1] => [3,3,1] => 110010 => 011101 => 4
[8,3,2,2] => [3,2,2] => 101100 => 110011 => 4
[8,3,2,1,1] => [3,2,1,1] => 1010110 => 1101011 => 5
[8,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01101111 => 6
[8,2,2,2,1] => [2,2,2,1] => 111010 => 111101 => 5
[8,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 1110111 => 6
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 11011111 => 7
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[7,7,1] => [7,1] => 100000010 => 000001101 => 3
[7,6,2] => [6,2] => 10000100 => 00011001 => 3
[7,5,3] => [5,3] => 1001000 => 0110001 => 3
[7,5,2,1] => [5,2,1] => 10001010 => 00110101 => 4
[7,4,4] => [4,4] => 110000 => 000111 => 3
[7,4,3,1] => [4,3,1] => 1010010 => 1100101 => 4
[7,4,2,2] => [4,2,2] => 1001100 => 0110011 => 4
[7,4,2,1,1] => [4,2,1,1] => 10010110 => 01101011 => 5
[7,3,3,2] => [3,3,2] => 110100 => 111001 => 4
[7,3,3,1,1] => [3,3,1,1] => 1100110 => 0111011 => 5
[7,3,2,2,1] => [3,2,2,1] => 1011010 => 1101101 => 5
[7,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 11010111 => 6
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011011111 => 7
[7,2,2,2,2] => [2,2,2,2] => 111100 => 011111 => 5
[7,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 1111011 => 6
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 11101111 => 7
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 111111111 => 9
[6,6,3] => [6,3] => 10001000 => 00110001 => 3
[6,6,2,1] => [6,2,1] => 100001010 => 000110101 => 4
[6,6,1,1,1] => [6,1,1,1] => 1000001110 => 0000110111 => 5
[6,5,4] => [5,4] => 1010000 => 1100001 => 3
[6,5,3,1] => [5,3,1] => 10010010 => 01100101 => 4
[6,5,2,2] => [5,2,2] => 10001100 => 00110011 => 4
[6,4,4,1] => [4,4,1] => 1100010 => 0011101 => 4
[6,4,3,2] => [4,3,2] => 1010100 => 1101001 => 4
[6,4,3,1,1] => [4,3,1,1] => 10100110 => 11001011 => 5
[6,4,2,2,1] => [4,2,2,1] => 10011010 => 01101101 => 5
[6,3,3,3] => [3,3,3] => 111000 => 001111 => 4
[6,3,3,2,1] => [3,3,2,1] => 1101010 => 1110101 => 5
[6,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 01110111 => 6
[6,3,2,2,2] => [3,2,2,2] => 1011100 => 1100111 => 5
[6,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 11011011 => 6
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110111111 => 8
[6,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 1111101 => 6
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 11110111 => 7
[5,5,5] => [5,5] => 1100000 => 0000111 => 3
[5,5,4,1] => [5,4,1] => 10100010 => 11000101 => 4
[5,5,3,2] => [5,3,2] => 10010100 => 01101001 => 4
[5,5,2,2,1] => [5,2,2,1] => 100011010 => 001101101 => 5
[5,4,4,2] => [4,4,2] => 1100100 => 0111001 => 4
[5,4,4,1,1] => [4,4,1,1] => 11000110 => 00111011 => 5
[5,4,3,3] => [4,3,3] => 1011000 => 1100011 => 4
[5,4,3,2,1] => [4,3,2,1] => 10101010 => 11010101 => 5
[5,4,2,2,2] => [4,2,2,2] => 10011100 => 01100111 => 5
[5,3,3,3,1] => [3,3,3,1] => 1110010 => 0111101 => 5
[5,3,3,2,2] => [3,3,2,2] => 1101100 => 1110011 => 5
[5,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 11101011 => 6
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 011101111 => 7
[5,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 11011101 => 6
