Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
St000297: Binary words ⟶ ℤ
Values
[1,1] => [1] => 10 => 01 => 0
[2,1] => [1] => 10 => 01 => 0
[1,1,1] => [1,1] => 110 => 001 => 0
[3,1] => [1] => 10 => 01 => 0
[2,2] => [2] => 100 => 011 => 0
[2,1,1] => [1,1] => 110 => 001 => 0
[1,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[4,1] => [1] => 10 => 01 => 0
[3,2] => [2] => 100 => 011 => 0
[3,1,1] => [1,1] => 110 => 001 => 0
[2,2,1] => [2,1] => 1010 => 0101 => 0
[2,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[1,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[5,1] => [1] => 10 => 01 => 0
[4,2] => [2] => 100 => 011 => 0
[4,1,1] => [1,1] => 110 => 001 => 0
[3,3] => [3] => 1000 => 0111 => 0
[3,2,1] => [2,1] => 1010 => 0101 => 0
[3,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[2,2,2] => [2,2] => 1100 => 0011 => 0
[2,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[2,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[1,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[6,1] => [1] => 10 => 01 => 0
[5,2] => [2] => 100 => 011 => 0
[5,1,1] => [1,1] => 110 => 001 => 0
[4,3] => [3] => 1000 => 0111 => 0
[4,2,1] => [2,1] => 1010 => 0101 => 0
[4,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[3,3,1] => [3,1] => 10010 => 01101 => 0
[3,2,2] => [2,2] => 1100 => 0011 => 0
[3,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[3,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[2,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[2,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[2,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[7,1] => [1] => 10 => 01 => 0
[6,2] => [2] => 100 => 011 => 0
[6,1,1] => [1,1] => 110 => 001 => 0
[5,3] => [3] => 1000 => 0111 => 0
[5,2,1] => [2,1] => 1010 => 0101 => 0
[5,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[4,4] => [4] => 10000 => 01111 => 0
[4,3,1] => [3,1] => 10010 => 01101 => 0
[4,2,2] => [2,2] => 1100 => 0011 => 0
[4,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[4,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[3,3,2] => [3,2] => 10100 => 01011 => 0
[3,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[3,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[3,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[3,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[2,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[2,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[2,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[8,1] => [1] => 10 => 01 => 0
[7,2] => [2] => 100 => 011 => 0
[7,1,1] => [1,1] => 110 => 001 => 0
[6,3] => [3] => 1000 => 0111 => 0
[6,2,1] => [2,1] => 1010 => 0101 => 0
[6,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[5,4] => [4] => 10000 => 01111 => 0
[5,3,1] => [3,1] => 10010 => 01101 => 0
[5,2,2] => [2,2] => 1100 => 0011 => 0
[5,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[5,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[4,4,1] => [4,1] => 100010 => 011101 => 0
[4,3,2] => [3,2] => 10100 => 01011 => 0
[4,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[4,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[4,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[4,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[3,3,3] => [3,3] => 11000 => 00111 => 0
[3,3,2,1] => [3,2,1] => 101010 => 010101 => 0
[3,3,1,1,1] => [3,1,1,1] => 1001110 => 0110001 => 0
[3,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[3,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[3,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[2,2,2,2,1] => [2,2,2,1] => 111010 => 000101 => 0
[2,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0010001 => 0
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 01000001 => 0
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 000000001 => 0
[9,1] => [1] => 10 => 01 => 0
[8,2] => [2] => 100 => 011 => 0
[8,1,1] => [1,1] => 110 => 001 => 0
[7,3] => [3] => 1000 => 0111 => 0
[7,2,1] => [2,1] => 1010 => 0101 => 0
[7,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[6,4] => [4] => 10000 => 01111 => 0
[6,3,1] => [3,1] => 10010 => 01101 => 0
[6,2,2] => [2,2] => 1100 => 0011 => 0
[6,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[6,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[5,5] => [5] => 100000 => 011111 => 0
[5,4,1] => [4,1] => 100010 => 011101 => 0
[5,3,2] => [3,2] => 10100 => 01011 => 0
>>> Load all 1198 entries. <<<[5,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[5,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[5,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[5,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[4,4,2] => [4,2] => 100100 => 011011 => 0
[4,4,1,1] => [4,1,1] => 1000110 => 0111001 => 0
[4,3,3] => [3,3] => 11000 => 00111 => 0
[4,3,2,1] => [3,2,1] => 101010 => 010101 => 0
[4,3,1,1,1] => [3,1,1,1] => 1001110 => 0110001 => 0
[4,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[4,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[4,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[3,3,3,1] => [3,3,1] => 110010 => 001101 => 0
[3,3,2,2] => [3,2,2] => 101100 => 010011 => 0
[3,3,2,1,1] => [3,2,1,1] => 1010110 => 0101001 => 0
[3,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01100001 => 0
[3,2,2,2,1] => [2,2,2,1] => 111010 => 000101 => 0
[3,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0010001 => 0
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 01000001 => 0
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[2,2,2,2,2] => [2,2,2,2] => 111100 => 000011 => 0
[2,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0001001 => 0
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 00100001 => 0
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 010000001 => 0
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 000000001 => 0
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 0000000001 => 0
[10,1] => [1] => 10 => 01 => 0
[9,2] => [2] => 100 => 011 => 0
[9,1,1] => [1,1] => 110 => 001 => 0
[8,3] => [3] => 1000 => 0111 => 0
[8,2,1] => [2,1] => 1010 => 0101 => 0
[8,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[7,4] => [4] => 10000 => 01111 => 0
[7,3,1] => [3,1] => 10010 => 01101 => 0
[7,2,2] => [2,2] => 1100 => 0011 => 0
[7,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[7,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[6,5] => [5] => 100000 => 011111 => 0
[6,4,1] => [4,1] => 100010 => 011101 => 0
[6,3,2] => [3,2] => 10100 => 01011 => 0
[6,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[6,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[6,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[6,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[5,5,1] => [5,1] => 1000010 => 0111101 => 0
[5,4,2] => [4,2] => 100100 => 011011 => 0
[5,4,1,1] => [4,1,1] => 1000110 => 0111001 => 0
[5,3,3] => [3,3] => 11000 => 00111 => 0
[5,3,2,1] => [3,2,1] => 101010 => 010101 => 0
[5,3,1,1,1] => [3,1,1,1] => 1001110 => 0110001 => 0
[5,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[5,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[5,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[4,4,3] => [4,3] => 101000 => 010111 => 0
[4,4,2,1] => [4,2,1] => 1001010 => 0110101 => 0
[4,4,1,1,1] => [4,1,1,1] => 10001110 => 01110001 => 0
[4,3,3,1] => [3,3,1] => 110010 => 001101 => 0
[4,3,2,2] => [3,2,2] => 101100 => 010011 => 0
[4,3,2,1,1] => [3,2,1,1] => 1010110 => 0101001 => 0
[4,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01100001 => 0
[4,2,2,2,1] => [2,2,2,1] => 111010 => 000101 => 0
[4,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0010001 => 0
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 01000001 => 0
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[3,3,3,2] => [3,3,2] => 110100 => 001011 => 0
[3,3,3,1,1] => [3,3,1,1] => 1100110 => 0011001 => 0
[3,3,2,2,1] => [3,2,2,1] => 1011010 => 0100101 => 0
[3,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 01010001 => 0
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011000001 => 0
[3,2,2,2,2] => [2,2,2,2] => 111100 => 000011 => 0
[3,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0001001 => 0
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 00100001 => 0
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 010000001 => 0
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 000000001 => 0
[2,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0000101 => 0
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 00010001 => 0
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 001000001 => 0
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1011111110 => 0100000001 => 0
