Identifier
Mp00094:
Integer compositions
—to binary word⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Images
[1] => 1 => 1 => 1
[1,1] => 11 => 11 => 11
[2] => 10 => 01 => 10
[1,1,1] => 111 => 111 => 111
[1,2] => 110 => 011 => 101
[2,1] => 101 => 101 => 110
[3] => 100 => 001 => 100
[1,1,1,1] => 1111 => 1111 => 1111
[1,1,2] => 1110 => 0111 => 1011
[1,2,1] => 1101 => 1011 => 1101
[1,3] => 1100 => 0011 => 1001
[2,1,1] => 1011 => 1101 => 1110
[2,2] => 1010 => 0101 => 1010
[3,1] => 1001 => 1001 => 1100
[4] => 1000 => 0001 => 1000
[1,1,1,1,1] => 11111 => 11111 => 11111
[1,1,1,2] => 11110 => 01111 => 10111
[1,1,2,1] => 11101 => 10111 => 11011
[1,1,3] => 11100 => 00111 => 10011
[1,2,1,1] => 11011 => 11011 => 11101
[1,2,2] => 11010 => 01011 => 10101
[1,3,1] => 11001 => 10011 => 11001
[1,4] => 11000 => 00011 => 10001
[2,1,1,1] => 10111 => 11101 => 11110
[2,1,2] => 10110 => 01101 => 10110
[2,2,1] => 10101 => 10101 => 11010
[2,3] => 10100 => 00101 => 10010
[3,1,1] => 10011 => 11001 => 11100
[3,2] => 10010 => 01001 => 10100
[4,1] => 10001 => 10001 => 11000
[5] => 10000 => 00001 => 10000
[1,1,1,1,1,1] => 111111 => 111111 => 111111
[1,1,1,1,2] => 111110 => 011111 => 101111
[1,1,1,2,1] => 111101 => 101111 => 110111
[1,1,1,3] => 111100 => 001111 => 100111
[1,1,2,1,1] => 111011 => 110111 => 111011
[1,1,2,2] => 111010 => 010111 => 101011
[1,1,3,1] => 111001 => 100111 => 110011
[1,1,4] => 111000 => 000111 => 100011
[1,2,1,1,1] => 110111 => 111011 => 111101
[1,2,1,2] => 110110 => 011011 => 101101
[1,2,2,1] => 110101 => 101011 => 110101
[1,2,3] => 110100 => 001011 => 100101
[1,3,1,1] => 110011 => 110011 => 111001
[1,3,2] => 110010 => 010011 => 101001
[1,4,1] => 110001 => 100011 => 110001
[1,5] => 110000 => 000011 => 100001
[2,1,1,1,1] => 101111 => 111101 => 111110
[2,1,1,2] => 101110 => 011101 => 101110
[2,1,2,1] => 101101 => 101101 => 110110
[2,1,3] => 101100 => 001101 => 100110
[2,2,1,1] => 101011 => 110101 => 111010
[2,2,2] => 101010 => 010101 => 101010
[2,3,1] => 101001 => 100101 => 110010
[2,4] => 101000 => 000101 => 100010
[3,1,1,1] => 100111 => 111001 => 111100
[3,1,2] => 100110 => 011001 => 101100
[3,2,1] => 100101 => 101001 => 110100
[3,3] => 100100 => 001001 => 100100
[4,1,1] => 100011 => 110001 => 111000
[4,2] => 100010 => 010001 => 101000
[5,1] => 100001 => 100001 => 110000
[6] => 100000 => 000001 => 100000
[1,1,1,1,1,1,1] => 1111111 => 1111111 => 1111111
[1,1,1,1,1,2] => 1111110 => 0111111 => 1011111
[1,1,1,1,2,1] => 1111101 => 1011111 => 1101111
[1,1,1,1,3] => 1111100 => 0011111 => 1001111
[1,1,1,2,1,1] => 1111011 => 1101111 => 1110111
[1,1,1,2,2] => 1111010 => 0101111 => 1010111