[5,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0111111 => 6
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 11111011 => 7
[4,4,4,3] => [4,4,3] => 1101000 => 1110001 => 4
[4,4,4,2,1] => [4,4,2,1] => 11001010 => 01110101 => 5
[4,4,3,3,1] => [4,3,3,1] => 10110010 => 11001101 => 5
[4,4,3,2,2] => [4,3,2,2] => 10101100 => 11010011 => 5
[4,4,2,2,2,1] => [4,2,2,2,1] => 100111010 => 011011101 => 6
[4,3,3,3,2] => [3,3,3,2] => 1110100 => 1111001 => 5
[4,3,3,3,1,1] => [3,3,3,1,1] => 11100110 => 01111011 => 6
[4,3,3,2,2,1] => [3,3,2,2,1] => 11011010 => 11101101 => 6
[4,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 11001111 => 6
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 11111101 => 7
[3,3,3,3,3] => [3,3,3,3] => 1111000 => 0011111 => 5
[3,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 11110101 => 6
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => 111001110 => 011110111 => 7
[3,3,3,2,2,2] => [3,3,2,2,2] => 11011100 => 11100111 => 6
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => 101111010 => 110111101 => 7
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 01111111 => 7
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 111111010 => 111111101 => 8
[15,1] => [1] => 10 => 11 => 2
[14,2] => [2] => 100 => 011 => 2
[14,1,1] => [1,1] => 110 => 111 => 3
[13,3] => [3] => 1000 => 0011 => 2
[13,2,1] => [2,1] => 1010 => 1101 => 3
[13,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[12,4] => [4] => 10000 => 00011 => 2
[12,3,1] => [3,1] => 10010 => 01101 => 3
[12,2,2] => [2,2] => 1100 => 0111 => 3
[12,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[12,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[11,5] => [5] => 100000 => 000011 => 2
[11,4,1] => [4,1] => 100010 => 001101 => 3
[11,3,2] => [3,2] => 10100 => 11001 => 3
[11,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[11,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[11,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[11,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[10,6] => [6] => 1000000 => 0000011 => 2
[10,5,1] => [5,1] => 1000010 => 0001101 => 3
[10,4,2] => [4,2] => 100100 => 011001 => 3
[10,4,1,1] => [4,1,1] => 1000110 => 0011011 => 4
[10,3,3] => [3,3] => 11000 => 00111 => 3
[10,3,2,1] => [3,2,1] => 101010 => 110101 => 4
[10,3,1,1,1] => [3,1,1,1] => 1001110 => 0110111 => 5
[10,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[10,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[10,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[9,7] => [7] => 10000000 => 00000011 => 2
[9,6,1] => [6,1] => 10000010 => 00001101 => 3
[9,5,2] => [5,2] => 1000100 => 0011001 => 3
[9,5,1,1] => [5,1,1] => 10000110 => 00011011 => 4
[9,4,3] => [4,3] => 101000 => 110001 => 3
[9,4,2,1] => [4,2,1] => 1001010 => 0110101 => 4
[9,4,1,1,1] => [4,1,1,1] => 10001110 => 00110111 => 5
[9,3,3,1] => [3,3,1] => 110010 => 011101 => 4
[9,3,2,2] => [3,2,2] => 101100 => 110011 => 4
[9,3,2,1,1] => [3,2,1,1] => 1010110 => 1101011 => 5
[9,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01101111 => 6
[9,2,2,2,1] => [2,2,2,1] => 111010 => 111101 => 5
[9,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 1110111 => 6