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 0000000001 => 0
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 00000000001 => 0
[11,1] => [1] => 10 => 01 => 0
[10,2] => [2] => 100 => 011 => 0
[10,1,1] => [1,1] => 110 => 001 => 0
[9,3] => [3] => 1000 => 0111 => 0
[9,2,1] => [2,1] => 1010 => 0101 => 0
[9,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[8,4] => [4] => 10000 => 01111 => 0
[8,3,1] => [3,1] => 10010 => 01101 => 0
[8,2,2] => [2,2] => 1100 => 0011 => 0
[8,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[8,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[7,5] => [5] => 100000 => 011111 => 0
[7,4,1] => [4,1] => 100010 => 011101 => 0
[7,3,2] => [3,2] => 10100 => 01011 => 0
[7,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[7,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[7,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[7,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[6,6] => [6] => 1000000 => 0111111 => 0
[6,5,1] => [5,1] => 1000010 => 0111101 => 0
[6,4,2] => [4,2] => 100100 => 011011 => 0
[6,4,1,1] => [4,1,1] => 1000110 => 0111001 => 0
[6,3,3] => [3,3] => 11000 => 00111 => 0
[6,3,2,1] => [3,2,1] => 101010 => 010101 => 0
[6,3,1,1,1] => [3,1,1,1] => 1001110 => 0110001 => 0
[6,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[6,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[6,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[5,5,2] => [5,2] => 1000100 => 0111011 => 0
[5,5,1,1] => [5,1,1] => 10000110 => 01111001 => 0
[5,4,3] => [4,3] => 101000 => 010111 => 0
[5,4,2,1] => [4,2,1] => 1001010 => 0110101 => 0
[5,4,1,1,1] => [4,1,1,1] => 10001110 => 01110001 => 0
[5,3,3,1] => [3,3,1] => 110010 => 001101 => 0
[5,3,2,2] => [3,2,2] => 101100 => 010011 => 0
[5,3,2,1,1] => [3,2,1,1] => 1010110 => 0101001 => 0
[5,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01100001 => 0
[5,2,2,2,1] => [2,2,2,1] => 111010 => 000101 => 0
[5,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0010001 => 0
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 01000001 => 0
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[4,4,4] => [4,4] => 110000 => 001111 => 0
[4,4,3,1] => [4,3,1] => 1010010 => 0101101 => 0
[4,4,2,2] => [4,2,2] => 1001100 => 0110011 => 0
[4,4,2,1,1] => [4,2,1,1] => 10010110 => 01101001 => 0
[4,4,1,1,1,1] => [4,1,1,1,1] => 100011110 => 011100001 => 0
[4,3,3,2] => [3,3,2] => 110100 => 001011 => 0
[4,3,3,1,1] => [3,3,1,1] => 1100110 => 0011001 => 0
[4,3,2,2,1] => [3,2,2,1] => 1011010 => 0100101 => 0
[4,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 01010001 => 0
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011000001 => 0
[4,2,2,2,2] => [2,2,2,2] => 111100 => 000011 => 0
[4,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0001001 => 0
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 00100001 => 0
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 010000001 => 0
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 000000001 => 0
[3,3,3,3] => [3,3,3] => 111000 => 000111 => 0
[3,3,3,2,1] => [3,3,2,1] => 1101010 => 0010101 => 0
[3,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 00110001 => 0
[3,3,2,2,2] => [3,2,2,2] => 1011100 => 0100011 => 0
[3,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 01001001 => 0
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 010100001 => 0
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110000001 => 0
[3,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0000101 => 0
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 00010001 => 0
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 001000001 => 0
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1011111110 => 0100000001 => 0
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 0000000001 => 0
[2,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0000011 => 0
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 00001001 => 0
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 000100001 => 0
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1101111110 => 0010000001 => 0
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10111111110 => 01000000001 => 0
[2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 00000000001 => 0
[12,1] => [1] => 10 => 01 => 0
[11,2] => [2] => 100 => 011 => 0
[11,1,1] => [1,1] => 110 => 001 => 0
[10,3] => [3] => 1000 => 0111 => 0
[10,2,1] => [2,1] => 1010 => 0101 => 0
[10,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[9,4] => [4] => 10000 => 01111 => 0
[9,3,1] => [3,1] => 10010 => 01101 => 0
[9,2,2] => [2,2] => 1100 => 0011 => 0
[9,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[9,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[8,5] => [5] => 100000 => 011111 => 0
[8,4,1] => [4,1] => 100010 => 011101 => 0
[8,3,2] => [3,2] => 10100 => 01011 => 0
[8,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[8,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[8,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[8,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[7,6] => [6] => 1000000 => 0111111 => 0
[7,5,1] => [5,1] => 1000010 => 0111101 => 0
[7,4,2] => [4,2] => 100100 => 011011 => 0
[7,4,1,1] => [4,1,1] => 1000110 => 0111001 => 0
[7,3,3] => [3,3] => 11000 => 00111 => 0
[7,3,2,1] => [3,2,1] => 101010 => 010101 => 0
[7,3,1,1,1] => [3,1,1,1] => 1001110 => 0110001 => 0
[7,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[7,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[7,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[6,6,1] => [6,1] => 10000010 => 01111101 => 0
[6,5,2] => [5,2] => 1000100 => 0111011 => 0
[6,5,1,1] => [5,1,1] => 10000110 => 01111001 => 0
[6,4,3] => [4,3] => 101000 => 010111 => 0
[6,4,2,1] => [4,2,1] => 1001010 => 0110101 => 0
[6,4,1,1,1] => [4,1,1,1] => 10001110 => 01110001 => 0
[6,3,3,1] => [3,3,1] => 110010 => 001101 => 0
[6,3,2,2] => [3,2,2] => 101100 => 010011 => 0
[6,3,2,1,1] => [3,2,1,1] => 1010110 => 0101001 => 0
[6,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01100001 => 0
[6,2,2,2,1] => [2,2,2,1] => 111010 => 000101 => 0
[6,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0010001 => 0
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 01000001 => 0
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[5,5,3] => [5,3] => 1001000 => 0110111 => 0
[5,5,2,1] => [5,2,1] => 10001010 => 01110101 => 0
[5,5,1,1,1] => [5,1,1,1] => 100001110 => 011110001 => 0
[5,4,4] => [4,4] => 110000 => 001111 => 0
[5,4,3,1] => [4,3,1] => 1010010 => 0101101 => 0
[5,4,2,2] => [4,2,2] => 1001100 => 0110011 => 0
[5,4,2,1,1] => [4,2,1,1] => 10010110 => 01101001 => 0
[5,4,1,1,1,1] => [4,1,1,1,1] => 100011110 => 011100001 => 0
[5,3,3,2] => [3,3,2] => 110100 => 001011 => 0
[5,3,3,1,1] => [3,3,1,1] => 1100110 => 0011001 => 0
[5,3,2,2,1] => [3,2,2,1] => 1011010 => 0100101 => 0
[5,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 01010001 => 0
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011000001 => 0
[5,2,2,2,2] => [2,2,2,2] => 111100 => 000011 => 0
[5,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0001001 => 0
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 00100001 => 0
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 010000001 => 0
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 000000001 => 0
[4,4,4,1] => [4,4,1] => 1100010 => 0011101 => 0
[4,4,3,2] => [4,3,2] => 1010100 => 0101011 => 0
[4,4,3,1,1] => [4,3,1,1] => 10100110 => 01011001 => 0
[4,4,2,2,1] => [4,2,2,1] => 10011010 => 01100101 => 0
[4,4,2,1,1,1] => [4,2,1,1,1] => 100101110 => 011010001 => 0
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => 1000111110 => 0111000001 => 0
[4,3,3,3] => [3,3,3] => 111000 => 000111 => 0
[4,3,3,2,1] => [3,3,2,1] => 1101010 => 0010101 => 0
[4,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 00110001 => 0
[4,3,2,2,2] => [3,2,2,2] => 1011100 => 0100011 => 0
[4,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 01001001 => 0
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 010100001 => 0
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110000001 => 0
[4,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0000101 => 0
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 00010001 => 0
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 001000001 => 0
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1011111110 => 0100000001 => 0
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 0000000001 => 0
[3,3,3,3,1] => [3,3,3,1] => 1110010 => 0001101 => 0
[3,3,3,2,2] => [3,3,2,2] => 1101100 => 0010011 => 0
[3,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 00101001 => 0
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 001100001 => 0