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 11011111 => 7
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[8,8] => [8] => 100000000 => 000000011 => 2
[8,7,1] => [7,1] => 100000010 => 000001101 => 3
[8,6,2] => [6,2] => 10000100 => 00011001 => 3
[8,5,3] => [5,3] => 1001000 => 0110001 => 3
[8,5,2,1] => [5,2,1] => 10001010 => 00110101 => 4
[8,4,4] => [4,4] => 110000 => 000111 => 3
[8,4,3,1] => [4,3,1] => 1010010 => 1100101 => 4
[8,4,2,2] => [4,2,2] => 1001100 => 0110011 => 4
[8,4,2,1,1] => [4,2,1,1] => 10010110 => 01101011 => 5
[8,3,3,2] => [3,3,2] => 110100 => 111001 => 4
[8,3,3,1,1] => [3,3,1,1] => 1100110 => 0111011 => 5
[8,3,2,2,1] => [3,2,2,1] => 1011010 => 1101101 => 5
[8,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 11010111 => 6
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011011111 => 7
[8,2,2,2,2] => [2,2,2,2] => 111100 => 011111 => 5
[8,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 1111011 => 6
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 11101111 => 7
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 111111111 => 9
[7,7,2] => [7,2] => 100000100 => 000011001 => 3
[7,6,3] => [6,3] => 10001000 => 00110001 => 3
[7,6,2,1] => [6,2,1] => 100001010 => 000110101 => 4
[7,6,1,1,1] => [6,1,1,1] => 1000001110 => 0000110111 => 5
[7,5,4] => [5,4] => 1010000 => 1100001 => 3
[7,5,3,1] => [5,3,1] => 10010010 => 01100101 => 4
[7,5,2,2] => [5,2,2] => 10001100 => 00110011 => 4
[7,4,4,1] => [4,4,1] => 1100010 => 0011101 => 4
[7,4,3,2] => [4,3,2] => 1010100 => 1101001 => 4
[7,4,3,1,1] => [4,3,1,1] => 10100110 => 11001011 => 5
[7,4,2,2,1] => [4,2,2,1] => 10011010 => 01101101 => 5
[7,3,3,3] => [3,3,3] => 111000 => 001111 => 4
[7,3,3,2,1] => [3,3,2,1] => 1101010 => 1110101 => 5
[7,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 01110111 => 6
[7,3,2,2,2] => [3,2,2,2] => 1011100 => 1100111 => 5
[7,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 11011011 => 6
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110111111 => 8
[7,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 1111101 => 6
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 11110111 => 7
[6,6,4] => [6,4] => 10010000 => 01100001 => 3
[6,6,2,1,1] => [6,2,1,1] => 1000010110 => 0001101011 => 5
[6,5,5] => [5,5] => 1100000 => 0000111 => 3
[6,5,4,1] => [5,4,1] => 10100010 => 11000101 => 4
[6,5,3,2] => [5,3,2] => 10010100 => 01101001 => 4
[6,5,2,2,1] => [5,2,2,1] => 100011010 => 001101101 => 5
[6,4,4,2] => [4,4,2] => 1100100 => 0111001 => 4
[6,4,4,1,1] => [4,4,1,1] => 11000110 => 00111011 => 5
[6,4,3,3] => [4,3,3] => 1011000 => 1100011 => 4
[6,4,3,2,1] => [4,3,2,1] => 10101010 => 11010101 => 5
[6,4,2,2,2] => [4,2,2,2] => 10011100 => 01100111 => 5
[6,3,3,3,1] => [3,3,3,1] => 1110010 => 0111101 => 5
[6,3,3,2,2] => [3,3,2,2] => 1101100 => 1110011 => 5
[6,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 11101011 => 6
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 011101111 => 7
[6,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 11011101 => 6
[6,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0111111 => 6
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 11111011 => 7
[5,5,5,1] => [5,5,1] => 11000010 => 00011101 => 4
[5,5,4,2] => [5,4,2] => 10100100 => 11001001 => 4
[5,5,3,3] => [5,3,3] => 10011000 => 01100011 => 4
[5,4,4,3] => [4,4,3] => 1101000 => 1110001 => 4
[5,4,4,2,1] => [4,4,2,1] => 11001010 => 01110101 => 5
[5,4,3,3,1] => [4,3,3,1] => 10110010 => 11001101 => 5
[5,4,3,2,2] => [4,3,2,2] => 10101100 => 11010011 => 5
[5,4,2,2,2,1] => [4,2,2,2,1] => 100111010 => 011011101 => 6
[5,3,3,3,2] => [3,3,3,2] => 1110100 => 1111001 => 5
[5,3,3,3,1,1] => [3,3,3,1,1] => 11100110 => 01111011 => 6
[5,3,3,2,2,1] => [3,3,2,2,1] => 11011010 => 11101101 => 6
[5,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 11001111 => 6
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 11111101 => 7
[4,4,4,4] => [4,4,4] => 1110000 => 0001111 => 4
[4,4,4,3,1] => [4,4,3,1] => 11010010 => 11100101 => 5
[4,4,4,2,2] => [4,4,2,2] => 11001100 => 01110011 => 5
[4,4,3,3,2] => [4,3,3,2] => 10110100 => 11011001 => 5
[4,4,2,2,2,2] => [4,2,2,2,2] => 100111100 => 011001111 => 6
[4,3,3,3,3] => [3,3,3,3] => 1111000 => 0011111 => 5
[4,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 11110101 => 6
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => 111001110 => 011110111 => 7
[4,3,3,2,2,2] => [3,3,2,2,2] => 11011100 => 11100111 => 6
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => 101111010 => 110111101 => 7
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 01111111 => 7
[3,3,3,3,3,1] => [3,3,3,3,1] => 11110010 => 01111101 => 6
[3,3,3,3,2,2] => [3,3,3,2,2] => 11101100 => 11110011 => 6
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 111111010 => 111111101 => 8
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => 111111100 => 011111111 => 8
[16,1] => [1] => 10 => 11 => 2
[15,2] => [2] => 100 => 011 => 2
[15,1,1] => [1,1] => 110 => 111 => 3
[14,3] => [3] => 1000 => 0011 => 2
[14,2,1] => [2,1] => 1010 => 1101 => 3
[14,1,1,1] => [1,1,1] => 1110 => 1111 => 4
[13,4] => [4] => 10000 => 00011 => 2
[13,3,1] => [3,1] => 10010 => 01101 => 3
[13,2,2] => [2,2] => 1100 => 0111 => 3
[13,2,1,1] => [2,1,1] => 10110 => 11011 => 4
[13,1,1,1,1] => [1,1,1,1] => 11110 => 11111 => 5
[12,5] => [5] => 100000 => 000011 => 2
[12,4,1] => [4,1] => 100010 => 001101 => 3
[12,3,2] => [3,2] => 10100 => 11001 => 3
[12,3,1,1] => [3,1,1] => 100110 => 011011 => 4
[12,2,2,1] => [2,2,1] => 11010 => 11101 => 4
[12,2,1,1,1] => [2,1,1,1] => 101110 => 110111 => 5
[12,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 111111 => 6
[11,6] => [6] => 1000000 => 0000011 => 2
[11,5,1] => [5,1] => 1000010 => 0001101 => 3
[11,4,2] => [4,2] => 100100 => 011001 => 3
[11,4,1,1] => [4,1,1] => 1000110 => 0011011 => 4
[11,3,3] => [3,3] => 11000 => 00111 => 3
[11,3,2,1] => [3,2,1] => 101010 => 110101 => 4
[11,3,1,1,1] => [3,1,1,1] => 1001110 => 0110111 => 5
[11,2,2,2] => [2,2,2] => 11100 => 01111 => 4
[11,2,2,1,1] => [2,2,1,1] => 110110 => 111011 => 5
[11,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 1101111 => 6
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 1111111 => 7
[10,7] => [7] => 10000000 => 00000011 => 2
[10,6,1] => [6,1] => 10000010 => 00001101 => 3
[10,5,2] => [5,2] => 1000100 => 0011001 => 3