[3,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 01000101 => 0
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 101101110 => 010010001 => 0
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1010111110 => 0101000001 => 0
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 10011111110 => 01100000001 => 0
[3,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0000011 => 0
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 00001001 => 0
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 000100001 => 0
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1101111110 => 0010000001 => 0
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10111111110 => 01000000001 => 0
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 00000000001 => 0
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 00000101 => 0
[2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 111101110 => 000010001 => 0
[2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1110111110 => 0001000001 => 0
[13,1] => [1] => 10 => 01 => 0
[12,2] => [2] => 100 => 011 => 0
[12,1,1] => [1,1] => 110 => 001 => 0
[11,3] => [3] => 1000 => 0111 => 0
[11,2,1] => [2,1] => 1010 => 0101 => 0
[11,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[10,4] => [4] => 10000 => 01111 => 0
[10,3,1] => [3,1] => 10010 => 01101 => 0
[10,2,2] => [2,2] => 1100 => 0011 => 0
[10,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[10,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[9,5] => [5] => 100000 => 011111 => 0
[9,4,1] => [4,1] => 100010 => 011101 => 0
[9,3,2] => [3,2] => 10100 => 01011 => 0
[9,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[9,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[9,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[9,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[8,6] => [6] => 1000000 => 0111111 => 0
[8,5,1] => [5,1] => 1000010 => 0111101 => 0
[8,4,2] => [4,2] => 100100 => 011011 => 0
[8,4,1,1] => [4,1,1] => 1000110 => 0111001 => 0
[8,3,3] => [3,3] => 11000 => 00111 => 0
[8,3,2,1] => [3,2,1] => 101010 => 010101 => 0
[8,3,1,1,1] => [3,1,1,1] => 1001110 => 0110001 => 0
[8,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[8,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[8,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[7,7] => [7] => 10000000 => 01111111 => 0
[7,6,1] => [6,1] => 10000010 => 01111101 => 0
[7,5,2] => [5,2] => 1000100 => 0111011 => 0
[7,5,1,1] => [5,1,1] => 10000110 => 01111001 => 0
[7,4,3] => [4,3] => 101000 => 010111 => 0
[7,4,2,1] => [4,2,1] => 1001010 => 0110101 => 0
[7,4,1,1,1] => [4,1,1,1] => 10001110 => 01110001 => 0
[7,3,3,1] => [3,3,1] => 110010 => 001101 => 0
[7,3,2,2] => [3,2,2] => 101100 => 010011 => 0
[7,3,2,1,1] => [3,2,1,1] => 1010110 => 0101001 => 0
[7,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01100001 => 0
[7,2,2,2,1] => [2,2,2,1] => 111010 => 000101 => 0
[7,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0010001 => 0
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 01000001 => 0
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[6,6,2] => [6,2] => 10000100 => 01111011 => 0
[6,6,1,1] => [6,1,1] => 100000110 => 011111001 => 0
[6,5,3] => [5,3] => 1001000 => 0110111 => 0
[6,5,2,1] => [5,2,1] => 10001010 => 01110101 => 0
[6,5,1,1,1] => [5,1,1,1] => 100001110 => 011110001 => 0
[6,4,4] => [4,4] => 110000 => 001111 => 0
[6,4,3,1] => [4,3,1] => 1010010 => 0101101 => 0
[6,4,2,2] => [4,2,2] => 1001100 => 0110011 => 0
[6,4,2,1,1] => [4,2,1,1] => 10010110 => 01101001 => 0
[6,4,1,1,1,1] => [4,1,1,1,1] => 100011110 => 011100001 => 0
[6,3,3,2] => [3,3,2] => 110100 => 001011 => 0
[6,3,3,1,1] => [3,3,1,1] => 1100110 => 0011001 => 0
[6,3,2,2,1] => [3,2,2,1] => 1011010 => 0100101 => 0
[6,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 01010001 => 0
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011000001 => 0
[6,2,2,2,2] => [2,2,2,2] => 111100 => 000011 => 0
[6,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0001001 => 0
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 00100001 => 0
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 010000001 => 0
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 000000001 => 0
[5,5,4] => [5,4] => 1010000 => 0101111 => 0
[5,5,3,1] => [5,3,1] => 10010010 => 01101101 => 0
[5,5,2,2] => [5,2,2] => 10001100 => 01110011 => 0
[5,5,2,1,1] => [5,2,1,1] => 100010110 => 011101001 => 0
[5,5,1,1,1,1] => [5,1,1,1,1] => 1000011110 => 0111100001 => 0
[5,4,4,1] => [4,4,1] => 1100010 => 0011101 => 0
[5,4,3,2] => [4,3,2] => 1010100 => 0101011 => 0
[5,4,3,1,1] => [4,3,1,1] => 10100110 => 01011001 => 0
[5,4,2,2,1] => [4,2,2,1] => 10011010 => 01100101 => 0
[5,4,2,1,1,1] => [4,2,1,1,1] => 100101110 => 011010001 => 0
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => 1000111110 => 0111000001 => 0
[5,3,3,3] => [3,3,3] => 111000 => 000111 => 0
[5,3,3,2,1] => [3,3,2,1] => 1101010 => 0010101 => 0
[5,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 00110001 => 0
[5,3,2,2,2] => [3,2,2,2] => 1011100 => 0100011 => 0
[5,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 01001001 => 0
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 010100001 => 0
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110000001 => 0
[5,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0000101 => 0
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 00010001 => 0
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 001000001 => 0
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1011111110 => 0100000001 => 0
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 0000000001 => 0
[4,4,4,2] => [4,4,2] => 1100100 => 0011011 => 0
[4,4,4,1,1] => [4,4,1,1] => 11000110 => 00111001 => 0
[4,4,3,3] => [4,3,3] => 1011000 => 0100111 => 0
[4,4,3,2,1] => [4,3,2,1] => 10101010 => 01010101 => 0
[4,4,3,1,1,1] => [4,3,1,1,1] => 101001110 => 010110001 => 0
[4,4,2,2,2] => [4,2,2,2] => 10011100 => 01100011 => 0
[4,4,2,2,1,1] => [4,2,2,1,1] => 100110110 => 011001001 => 0
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => 1001011110 => 0110100001 => 0
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 10001111110 => 01110000001 => 0
[4,3,3,3,1] => [3,3,3,1] => 1110010 => 0001101 => 0
[4,3,3,2,2] => [3,3,2,2] => 1101100 => 0010011 => 0
[4,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 00101001 => 0
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 001100001 => 0
[4,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 01000101 => 0
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => 101101110 => 010010001 => 0
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1010111110 => 0101000001 => 0
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 10011111110 => 01100000001 => 0
[4,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0000011 => 0
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 00001001 => 0
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 000100001 => 0
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1101111110 => 0010000001 => 0
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10111111110 => 01000000001 => 0
[4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 00000000001 => 0
[3,3,3,3,2] => [3,3,3,2] => 1110100 => 0001011 => 0
[3,3,3,3,1,1] => [3,3,3,1,1] => 11100110 => 00011001 => 0
[3,3,3,2,2,1] => [3,3,2,2,1] => 11011010 => 00100101 => 0
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => 110101110 => 001010001 => 0
[3,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 01000011 => 0
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => 101110110 => 010001001 => 0
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 00000101 => 0
[3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 111101110 => 000010001 => 0
[3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1110111110 => 0001000001 => 0
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 00000011 => 0
[2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 111110110 => 000001001 => 0
[2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 1111011110 => 0000100001 => 0
[14,1] => [1] => 10 => 01 => 0
[13,2] => [2] => 100 => 011 => 0
[13,1,1] => [1,1] => 110 => 001 => 0
[12,3] => [3] => 1000 => 0111 => 0
[12,2,1] => [2,1] => 1010 => 0101 => 0
[12,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[11,4] => [4] => 10000 => 01111 => 0
[11,3,1] => [3,1] => 10010 => 01101 => 0
[11,2,2] => [2,2] => 1100 => 0011 => 0
[11,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[11,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[10,5] => [5] => 100000 => 011111 => 0
[10,4,1] => [4,1] => 100010 => 011101 => 0
[10,3,2] => [3,2] => 10100 => 01011 => 0
[10,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[10,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[10,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[10,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[9,6] => [6] => 1000000 => 0111111 => 0
[9,5,1] => [5,1] => 1000010 => 0111101 => 0
[9,4,2] => [4,2] => 100100 => 011011 => 0
[9,4,1,1] => [4,1,1] => 1000110 => 0111001 => 0
[9,3,3] => [3,3] => 11000 => 00111 => 0
[9,3,2,1] => [3,2,1] => 101010 => 010101 => 0
[9,3,1,1,1] => [3,1,1,1] => 1001110 => 0110001 => 0
[9,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[9,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[9,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[8,7] => [7] => 10000000 => 01111111 => 0
[8,6,1] => [6,1] => 10000010 => 01111101 => 0
[8,5,2] => [5,2] => 1000100 => 0111011 => 0
[8,5,1,1] => [5,1,1] => 10000110 => 01111001 => 0
[8,4,3] => [4,3] => 101000 => 010111 => 0
[8,4,2,1] => [4,2,1] => 1001010 => 0110101 => 0
[8,4,1,1,1] => [4,1,1,1] => 10001110 => 01110001 => 0
[8,3,3,1] => [3,3,1] => 110010 => 001101 => 0
[8,3,2,2] => [3,2,2] => 101100 => 010011 => 0
[8,3,2,1,1] => [3,2,1,1] => 1010110 => 0101001 => 0
[8,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01100001 => 0
[8,2,2,2,1] => [2,2,2,1] => 111010 => 000101 => 0
[8,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0010001 => 0
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 01000001 => 0
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[7,7,1] => [7,1] => 100000010 => 011111101 => 0
[7,6,2] => [6,2] => 10000100 => 01111011 => 0
[7,6,1,1] => [6,1,1] => 100000110 => 011111001 => 0
[7,5,3] => [5,3] => 1001000 => 0110111 => 0
[7,5,2,1] => [5,2,1] => 10001010 => 01110101 => 0
[7,5,1,1,1] => [5,1,1,1] => 100001110 => 011110001 => 0
[7,4,4] => [4,4] => 110000 => 001111 => 0
[7,4,3,1] => [4,3,1] => 1010010 => 0101101 => 0
[7,4,2,2] => [4,2,2] => 1001100 => 0110011 => 0
[7,4,2,1,1] => [4,2,1,1] => 10010110 => 01101001 => 0
[7,4,1,1,1,1] => [4,1,1,1,1] => 100011110 => 011100001 => 0
[7,3,3,2] => [3,3,2] => 110100 => 001011 => 0
[7,3,3,1,1] => [3,3,1,1] => 1100110 => 0011001 => 0
[7,3,2,2,1] => [3,2,2,1] => 1011010 => 0100101 => 0
[7,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 01010001 => 0
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011000001 => 0
[7,2,2,2,2] => [2,2,2,2] => 111100 => 000011 => 0
[7,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0001001 => 0
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 00100001 => 0
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 010000001 => 0
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 000000001 => 0
[6,6,3] => [6,3] => 10001000 => 01110111 => 0
[6,6,2,1] => [6,2,1] => 100001010 => 011110101 => 0
[6,6,1,1,1] => [6,1,1,1] => 1000001110 => 0111110001 => 0
[6,5,4] => [5,4] => 1010000 => 0101111 => 0
[6,5,3,1] => [5,3,1] => 10010010 => 01101101 => 0
[6,5,2,2] => [5,2,2] => 10001100 => 01110011 => 0
[6,5,2,1,1] => [5,2,1,1] => 100010110 => 011101001 => 0
[6,5,1,1,1,1] => [5,1,1,1,1] => 1000011110 => 0111100001 => 0
[6,4,4,1] => [4,4,1] => 1100010 => 0011101 => 0
[6,4,3,2] => [4,3,2] => 1010100 => 0101011 => 0
[6,4,3,1,1] => [4,3,1,1] => 10100110 => 01011001 => 0
[6,4,2,2,1] => [4,2,2,1] => 10011010 => 01100101 => 0
[6,4,2,1,1,1] => [4,2,1,1,1] => 100101110 => 011010001 => 0
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => 1000111110 => 0111000001 => 0
[6,3,3,3] => [3,3,3] => 111000 => 000111 => 0
[6,3,3,2,1] => [3,3,2,1] => 1101010 => 0010101 => 0
[6,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 00110001 => 0
[6,3,2,2,2] => [3,2,2,2] => 1011100 => 0100011 => 0
[6,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 01001001 => 0
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 010100001 => 0
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110000001 => 0
[6,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0000101 => 0
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 00010001 => 0
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 001000001 => 0
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1011111110 => 0100000001 => 0
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 0000000001 => 0
[5,5,5] => [5,5] => 1100000 => 0011111 => 0
[5,5,4,1] => [5,4,1] => 10100010 => 01011101 => 0
[5,5,3,2] => [5,3,2] => 10010100 => 01101011 => 0
[5,5,3,1,1] => [5,3,1,1] => 100100110 => 011011001 => 0
[5,5,2,2,1] => [5,2,2,1] => 100011010 => 011100101 => 0
[5,5,2,1,1,1] => [5,2,1,1,1] => 1000101110 => 0111010001 => 0
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => 10000111110 => 01111000001 => 0
[5,4,4,2] => [4,4,2] => 1100100 => 0011011 => 0
[5,4,4,1,1] => [4,4,1,1] => 11000110 => 00111001 => 0
[5,4,3,3] => [4,3,3] => 1011000 => 0100111 => 0
[5,4,3,2,1] => [4,3,2,1] => 10101010 => 01010101 => 0
[5,4,3,1,1,1] => [4,3,1,1,1] => 101001110 => 010110001 => 0
[5,4,2,2,2] => [4,2,2,2] => 10011100 => 01100011 => 0
[5,4,2,2,1,1] => [4,2,2,1,1] => 100110110 => 011001001 => 0
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => 1001011110 => 0110100001 => 0
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 10001111110 => 01110000001 => 0
[5,3,3,3,1] => [3,3,3,1] => 1110010 => 0001101 => 0
[5,3,3,2,2] => [3,3,2,2] => 1101100 => 0010011 => 0
[5,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 00101001 => 0
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 001100001 => 0
[5,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 01000101 => 0
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => 101101110 => 010010001 => 0
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1010111110 => 0101000001 => 0
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 10011111110 => 01100000001 => 0
[5,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0000011 => 0
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 00001001 => 0
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 000100001 => 0
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1101111110 => 0010000001 => 0
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10111111110 => 01000000001 => 0
[5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 00000000001 => 0
[4,4,4,3] => [4,4,3] => 1101000 => 0010111 => 0
[4,4,4,2,1] => [4,4,2,1] => 11001010 => 00110101 => 0
[4,4,4,1,1,1] => [4,4,1,1,1] => 110001110 => 001110001 => 0
[4,4,3,3,1] => [4,3,3,1] => 10110010 => 01001101 => 0
[4,4,3,2,2] => [4,3,2,2] => 10101100 => 01010011 => 0
[4,4,3,2,1,1] => [4,3,2,1,1] => 101010110 => 010101001 => 0
[4,4,2,2,2,1] => [4,2,2,2,1] => 100111010 => 011000101 => 0
[4,3,3,3,2] => [3,3,3,2] => 1110100 => 0001011 => 0
[4,3,3,3,1,1] => [3,3,3,1,1] => 11100110 => 00011001 => 0
[4,3,3,2,2,1] => [3,3,2,2,1] => 11011010 => 00100101 => 0
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => 110101110 => 001010001 => 0
[4,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 01000011 => 0
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => 101110110 => 010001001 => 0
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 00000101 => 0
[4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 111101110 => 000010001 => 0
[4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1110111110 => 0001000001 => 0
[3,3,3,3,3] => [3,3,3,3] => 1111000 => 0000111 => 0
[3,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 00010101 => 0
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => 111001110 => 000110001 => 0
[3,3,3,2,2,2] => [3,3,2,2,2] => 11011100 => 00100011 => 0
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => 110110110 => 001001001 => 0
[3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 1101011110 => 0010100001 => 0
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => 101111010 => 010000101 => 0
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 00000011 => 0
[3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 111110110 => 000001001 => 0
[3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 1111011110 => 0000100001 => 0
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 111111010 => 000000101 => 0
[2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => 1111101110 => 0000010001 => 0
[2,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => 11110111110 => 00001000001 => 0
[15,1] => [1] => 10 => 01 => 0
[14,2] => [2] => 100 => 011 => 0
[14,1,1] => [1,1] => 110 => 001 => 0
[13,3] => [3] => 1000 => 0111 => 0
[13,2,1] => [2,1] => 1010 => 0101 => 0
[13,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[12,4] => [4] => 10000 => 01111 => 0
[12,3,1] => [3,1] => 10010 => 01101 => 0
[12,2,2] => [2,2] => 1100 => 0011 => 0