[10,5,1,1] => [5,1,1] => 10000110 => 00011011 => 4
[10,4,3] => [4,3] => 101000 => 110001 => 3
[10,4,2,1] => [4,2,1] => 1001010 => 0110101 => 4
[10,4,1,1,1] => [4,1,1,1] => 10001110 => 00110111 => 5
[10,3,3,1] => [3,3,1] => 110010 => 011101 => 4
[10,3,2,2] => [3,2,2] => 101100 => 110011 => 4
[10,3,2,1,1] => [3,2,1,1] => 1010110 => 1101011 => 5
[10,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01101111 => 6
[10,2,2,2,1] => [2,2,2,1] => 111010 => 111101 => 5
[10,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 1110111 => 6
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 11011111 => 7
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 11111111 => 8
[9,8] => [8] => 100000000 => 000000011 => 2
[9,7,1] => [7,1] => 100000010 => 000001101 => 3
[9,6,2] => [6,2] => 10000100 => 00011001 => 3
[9,5,3] => [5,3] => 1001000 => 0110001 => 3
[9,5,2,1] => [5,2,1] => 10001010 => 00110101 => 4
[9,4,4] => [4,4] => 110000 => 000111 => 3
[9,4,3,1] => [4,3,1] => 1010010 => 1100101 => 4
[9,4,2,2] => [4,2,2] => 1001100 => 0110011 => 4
[9,4,2,1,1] => [4,2,1,1] => 10010110 => 01101011 => 5
[9,3,3,2] => [3,3,2] => 110100 => 111001 => 4
[9,3,3,1,1] => [3,3,1,1] => 1100110 => 0111011 => 5
[9,3,2,2,1] => [3,2,2,1] => 1011010 => 1101101 => 5
[9,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 11010111 => 6
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011011111 => 7
[9,2,2,2,2] => [2,2,2,2] => 111100 => 011111 => 5
[9,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 1111011 => 6
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 11101111 => 7
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 111111111 => 9
[8,8,1] => [8,1] => 1000000010 => 0000001101 => 3
[8,7,2] => [7,2] => 100000100 => 000011001 => 3
[8,6,3] => [6,3] => 10001000 => 00110001 => 3
[8,6,2,1] => [6,2,1] => 100001010 => 000110101 => 4
[8,6,1,1,1] => [6,1,1,1] => 1000001110 => 0000110111 => 5
[8,5,4] => [5,4] => 1010000 => 1100001 => 3
[8,5,3,1] => [5,3,1] => 10010010 => 01100101 => 4
[8,5,2,2] => [5,2,2] => 10001100 => 00110011 => 4
[8,4,4,1] => [4,4,1] => 1100010 => 0011101 => 4
[8,4,3,2] => [4,3,2] => 1010100 => 1101001 => 4
[8,4,3,1,1] => [4,3,1,1] => 10100110 => 11001011 => 5
[8,4,2,2,1] => [4,2,2,1] => 10011010 => 01101101 => 5
[8,3,3,3] => [3,3,3] => 111000 => 001111 => 4
[8,3,3,2,1] => [3,3,2,1] => 1101010 => 1110101 => 5
[8,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 01110111 => 6
[8,3,2,2,2] => [3,2,2,2] => 1011100 => 1100111 => 5
[8,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 11011011 => 6
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110111111 => 8
[8,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 1111101 => 6
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 11110111 => 7
[7,6,4] => [6,4] => 10010000 => 01100001 => 3
[7,6,2,1,1] => [6,2,1,1] => 1000010110 => 0001101011 => 5
[7,5,5] => [5,5] => 1100000 => 0000111 => 3
[7,5,4,1] => [5,4,1] => 10100010 => 11000101 => 4
[7,5,3,2] => [5,3,2] => 10010100 => 01101001 => 4
[7,5,2,2,1] => [5,2,2,1] => 100011010 => 001101101 => 5
[7,4,4,2] => [4,4,2] => 1100100 => 0111001 => 4
[7,4,4,1,1] => [4,4,1,1] => 11000110 => 00111011 => 5