[12,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[12,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[11,5] => [5] => 100000 => 011111 => 0
[11,4,1] => [4,1] => 100010 => 011101 => 0
[11,3,2] => [3,2] => 10100 => 01011 => 0
[11,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[11,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[11,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[11,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[10,6] => [6] => 1000000 => 0111111 => 0
[10,5,1] => [5,1] => 1000010 => 0111101 => 0
[10,4,2] => [4,2] => 100100 => 011011 => 0
[10,4,1,1] => [4,1,1] => 1000110 => 0111001 => 0
[10,3,3] => [3,3] => 11000 => 00111 => 0
[10,3,2,1] => [3,2,1] => 101010 => 010101 => 0
[10,3,1,1,1] => [3,1,1,1] => 1001110 => 0110001 => 0
[10,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[10,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[10,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[9,7] => [7] => 10000000 => 01111111 => 0
[9,6,1] => [6,1] => 10000010 => 01111101 => 0
[9,5,2] => [5,2] => 1000100 => 0111011 => 0
[9,5,1,1] => [5,1,1] => 10000110 => 01111001 => 0
[9,4,3] => [4,3] => 101000 => 010111 => 0
[9,4,2,1] => [4,2,1] => 1001010 => 0110101 => 0
[9,4,1,1,1] => [4,1,1,1] => 10001110 => 01110001 => 0
[9,3,3,1] => [3,3,1] => 110010 => 001101 => 0
[9,3,2,2] => [3,2,2] => 101100 => 010011 => 0
[9,3,2,1,1] => [3,2,1,1] => 1010110 => 0101001 => 0
[9,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01100001 => 0
[9,2,2,2,1] => [2,2,2,1] => 111010 => 000101 => 0
[9,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0010001 => 0
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 01000001 => 0
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[8,8] => [8] => 100000000 => 011111111 => 0
[8,7,1] => [7,1] => 100000010 => 011111101 => 0
[8,6,2] => [6,2] => 10000100 => 01111011 => 0
[8,6,1,1] => [6,1,1] => 100000110 => 011111001 => 0
[8,5,3] => [5,3] => 1001000 => 0110111 => 0
[8,5,2,1] => [5,2,1] => 10001010 => 01110101 => 0
[8,5,1,1,1] => [5,1,1,1] => 100001110 => 011110001 => 0
[8,4,4] => [4,4] => 110000 => 001111 => 0
[8,4,3,1] => [4,3,1] => 1010010 => 0101101 => 0
[8,4,2,2] => [4,2,2] => 1001100 => 0110011 => 0
[8,4,2,1,1] => [4,2,1,1] => 10010110 => 01101001 => 0
[8,4,1,1,1,1] => [4,1,1,1,1] => 100011110 => 011100001 => 0
[8,3,3,2] => [3,3,2] => 110100 => 001011 => 0
[8,3,3,1,1] => [3,3,1,1] => 1100110 => 0011001 => 0
[8,3,2,2,1] => [3,2,2,1] => 1011010 => 0100101 => 0
[8,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 01010001 => 0
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011000001 => 0
[8,2,2,2,2] => [2,2,2,2] => 111100 => 000011 => 0
[8,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0001001 => 0
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 00100001 => 0
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 010000001 => 0
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 000000001 => 0
[7,7,2] => [7,2] => 100000100 => 011111011 => 0
[7,7,1,1] => [7,1,1] => 1000000110 => 0111111001 => 0
[7,6,3] => [6,3] => 10001000 => 01110111 => 0
[7,6,2,1] => [6,2,1] => 100001010 => 011110101 => 0
[7,6,1,1,1] => [6,1,1,1] => 1000001110 => 0111110001 => 0
[7,5,4] => [5,4] => 1010000 => 0101111 => 0
[7,5,3,1] => [5,3,1] => 10010010 => 01101101 => 0
[7,5,2,2] => [5,2,2] => 10001100 => 01110011 => 0
[7,5,2,1,1] => [5,2,1,1] => 100010110 => 011101001 => 0
[7,5,1,1,1,1] => [5,1,1,1,1] => 1000011110 => 0111100001 => 0
[7,4,4,1] => [4,4,1] => 1100010 => 0011101 => 0
[7,4,3,2] => [4,3,2] => 1010100 => 0101011 => 0
[7,4,3,1,1] => [4,3,1,1] => 10100110 => 01011001 => 0
[7,4,2,2,1] => [4,2,2,1] => 10011010 => 01100101 => 0
[7,4,2,1,1,1] => [4,2,1,1,1] => 100101110 => 011010001 => 0
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => 1000111110 => 0111000001 => 0
[7,3,3,3] => [3,3,3] => 111000 => 000111 => 0
[7,3,3,2,1] => [3,3,2,1] => 1101010 => 0010101 => 0
[7,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 00110001 => 0
[7,3,2,2,2] => [3,2,2,2] => 1011100 => 0100011 => 0
[7,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 01001001 => 0
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 010100001 => 0
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110000001 => 0
[7,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0000101 => 0
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 00010001 => 0
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 001000001 => 0
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1011111110 => 0100000001 => 0
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 0000000001 => 0
[6,6,4] => [6,4] => 10010000 => 01101111 => 0
[6,6,3,1] => [6,3,1] => 100010010 => 011101101 => 0
[6,6,2,2] => [6,2,2] => 100001100 => 011110011 => 0
[6,6,2,1,1] => [6,2,1,1] => 1000010110 => 0111101001 => 0
[6,6,1,1,1,1] => [6,1,1,1,1] => 10000011110 => 01111100001 => 0
[6,5,5] => [5,5] => 1100000 => 0011111 => 0
[6,5,4,1] => [5,4,1] => 10100010 => 01011101 => 0
[6,5,3,2] => [5,3,2] => 10010100 => 01101011 => 0
[6,5,3,1,1] => [5,3,1,1] => 100100110 => 011011001 => 0
[6,5,2,2,1] => [5,2,2,1] => 100011010 => 011100101 => 0
[6,5,2,1,1,1] => [5,2,1,1,1] => 1000101110 => 0111010001 => 0
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => 10000111110 => 01111000001 => 0
[6,4,4,2] => [4,4,2] => 1100100 => 0011011 => 0
[6,4,4,1,1] => [4,4,1,1] => 11000110 => 00111001 => 0
[6,4,3,3] => [4,3,3] => 1011000 => 0100111 => 0
[6,4,3,2,1] => [4,3,2,1] => 10101010 => 01010101 => 0
[6,4,3,1,1,1] => [4,3,1,1,1] => 101001110 => 010110001 => 0
[6,4,2,2,2] => [4,2,2,2] => 10011100 => 01100011 => 0
[6,4,2,2,1,1] => [4,2,2,1,1] => 100110110 => 011001001 => 0
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => 1001011110 => 0110100001 => 0
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 10001111110 => 01110000001 => 0
[6,3,3,3,1] => [3,3,3,1] => 1110010 => 0001101 => 0
[6,3,3,2,2] => [3,3,2,2] => 1101100 => 0010011 => 0
[6,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 00101001 => 0
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 001100001 => 0
[6,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 01000101 => 0
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => 101101110 => 010010001 => 0
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1010111110 => 0101000001 => 0
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 10011111110 => 01100000001 => 0
[6,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0000011 => 0
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 00001001 => 0
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 000100001 => 0
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1101111110 => 0010000001 => 0
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10111111110 => 01000000001 => 0
[6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 00000000001 => 0
[5,5,5,1] => [5,5,1] => 11000010 => 00111101 => 0
[5,5,4,2] => [5,4,2] => 10100100 => 01011011 => 0
[5,5,4,1,1] => [5,4,1,1] => 101000110 => 010111001 => 0
[5,5,3,3] => [5,3,3] => 10011000 => 01100111 => 0
[5,5,3,2,1] => [5,3,2,1] => 100101010 => 011010101 => 0
[5,5,3,1,1,1] => [5,3,1,1,1] => 1001001110 => 0110110001 => 0
[5,5,2,2,2] => [5,2,2,2] => 100011100 => 011100011 => 0
[5,5,2,2,1,1] => [5,2,2,1,1] => 1000110110 => 0111001001 => 0
[5,4,4,3] => [4,4,3] => 1101000 => 0010111 => 0
[5,4,4,2,1] => [4,4,2,1] => 11001010 => 00110101 => 0
[5,4,4,1,1,1] => [4,4,1,1,1] => 110001110 => 001110001 => 0
[5,4,3,3,1] => [4,3,3,1] => 10110010 => 01001101 => 0
[5,4,3,2,2] => [4,3,2,2] => 10101100 => 01010011 => 0
[5,4,3,2,1,1] => [4,3,2,1,1] => 101010110 => 010101001 => 0
[5,4,2,2,2,1] => [4,2,2,2,1] => 100111010 => 011000101 => 0
[5,3,3,3,2] => [3,3,3,2] => 1110100 => 0001011 => 0
[5,3,3,3,1,1] => [3,3,3,1,1] => 11100110 => 00011001 => 0
[5,3,3,2,2,1] => [3,3,2,2,1] => 11011010 => 00100101 => 0
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => 110101110 => 001010001 => 0
[5,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 01000011 => 0
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => 101110110 => 010001001 => 0
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 00000101 => 0
[5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 111101110 => 000010001 => 0
[5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1110111110 => 0001000001 => 0
[4,4,4,4] => [4,4,4] => 1110000 => 0001111 => 0
[4,4,4,3,1] => [4,4,3,1] => 11010010 => 00101101 => 0
[4,4,4,2,2] => [4,4,2,2] => 11001100 => 00110011 => 0
[4,4,4,2,1,1] => [4,4,2,1,1] => 110010110 => 001101001 => 0
[4,4,3,3,2] => [4,3,3,2] => 10110100 => 01001011 => 0
[4,4,3,3,1,1] => [4,3,3,1,1] => 101100110 => 010011001 => 0
[4,4,3,2,2,1] => [4,3,2,2,1] => 101011010 => 010100101 => 0
[4,4,2,2,2,2] => [4,2,2,2,2] => 100111100 => 011000011 => 0
[4,3,3,3,3] => [3,3,3,3] => 1111000 => 0000111 => 0
[4,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 00010101 => 0
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => 111001110 => 000110001 => 0
[4,3,3,2,2,2] => [3,3,2,2,2] => 11011100 => 00100011 => 0
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => 110110110 => 001001001 => 0
[4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 1101011110 => 0010100001 => 0
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => 101111010 => 010000101 => 0
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 00000011 => 0
[4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 111110110 => 000001001 => 0
[4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 1111011110 => 0000100001 => 0
[3,3,3,3,3,1] => [3,3,3,3,1] => 11110010 => 00001101 => 0
[3,3,3,3,2,2] => [3,3,3,2,2] => 11101100 => 00010011 => 0
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => 111010110 => 000101001 => 0
[3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => 1110011110 => 0001100001 => 0
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => 110111010 => 001000101 => 0
[3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => 1101101110 => 0010010001 => 0
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => 101111100 => 010000011 => 0
[3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => 10111011110 => 01000100001 => 0
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 111111010 => 000000101 => 0
[3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => 1111101110 => 0000010001 => 0
[3,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => 11110111110 => 00001000001 => 0
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => 111111100 => 000000011 => 0
[2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => 1111110110 => 0000001001 => 0
[16,1] => [1] => 10 => 01 => 0
[15,2] => [2] => 100 => 011 => 0
[15,1,1] => [1,1] => 110 => 001 => 0
[14,3] => [3] => 1000 => 0111 => 0
[14,2,1] => [2,1] => 1010 => 0101 => 0
[14,1,1,1] => [1,1,1] => 1110 => 0001 => 0
[13,4] => [4] => 10000 => 01111 => 0
[13,3,1] => [3,1] => 10010 => 01101 => 0
[13,2,2] => [2,2] => 1100 => 0011 => 0
[13,2,1,1] => [2,1,1] => 10110 => 01001 => 0
[13,1,1,1,1] => [1,1,1,1] => 11110 => 00001 => 0
[12,5] => [5] => 100000 => 011111 => 0
[12,4,1] => [4,1] => 100010 => 011101 => 0
[12,3,2] => [3,2] => 10100 => 01011 => 0
[12,3,1,1] => [3,1,1] => 100110 => 011001 => 0
[12,2,2,1] => [2,2,1] => 11010 => 00101 => 0
[12,2,1,1,1] => [2,1,1,1] => 101110 => 010001 => 0
[12,1,1,1,1,1] => [1,1,1,1,1] => 111110 => 000001 => 0
[11,6] => [6] => 1000000 => 0111111 => 0
[11,5,1] => [5,1] => 1000010 => 0111101 => 0
[11,4,2] => [4,2] => 100100 => 011011 => 0
[11,4,1,1] => [4,1,1] => 1000110 => 0111001 => 0
[11,3,3] => [3,3] => 11000 => 00111 => 0
[11,3,2,1] => [3,2,1] => 101010 => 010101 => 0
[11,3,1,1,1] => [3,1,1,1] => 1001110 => 0110001 => 0
[11,2,2,2] => [2,2,2] => 11100 => 00011 => 0
[11,2,2,1,1] => [2,2,1,1] => 110110 => 001001 => 0
[11,2,1,1,1,1] => [2,1,1,1,1] => 1011110 => 0100001 => 0
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1111110 => 0000001 => 0
[10,7] => [7] => 10000000 => 01111111 => 0
[10,6,1] => [6,1] => 10000010 => 01111101 => 0
[10,5,2] => [5,2] => 1000100 => 0111011 => 0
[10,5,1,1] => [5,1,1] => 10000110 => 01111001 => 0
[10,4,3] => [4,3] => 101000 => 010111 => 0
[10,4,2,1] => [4,2,1] => 1001010 => 0110101 => 0
[10,4,1,1,1] => [4,1,1,1] => 10001110 => 01110001 => 0
[10,3,3,1] => [3,3,1] => 110010 => 001101 => 0
[10,3,2,2] => [3,2,2] => 101100 => 010011 => 0
[10,3,2,1,1] => [3,2,1,1] => 1010110 => 0101001 => 0
[10,3,1,1,1,1] => [3,1,1,1,1] => 10011110 => 01100001 => 0
[10,2,2,2,1] => [2,2,2,1] => 111010 => 000101 => 0
[10,2,2,1,1,1] => [2,2,1,1,1] => 1101110 => 0010001 => 0
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => 10111110 => 01000001 => 0
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 11111110 => 00000001 => 0
[9,8] => [8] => 100000000 => 011111111 => 0
[9,7,1] => [7,1] => 100000010 => 011111101 => 0
[9,6,2] => [6,2] => 10000100 => 01111011 => 0
[9,6,1,1] => [6,1,1] => 100000110 => 011111001 => 0
[9,5,3] => [5,3] => 1001000 => 0110111 => 0
[9,5,2,1] => [5,2,1] => 10001010 => 01110101 => 0
[9,5,1,1,1] => [5,1,1,1] => 100001110 => 011110001 => 0
[9,4,4] => [4,4] => 110000 => 001111 => 0
[9,4,3,1] => [4,3,1] => 1010010 => 0101101 => 0
[9,4,2,2] => [4,2,2] => 1001100 => 0110011 => 0
[9,4,2,1,1] => [4,2,1,1] => 10010110 => 01101001 => 0
[9,4,1,1,1,1] => [4,1,1,1,1] => 100011110 => 011100001 => 0
[9,3,3,2] => [3,3,2] => 110100 => 001011 => 0
[9,3,3,1,1] => [3,3,1,1] => 1100110 => 0011001 => 0
[9,3,2,2,1] => [3,2,2,1] => 1011010 => 0100101 => 0
[9,3,2,1,1,1] => [3,2,1,1,1] => 10101110 => 01010001 => 0
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => 100111110 => 011000001 => 0
[9,2,2,2,2] => [2,2,2,2] => 111100 => 000011 => 0
[9,2,2,2,1,1] => [2,2,2,1,1] => 1110110 => 0001001 => 0
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => 11011110 => 00100001 => 0
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 101111110 => 010000001 => 0
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 111111110 => 000000001 => 0
[8,8,1] => [8,1] => 1000000010 => 0111111101 => 0
[8,7,2] => [7,2] => 100000100 => 011111011 => 0
[8,7,1,1] => [7,1,1] => 1000000110 => 0111111001 => 0
[8,6,3] => [6,3] => 10001000 => 01110111 => 0
[8,6,2,1] => [6,2,1] => 100001010 => 011110101 => 0
[8,6,1,1,1] => [6,1,1,1] => 1000001110 => 0111110001 => 0
[8,5,4] => [5,4] => 1010000 => 0101111 => 0
[8,5,3,1] => [5,3,1] => 10010010 => 01101101 => 0
[8,5,2,2] => [5,2,2] => 10001100 => 01110011 => 0
[8,5,2,1,1] => [5,2,1,1] => 100010110 => 011101001 => 0
[8,5,1,1,1,1] => [5,1,1,1,1] => 1000011110 => 0111100001 => 0
[8,4,4,1] => [4,4,1] => 1100010 => 0011101 => 0
[8,4,3,2] => [4,3,2] => 1010100 => 0101011 => 0
[8,4,3,1,1] => [4,3,1,1] => 10100110 => 01011001 => 0
[8,4,2,2,1] => [4,2,2,1] => 10011010 => 01100101 => 0
[8,4,2,1,1,1] => [4,2,1,1,1] => 100101110 => 011010001 => 0
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => 1000111110 => 0111000001 => 0
[8,3,3,3] => [3,3,3] => 111000 => 000111 => 0
[8,3,3,2,1] => [3,3,2,1] => 1101010 => 0010101 => 0
[8,3,3,1,1,1] => [3,3,1,1,1] => 11001110 => 00110001 => 0
[8,3,2,2,2] => [3,2,2,2] => 1011100 => 0100011 => 0
[8,3,2,2,1,1] => [3,2,2,1,1] => 10110110 => 01001001 => 0
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => 101011110 => 010100001 => 0
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1001111110 => 0110000001 => 0
[8,2,2,2,2,1] => [2,2,2,2,1] => 1111010 => 0000101 => 0
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => 11101110 => 00010001 => 0
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 110111110 => 001000001 => 0
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1011111110 => 0100000001 => 0
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 0000000001 => 0
[7,7,3] => [7,3] => 100001000 => 011110111 => 0
[7,7,2,1] => [7,2,1] => 1000001010 => 0111110101 => 0
[7,7,1,1,1] => [7,1,1,1] => 10000001110 => 01111110001 => 0
[7,6,4] => [6,4] => 10010000 => 01101111 => 0
[7,6,3,1] => [6,3,1] => 100010010 => 011101101 => 0
[7,6,2,2] => [6,2,2] => 100001100 => 011110011 => 0
[7,6,2,1,1] => [6,2,1,1] => 1000010110 => 0111101001 => 0
[7,6,1,1,1,1] => [6,1,1,1,1] => 10000011110 => 01111100001 => 0
[7,5,5] => [5,5] => 1100000 => 0011111 => 0
[7,5,4,1] => [5,4,1] => 10100010 => 01011101 => 0
[7,5,3,2] => [5,3,2] => 10010100 => 01101011 => 0
[7,5,3,1,1] => [5,3,1,1] => 100100110 => 011011001 => 0
[7,5,2,2,1] => [5,2,2,1] => 100011010 => 011100101 => 0
[7,5,2,1,1,1] => [5,2,1,1,1] => 1000101110 => 0111010001 => 0
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => 10000111110 => 01111000001 => 0
[7,4,4,2] => [4,4,2] => 1100100 => 0011011 => 0
[7,4,4,1,1] => [4,4,1,1] => 11000110 => 00111001 => 0
[7,4,3,3] => [4,3,3] => 1011000 => 0100111 => 0
[7,4,3,2,1] => [4,3,2,1] => 10101010 => 01010101 => 0
[7,4,3,1,1,1] => [4,3,1,1,1] => 101001110 => 010110001 => 0
[7,4,2,2,2] => [4,2,2,2] => 10011100 => 01100011 => 0
[7,4,2,2,1,1] => [4,2,2,1,1] => 100110110 => 011001001 => 0
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => 1001011110 => 0110100001 => 0
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 10001111110 => 01110000001 => 0
[7,3,3,3,1] => [3,3,3,1] => 1110010 => 0001101 => 0
[7,3,3,2,2] => [3,3,2,2] => 1101100 => 0010011 => 0
[7,3,3,2,1,1] => [3,3,2,1,1] => 11010110 => 00101001 => 0
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => 110011110 => 001100001 => 0