[7,4,3,3] => [4,3,3] => 1011000 => 1100011 => 4
[7,4,3,2,1] => [4,3,2,1] => 10101010 => 11010101 => 5
[7,4,2,2,2] => [4,2,2,2] => 10011100 => 01100111 => 5
[7,3,3,3,1] => [3,3,3,1] => 1110010 => 0111101 => 5
[7,3,3,2,2] => [3,3,2,2] => 1101100 => 1110011 => 5
[7,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 11101011 => 6
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 011101111 => 7
[7,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 11011101 => 6
[7,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0111111 => 6
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 11111011 => 7
[6,6,5] => [6,5] => 10100000 => 11000001 => 3
[6,5,5,1] => [5,5,1] => 11000010 => 00011101 => 4
[6,5,4,2] => [5,4,2] => 10100100 => 11001001 => 4
[6,5,3,3] => [5,3,3] => 10011000 => 01100011 => 4
[6,4,4,3] => [4,4,3] => 1101000 => 1110001 => 4
[6,4,4,2,1] => [4,4,2,1] => 11001010 => 01110101 => 5
[6,4,3,3,1] => [4,3,3,1] => 10110010 => 11001101 => 5
[6,4,3,2,2] => [4,3,2,2] => 10101100 => 11010011 => 5
[6,4,2,2,2,1] => [4,2,2,2,1] => 100111010 => 011011101 => 6
[6,3,3,3,2] => [3,3,3,2] => 1110100 => 1111001 => 5
[6,3,3,3,1,1] => [3,3,3,1,1] => 11100110 => 01111011 => 6
[6,3,3,2,2,1] => [3,3,2,2,1] => 11011010 => 11101101 => 6
[6,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 11001111 => 6
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 11111101 => 7
[5,5,5,2] => [5,5,2] => 11000100 => 00111001 => 4
[5,5,4,3] => [5,4,3] => 10101000 => 11010001 => 4
[5,4,4,4] => [4,4,4] => 1110000 => 0001111 => 4
[5,4,4,3,1] => [4,4,3,1] => 11010010 => 11100101 => 5
[5,4,4,2,2] => [4,4,2,2] => 11001100 => 01110011 => 5
[5,4,3,3,2] => [4,3,3,2] => 10110100 => 11011001 => 5
[5,4,2,2,2,2] => [4,2,2,2,2] => 100111100 => 011001111 => 6
[5,3,3,3,3] => [3,3,3,3] => 1111000 => 0011111 => 5
[5,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 11110101 => 6
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => 111001110 => 011110111 => 7
[5,3,3,2,2,2] => [3,3,2,2,2] => 11011100 => 11100111 => 6
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => 101111010 => 110111101 => 7
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 01111111 => 7
[4,4,4,4,1] => [4,4,4,1] => 11100010 => 00111101 => 5
[4,4,4,3,2] => [4,4,3,2] => 11010100 => 11101001 => 5
[4,4,4,2,2,1] => [4,4,2,2,1] => 110011010 => 011101101 => 6
[4,4,3,3,3] => [4,3,3,3] => 10111000 => 11000111 => 5
[4,3,3,3,3,1] => [3,3,3,3,1] => 11110010 => 01111101 => 6
[4,3,3,3,2,2] => [3,3,3,2,2] => 11101100 => 11110011 => 6
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 111111010 => 111111101 => 8
[3,3,3,3,3,2] => [3,3,3,3,2] => 11110100 => 11111001 => 6
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => 111100110 => 011111011 => 7
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => 111111100 => 011111111 => 8
[6,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 11110101 => 6
[6,4,4,2,2,1] => [4,4,2,2,1] => 110011010 => 011101101 => 6
[5,4,4,2,2,1] => [4,4,2,2,1] => 110011010 => 011101101 => 6
[6,4,4,3,2] => [4,4,3,2] => 11010100 => 11101001 => 5
[5,4,4,3,2] => [4,4,3,2] => 11010100 => 11101001 => 5