[7,3,2,2,2,1] => [3,2,2,2,1] => 10111010 => 01000101 => 0
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => 101101110 => 010010001 => 0
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1010111110 => 0101000001 => 0
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 10011111110 => 01100000001 => 0
[7,2,2,2,2,2] => [2,2,2,2,2] => 1111100 => 0000011 => 0
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => 11110110 => 00001001 => 0
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 111011110 => 000100001 => 0
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1101111110 => 0010000001 => 0
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10111111110 => 01000000001 => 0
[7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 00000000001 => 0
[6,6,5] => [6,5] => 10100000 => 01011111 => 0
[6,6,4,1] => [6,4,1] => 100100010 => 011011101 => 0
[6,6,3,2] => [6,3,2] => 100010100 => 011101011 => 0
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => 100000111110 => 011111000001 => 0
[6,5,5,1] => [5,5,1] => 11000010 => 00111101 => 0
[6,5,4,2] => [5,4,2] => 10100100 => 01011011 => 0
[6,5,4,1,1] => [5,4,1,1] => 101000110 => 010111001 => 0
[6,5,3,3] => [5,3,3] => 10011000 => 01100111 => 0
[6,5,3,2,1] => [5,3,2,1] => 100101010 => 011010101 => 0
[6,5,3,1,1,1] => [5,3,1,1,1] => 1001001110 => 0110110001 => 0
[6,5,2,2,2] => [5,2,2,2] => 100011100 => 011100011 => 0
[6,5,2,2,1,1] => [5,2,2,1,1] => 1000110110 => 0111001001 => 0
[6,4,4,3] => [4,4,3] => 1101000 => 0010111 => 0
[6,4,4,2,1] => [4,4,2,1] => 11001010 => 00110101 => 0
[6,4,4,1,1,1] => [4,4,1,1,1] => 110001110 => 001110001 => 0
[6,4,3,3,1] => [4,3,3,1] => 10110010 => 01001101 => 0
[6,4,3,2,2] => [4,3,2,2] => 10101100 => 01010011 => 0
[6,4,3,2,1,1] => [4,3,2,1,1] => 101010110 => 010101001 => 0
[6,4,2,2,2,1] => [4,2,2,2,1] => 100111010 => 011000101 => 0
[6,3,3,3,2] => [3,3,3,2] => 1110100 => 0001011 => 0
[6,3,3,3,1,1] => [3,3,3,1,1] => 11100110 => 00011001 => 0
[6,3,3,2,2,1] => [3,3,2,2,1] => 11011010 => 00100101 => 0
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => 110101110 => 001010001 => 0
[6,3,2,2,2,2] => [3,2,2,2,2] => 10111100 => 01000011 => 0
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => 101110110 => 010001001 => 0
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 00000101 => 0
[6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 111101110 => 000010001 => 0
[6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1110111110 => 0001000001 => 0
[5,5,5,2] => [5,5,2] => 11000100 => 00111011 => 0
[5,5,5,1,1] => [5,5,1,1] => 110000110 => 001111001 => 0
[5,5,4,3] => [5,4,3] => 10101000 => 01010111 => 0
[5,5,4,2,1] => [5,4,2,1] => 101001010 => 010110101 => 0
[5,5,4,1,1,1] => [5,4,1,1,1] => 1010001110 => 0101110001 => 0
[5,5,3,3,1] => [5,3,3,1] => 100110010 => 011001101 => 0
[5,5,3,2,2] => [5,3,2,2] => 100101100 => 011010011 => 0
[5,5,3,2,1,1] => [5,3,2,1,1] => 1001010110 => 0110101001 => 0
[5,5,2,2,2,1] => [5,2,2,2,1] => 1000111010 => 0111000101 => 0
[5,4,4,4] => [4,4,4] => 1110000 => 0001111 => 0
[5,4,4,3,1] => [4,4,3,1] => 11010010 => 00101101 => 0
[5,4,4,2,2] => [4,4,2,2] => 11001100 => 00110011 => 0
[5,4,4,2,1,1] => [4,4,2,1,1] => 110010110 => 001101001 => 0
[5,4,3,3,2] => [4,3,3,2] => 10110100 => 01001011 => 0
[5,4,3,3,1,1] => [4,3,3,1,1] => 101100110 => 010011001 => 0
[5,4,3,2,2,1] => [4,3,2,2,1] => 101011010 => 010100101 => 0
[5,4,2,2,2,2] => [4,2,2,2,2] => 100111100 => 011000011 => 0
[5,3,3,3,3] => [3,3,3,3] => 1111000 => 0000111 => 0
[5,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 00010101 => 0
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => 111001110 => 000110001 => 0
[5,3,3,2,2,2] => [3,3,2,2,2] => 11011100 => 00100011 => 0
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => 110110110 => 001001001 => 0
[5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 1101011110 => 0010100001 => 0
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => 101111010 => 010000101 => 0
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 00000011 => 0
[5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 111110110 => 000001001 => 0
[5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 1111011110 => 0000100001 => 0
[4,4,4,4,1] => [4,4,4,1] => 11100010 => 00011101 => 0
[4,4,4,3,2] => [4,4,3,2] => 11010100 => 00101011 => 0
[4,4,4,3,1,1] => [4,4,3,1,1] => 110100110 => 001011001 => 0
[4,4,4,2,2,1] => [4,4,2,2,1] => 110011010 => 001100101 => 0
[4,4,3,3,3] => [4,3,3,3] => 10111000 => 01000111 => 0
[4,4,3,3,2,1] => [4,3,3,2,1] => 101101010 => 010010101 => 0
[4,4,3,2,2,2] => [4,3,2,2,2] => 101011100 => 010100011 => 0
[4,3,3,3,3,1] => [3,3,3,3,1] => 11110010 => 00001101 => 0
[4,3,3,3,2,2] => [3,3,3,2,2] => 11101100 => 00010011 => 0
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => 111010110 => 000101001 => 0
[4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => 1110011110 => 0001100001 => 0
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => 110111010 => 001000101 => 0
[4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => 1101101110 => 0010010001 => 0
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => 101111100 => 010000011 => 0
[4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => 10111011110 => 01000100001 => 0
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 111111010 => 000000101 => 0
[4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => 1111101110 => 0000010001 => 0
[4,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => 11110111110 => 00001000001 => 0
[3,3,3,3,3,2] => [3,3,3,3,2] => 11110100 => 00001011 => 0
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => 111100110 => 000011001 => 0
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => 111011010 => 000100101 => 0
[3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => 1110101110 => 0001010001 => 0
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => 110111100 => 001000011 => 0
[3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => 1101110110 => 0010001001 => 0
[3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => 1011111010 => 0100000101 => 0
[3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => 10111101110 => 01000010001 => 0
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => 111111100 => 000000011 => 0
[3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => 1111110110 => 0000001001 => 0
[2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,1] => 1111111010 => 0000000101 => 0
[6,5,4,3,2,1] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[5,5,4,3,2,1] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[6,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 001010101 => 0
[5,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 001010101 => 0
[4,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 001010101 => 0
[6,5,3,3,2,1] => [5,3,3,2,1] => 1001101010 => 0110010101 => 0
[5,5,3,3,2,1] => [5,3,3,2,1] => 1001101010 => 0110010101 => 0
[6,4,3,3,2,1] => [4,3,3,2,1] => 101101010 => 010010101 => 0
[5,4,3,3,2,1] => [4,3,3,2,1] => 101101010 => 010010101 => 0
[6,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 00010101 => 0
[6,5,4,2,2,1] => [5,4,2,2,1] => 1010011010 => 0101100101 => 0
[5,5,4,2,2,1] => [5,4,2,2,1] => 1010011010 => 0101100101 => 0
[6,4,4,2,2,1] => [4,4,2,2,1] => 110011010 => 001100101 => 0
[5,4,4,2,2,1] => [4,4,2,2,1] => 110011010 => 001100101 => 0
[6,5,3,2,2,1] => [5,3,2,2,1] => 1001011010 => 0110100101 => 0
[5,5,3,2,2,1] => [5,3,2,2,1] => 1001011010 => 0110100101 => 0
[6,4,3,2,2,1] => [4,3,2,2,1] => 101011010 => 010100101 => 0
[6,5,2,2,2,1] => [5,2,2,2,1] => 1000111010 => 0111000101 => 0
[6,5,4,3,1,1] => [5,4,3,1,1] => 1010100110 => 0101011001 => 0
[5,5,4,3,1,1] => [5,4,3,1,1] => 1010100110 => 0101011001 => 0
[6,4,4,3,1,1] => [4,4,3,1,1] => 110100110 => 001011001 => 0
[5,4,4,3,1,1] => [4,4,3,1,1] => 110100110 => 001011001 => 0
[6,5,3,3,1,1] => [5,3,3,1,1] => 1001100110 => 0110011001 => 0
[5,5,3,3,1,1] => [5,3,3,1,1] => 1001100110 => 0110011001 => 0
[6,4,3,3,1,1] => [4,3,3,1,1] => 101100110 => 010011001 => 0
[6,5,4,2,1,1] => [5,4,2,1,1] => 1010010110 => 0101101001 => 0
[5,5,4,2,1,1] => [5,4,2,1,1] => 1010010110 => 0101101001 => 0
[6,4,4,2,1,1] => [4,4,2,1,1] => 110010110 => 001101001 => 0
[6,5,3,2,1,1] => [5,3,2,1,1] => 1001010110 => 0110101001 => 0
[6,5,4,1,1,1] => [5,4,1,1,1] => 1010001110 => 0101110001 => 0
[6,5,4,3,2] => [5,4,3,2] => 101010100 => 010101011 => 0
[5,5,4,3,2] => [5,4,3,2] => 101010100 => 010101011 => 0
[6,4,4,3,2] => [4,4,3,2] => 11010100 => 00101011 => 0
[5,4,4,3,2] => [4,4,3,2] => 11010100 => 00101011 => 0
[6,5,3,3,2] => [5,3,3,2] => 100110100 => 011001011 => 0
[5,5,3,3,2] => [5,3,3,2] => 100110100 => 011001011 => 0
[6,4,3,3,2] => [4,3,3,2] => 10110100 => 01001011 => 0
[6,5,4,2,2] => [5,4,2,2] => 101001100 => 010110011 => 0
[5,5,4,2,2] => [5,4,2,2] => 101001100 => 010110011 => 0
[6,4,4,2,2] => [4,4,2,2] => 11001100 => 00110011 => 0
[6,5,3,2,2] => [5,3,2,2] => 100101100 => 011010011 => 0
[6,5,4,3,1] => [5,4,3,1] => 101010010 => 010101101 => 0
[5,5,4,3,1] => [5,4,3,1] => 101010010 => 010101101 => 0
[6,4,4,3,1] => [4,4,3,1] => 11010010 => 00101101 => 0
[6,5,3,3,1] => [5,3,3,1] => 100110010 => 011001101 => 0
[6,5,4,2,1] => [5,4,2,1] => 101001010 => 010110101 => 0
[6,5,4,3] => [5,4,3] => 10101000 => 01010111 => 0
[7,6,5,4,3,2,1] => [6,5,4,3,2,1] => 101010101010 => 010101010101 => 0
[6,6,5,4,3,2,1] => [6,5,4,3,2,1] => 101010101010 => 010101010101 => 0
[7,6,4,4,3,2,1] => [6,4,4,3,2,1] => 100110101010 => 011001010101 => 0
[6,6,4,4,3,2,1] => [6,4,4,3,2,1] => 100110101010 => 011001010101 => 0
[7,5,4,4,3,2,1] => [5,4,4,3,2,1] => 10110101010 => 01001010101 => 0
[6,5,4,4,3,2,1] => [5,4,4,3,2,1] => 10110101010 => 01001010101 => 0
[5,5,4,4,3,2,1] => [5,4,4,3,2,1] => 10110101010 => 01001010101 => 0
[7,4,4,4,3,2,1] => [4,4,4,3,2,1] => 1110101010 => 0001010101 => 0
[6,4,4,4,3,2,1] => [4,4,4,3,2,1] => 1110101010 => 0001010101 => 0
[5,4,4,4,3,2,1] => [4,4,4,3,2,1] => 1110101010 => 0001010101 => 0
[4,4,4,4,3,2,1] => [4,4,4,3,2,1] => 1110101010 => 0001010101 => 0
[6,6,5,3,3,2,1] => [6,5,3,3,2,1] => 101001101010 => 010110010101 => 0
[6,5,4,3,3,2,1] => [5,4,3,3,2,1] => 10101101010 => 01010010101 => 0
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => 111101010 => 000010101 => 0
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => 111101010 => 000010101 => 0
[6,6,5,4,2,2,1] => [6,5,4,2,2,1] => 101010011010 => 010101100101 => 0
[6,5,4,3,2,2,1] => [5,4,3,2,2,1] => 10101011010 => 01010100101 => 0
[5,5,4,3,2,2,1] => [5,4,3,2,2,1] => 10101011010 => 01010100101 => 0
[7,6,5,2,2,2,1] => [6,5,2,2,2,1] => 101000111010 => 010111000101 => 0
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => 11111010 => 00000101 => 0
[7,6,5,4,3,1,1] => [6,5,4,3,1,1] => 101010100110 => 010101011001 => 0
[6,6,5,4,3,1,1] => [6,5,4,3,1,1] => 101010100110 => 010101011001 => 0
[6,6,5,4,2,1,1] => [6,5,4,2,1,1] => 101010010110 => 010101101001 => 0
[4,4,4,4,2,1,1] => [4,4,4,2,1,1] => 1110010110 => 0001101001 => 0
[6,5,4,3,2,1,1] => [5,4,3,2,1,1] => 10101010110 => 01010101001 => 0
[5,5,4,3,2,1,1] => [5,4,3,2,1,1] => 10101010110 => 01010101001 => 0
[5,4,4,3,2,1,1] => [4,4,3,2,1,1] => 1101010110 => 0010101001 => 0
[7,6,5,4,1,1,1] => [6,5,4,1,1,1] => 101010001110 => 010101110001 => 0
[7,6,5,2,1,1,1] => [6,5,2,1,1,1] => 101000101110 => 010111010001 => 0
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => 100010101110 => 011101010001 => 0
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => 100001011110 => 011110100001 => 0
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => 100000111110 => 011111000001 => 0
[7,5,5,4,3,2] => [5,5,4,3,2] => 1101010100 => 0010101011 => 0
[6,5,5,4,3,2] => [5,5,4,3,2] => 1101010100 => 0010101011 => 0
[5,5,5,4,3,2] => [5,5,4,3,2] => 1101010100 => 0010101011 => 0
[6,5,4,4,3,2] => [5,4,4,3,2] => 1011010100 => 0100101011 => 0
[6,5,4,3,3,2] => [5,4,3,3,2] => 1010110100 => 0101001011 => 0
[5,4,3,3,3,2] => [4,3,3,3,2] => 101110100 => 010001011 => 0
[4,3,3,3,3,2] => [3,3,3,3,2] => 11110100 => 00001011 => 0
[6,5,4,3,2,2] => [5,4,3,2,2] => 1010101100 => 0101010011 => 0
[4,4,4,3,2,2] => [4,4,3,2,2] => 110101100 => 001010011 => 0
[5,4,3,2,2,2] => [4,3,2,2,2] => 101011100 => 010100011 => 0
[6,5,5,4,3,1] => [5,5,4,3,1] => 1101010010 => 0010101101 => 0
[4,4,4,4,3,1] => [4,4,4,3,1] => 111010010 => 000101101 => 0
[5,5,5,4,2,1] => [5,5,4,2,1] => 1101001010 => 0010110101 => 0
[4,4,4,4,2,1] => [4,4,4,2,1] => 111001010 => 000110101 => 0
[5,5,5,3,2,1] => [5,5,3,2,1] => 1100101010 => 0011010101 => 0
[7,5,4,3,2,1] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[7,4,4,3,2,1] => [4,4,3,2,1] => 110101010 => 001010101 => 0
[7,4,3,3,2,1] => [4,3,3,2,1] => 101101010 => 010010101 => 0
[7,3,3,3,2,1] => [3,3,3,2,1] => 11101010 => 00010101 => 0
[7,4,3,2,1,1] => [4,3,2,1,1] => 101010110 => 010101001 => 0
[6,5,5,4,3] => [5,5,4,3] => 110101000 => 001010111 => 0
[5,4,4,4,3] => [4,4,4,3] => 11101000 => 00010111 => 0
[5,4,3,3,3] => [4,3,3,3] => 10111000 => 01000111 => 0
[7,3,3,3,3] => [3,3,3,3] => 1111000 => 0000111 => 0
[4,4,4,4,2] => [4,4,4,2] => 11100100 => 00011011 => 0
[7,5,4,3,2] => [5,4,3,2] => 101010100 => 010101011 => 0
[7,5,4,3,1] => [5,4,3,1] => 101010010 => 010101101 => 0
[7,5,4,2,1] => [5,4,2,1] => 101001010 => 010110101 => 0
[7,6,5,4] => [6,5,4] => 101010000 => 010101111 => 0
[6,5,5,4] => [5,5,4] => 11010000 => 00101111 => 0
[7,6,5,3] => [6,5,3] => 101001000 => 010110111 => 0
[7,6,4,3] => [6,4,3] => 100101000 => 011010111 => 0
[7,5,4,3] => [5,4,3] => 10101000 => 01010111 => 0
[7,6,5,2] => [6,5,2] => 101000100 => 010111011 => 0
[7,6,5] => [6,5] => 10100000 => 01011111 => 0
[2,2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2,2] => 1111111100 => 0000000011 => 0
[3,3,3,3,3,3] => [3,3,3,3,3] => 11111000 => 00000111 => 0
[3,3,3,3,3,3,3,3] => [3,3,3,3,3,3,3] => 1111111000 => 0000000111 => 0
[3,3,3,3,3,3,1] => [3,3,3,3,3,1] => 111110010 => 000001101 => 0
[3,3,3,3,3,3,3] => [3,3,3,3,3,3] => 111111000 => 000000111 => 0
[3,3,3,3,3,2,2] => [3,3,3,3,2,2] => 111101100 => 000010011 => 0
[4,3,3,3,3,3] => [3,3,3,3,3] => 11111000 => 00000111 => 0
[4,4,4,4,4] => [4,4,4,4] => 11110000 => 00001111 => 0
[4,4,4,3,3,3] => [4,4,3,3,3] => 110111000 => 001000111 => 0
[4,4,4,4,4,4] => [4,4,4,4,4] => 111110000 => 000001111 => 0
[5,5,5,5] => [5,5,5] => 11100000 => 00011111 => 0
[6,6,6,6] => [6,6,6] => 111000000 => 000111111 => 0
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 00000011 => 0
[6,6,6] => [6,6] => 11000000 => 00111111 => 0
[7,6,6] => [6,6] => 11000000 => 00111111 => 0
[10,4,4] => [4,4] => 110000 => 001111 => 0
[10,10] => [10] => 10000000000 => 01111111111 => 0
[6,6,6,6,6] => [6,6,6,6] => 1111000000 => 0000111111 => 0
[11,7,3] => [7,3] => 100001000 => 011110111 => 0
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => 11111100 => 00000011 => 0
[9,6,3] => [6,3] => 10001000 => 01110111 => 0
[8,6,4,2] => [6,4,2] => 100100100 => 011011011 => 0
[8,6,4] => [6,4] => 10010000 => 01101111 => 0
[10,6,4] => [6,4] => 10010000 => 01101111 => 0
[8,7,6] => [7,6] => 101000000 => 010111111 => 0
[9,8,7] => [8,7] => 1010000000 => 0101111111 => 0
[5,5,5,5,5,5] => [5,5,5,5,5] => 1111100000 => 0000011111 => 0
[15,5,5] => [5,5] => 1100000 => 0011111 => 0
[7,7,7,7] => [7,7,7] => 1110000000 => 0001111111 => 0
[7,7,7] => [7,7] => 110000000 => 001111111 => 0
[8,6,5,4,3,2,1] => [6,5,4,3,2,1] => 101010101010 => 010101010101 => 0
[9,6,4] => [6,4] => 10010000 => 01101111 => 0
[10,7,3] => [7,3] => 100001000 => 011110111 => 0
[8,5,4,2] => [5,4,2] => 10100100 => 01011011 => 0
[9,6,5,3] => [6,5,3] => 101001000 => 010110111 => 0
[9,6,4,3] => [6,4,3] => 100101000 => 011010111 => 0
[9,7,4] => [7,4] => 100010000 => 011101111 => 0
[8,5,5,1] => [5,5,1] => 11000010 => 00111101 => 0
[9,5,5,1] => [5,5,1] => 11000010 => 00111101 => 0
[5,5,5,5,5] => [5,5,5,5] => 111100000 => 000011111 => 0
[9,9] => [9] => 1000000000 => 0111111111 => 0
[4,4,4,4,4,4,4] => [4,4,4,4,4,4] => 1111110000 => 0000001111 => 0
[8,5,4,3,2,1] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[6,6,6,4,3,2,1] => [6,6,4,3,2,1] => 110010101010 => 001101010101 => 0
[5,4,4,4,4,2,1] => [4,4,4,4,2,1] => 1111001010 => 0000110101 => 0
[6,5,5,5] => [5,5,5] => 11100000 => 00011111 => 0
[5,4,4,4,4] => [4,4,4,4] => 11110000 => 00001111 => 0
[7,6,6,5,4,3,2] => [6,6,5,4,3,2] => 110101010100 => 001010101011 => 0
[7,6,6,5,4,3,1] => [6,6,5,4,3,1] => 110101010010 => 001010101101 => 0
[8,6,6,5,4,3,2] => [6,6,5,4,3,2] => 110101010100 => 001010101011 => 0
[8,7,6,5] => [7,6,5] => 1010100000 => 0101011111 => 0
[8,7,5] => [7,5] => 100100000 => 011011111 => 0
[4,4,4,4,4,1] => [4,4,4,4,1] => 111100010 => 000011101 => 0
[5,5,5,5,1] => [5,5,5,1] => 111000010 => 000111101 => 0
[6,6,6,1] => [6,6,1] => 110000010 => 001111101 => 0
[8,5,4,3,2,1,1] => [5,4,3,2,1,1] => 10101010110 => 01010101001 => 0
[7,6,5,4,3,2,2] => [6,5,4,3,2,2] => 101010101100 => 010101010011 => 0
search for individual values
searching the database for the individual values of this statistic
Description
The number of leading ones in a binary word.
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
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
Map
first row removal
Description
Removes the first entry of an integer partition
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