[6,5,3,3,2] => [5,3,3,2] => 100110100 => 011011001 => 5
[5,5,3,3,2] => [5,3,3,2] => 100110100 => 011011001 => 5
[6,4,3,3,2] => [4,3,3,2] => 10110100 => 11011001 => 5
[6,4,4,2,2] => [4,4,2,2] => 11001100 => 01110011 => 5
[6,4,4,3,1] => [4,4,3,1] => 11010010 => 11100101 => 5
[6,5,4,3] => [5,4,3] => 10101000 => 11010001 => 4
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 11111101 => 7
[4,3,3,3,3,2] => [3,3,3,3,2] => 11110100 => 11111001 => 6
[4,4,4,4,2,1] => [4,4,4,2,1] => 111001010 => 011110101 => 6
[7,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 11110101 => 6
[5,4,4,4,3] => [4,4,4,3] => 11101000 => 11110001 => 5
[5,4,3,3,3] => [4,3,3,3] => 10111000 => 11000111 => 5
[7,3,3,3,3] => [3,3,3,3] => 1111000 => 0011111 => 5
[4,4,4,4,2] => [4,4,4,2] => 11100100 => 01111001 => 5
[6,5,5,4] => [5,5,4] => 11010000 => 11100001 => 4
[7,6,4,3] => [6,4,3] => 100101000 => 011010001 => 4
[7,5,4,3] => [5,4,3] => 10101000 => 11010001 => 4
[7,6,5] => [6,5] => 10100000 => 11000001 => 3
[3,3,3,3,3,3] => [3,3,3,3,3] => 11111000 => 00111111 => 6
[3,3,3,3,3,3,1] => [3,3,3,3,3,1] => 111110010 => 011111101 => 7
[3,3,3,3,3,3,3] => [3,3,3,3,3,3] => 111111000 => 001111111 => 7
[4,3,3,3,3,3] => [3,3,3,3,3] => 11111000 => 00111111 => 6
[4,4,4,4,4] => [4,4,4,4] => 11110000 => 00011111 => 5
[4,4,4,4,4,4] => [4,4,4,4,4] => 111110000 => 000111111 => 6
[5,5,5,5] => [5,5,5] => 11100000 => 00001111 => 4
[6,6,6,6] => [6,6,6] => 111000000 => 000001111 => 4
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 01111111 => 7
[6,6,6] => [6,6] => 11000000 => 00000111 => 3
[7,6,6] => [6,6] => 11000000 => 00000111 => 3
[10,4,4] => [4,4] => 110000 => 000111 => 3
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 01111111 => 7
[9,6,3] => [6,3] => 10001000 => 00110001 => 3
[8,6,4,2] => [6,4,2] => 100100100 => 011001001 => 4
[8,6,4] => [6,4] => 10010000 => 01100001 => 3
[10,6,4] => [6,4] => 10010000 => 01100001 => 3
[15,5,5] => [5,5] => 1100000 => 0000111 => 3
[7,7,7] => [7,7] => 110000000 => 000000111 => 3
[9,6,4] => [6,4] => 10010000 => 01100001 => 3
[8,5,4,2] => [5,4,2] => 10100100 => 11001001 => 4
[9,6,4,3] => [6,4,3] => 100101000 => 011010001 => 4
[9,7,4] => [7,4] => 100010000 => 001100001 => 3
[8,5,5,1] => [5,5,1] => 11000010 => 00011101 => 4
[9,5,5,1] => [5,5,1] => 11000010 => 00011101 => 4
[5,5,5,5,5] => [5,5,5,5] => 111100000 => 000011111 => 5
[6,5,5,5] => [5,5,5] => 11100000 => 00001111 => 4
[5,4,4,4,4] => [4,4,4,4] => 11110000 => 00011111 => 5
[8,7,5] => [7,5] => 100100000 => 011000001 => 3
[4,4,4,4,4,1] => [4,4,4,4,1] => 111100010 => 001111101 => 6
[5,5,5,5,1] => [5,5,5,1] => 111000010 => 000111101 => 5
[6,6,6,1] => [6,6,1] => 110000010 => 000011101 => 4
search for individual values
searching the database for the individual values of this statistic
Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
Map
path rowmotion
Description
Return the rowmotion of the binary word, regarded as a lattice path.
Consider the binary word of length $n$ as a lattice path with $n$ steps, where a 1 corresponds to an up step and a 0 corresponds to a down step.
This map returns the path whose peaks are the valleys of the original path with an up step appended.