[1,1,1,3,1] => 1111001 => 1001111 => 1100111
[1,1,1,4] => 1111000 => 0001111 => 1000111
[1,1,2,1,1,1] => 1110111 => 1110111 => 1111011
[1,1,2,1,2] => 1110110 => 0110111 => 1011011
[1,1,2,2,1] => 1110101 => 1010111 => 1101011
[1,1,2,3] => 1110100 => 0010111 => 1001011
[1,1,3,1,1] => 1110011 => 1100111 => 1110011
[1,1,3,2] => 1110010 => 0100111 => 1010011
[1,1,4,1] => 1110001 => 1000111 => 1100011
[1,1,5] => 1110000 => 0000111 => 1000011
[1,2,1,1,1,1] => 1101111 => 1111011 => 1111101
[1,2,1,1,2] => 1101110 => 0111011 => 1011101
[1,2,1,2,1] => 1101101 => 1011011 => 1101101
[1,2,1,3] => 1101100 => 0011011 => 1001101
[1,2,2,1,1] => 1101011 => 1101011 => 1110101
[1,2,2,2] => 1101010 => 0101011 => 1010101
[1,2,3,1] => 1101001 => 1001011 => 1100101
[1,2,4] => 1101000 => 0001011 => 1000101
[1,3,1,1,1] => 1100111 => 1110011 => 1111001
[1,3,1,2] => 1100110 => 0110011 => 1011001
[1,3,2,1] => 1100101 => 1010011 => 1101001
[1,3,3] => 1100100 => 0010011 => 1001001
[1,4,1,1] => 1100011 => 1100011 => 1110001
[1,4,2] => 1100010 => 0100011 => 1010001
[1,5,1] => 1100001 => 1000011 => 1100001
[1,6] => 1100000 => 0000011 => 1000001
[2,1,1,1,1,1] => 1011111 => 1111101 => 1111110
[2,1,1,1,2] => 1011110 => 0111101 => 1011110
[2,1,1,2,1] => 1011101 => 1011101 => 1101110
[2,1,1,3] => 1011100 => 0011101 => 1001110
[2,1,2,1,1] => 1011011 => 1101101 => 1110110
[2,1,2,2] => 1011010 => 0101101 => 1010110
>>> Load all 1346 entries. <<<
[2,1,3,1] => 1011001 => 1001101 => 1100110
[2,1,4] => 1011000 => 0001101 => 1000110
[2,2,1,1,1] => 1010111 => 1110101 => 1111010
[2,2,1,2] => 1010110 => 0110101 => 1011010
[2,2,2,1] => 1010101 => 1010101 => 1101010
[2,2,3] => 1010100 => 0010101 => 1001010
[2,3,1,1] => 1010011 => 1100101 => 1110010
[2,3,2] => 1010010 => 0100101 => 1010010
[2,4,1] => 1010001 => 1000101 => 1100010
[2,5] => 1010000 => 0000101 => 1000010
[3,1,1,1,1] => 1001111 => 1111001 => 1111100
[3,1,1,2] => 1001110 => 0111001 => 1011100
[3,1,2,1] => 1001101 => 1011001 => 1101100
[3,1,3] => 1001100 => 0011001 => 1001100
[3,2,1,1] => 1001011 => 1101001 => 1110100
[3,2,2] => 1001010 => 0101001 => 1010100
[3,3,1] => 1001001 => 1001001 => 1100100
[3,4] => 1001000 => 0001001 => 1000100
[4,1,1,1] => 1000111 => 1110001 => 1111000
[4,1,2] => 1000110 => 0110001 => 1011000
[4,2,1] => 1000101 => 1010001 => 1101000
[4,3] => 1000100 => 0010001 => 1001000
[5,1,1] => 1000011 => 1100001 => 1110000
[5,2] => 1000010 => 0100001 => 1010000
[6,1] => 1000001 => 1000001 => 1100000
[7] => 1000000 => 0000001 => 1000000
[1,1,1,1,1,1,1,1] => 11111111 => 11111111 => 11111111
[1,1,1,1,1,1,2] => 11111110 => 01111111 => 10111111
[1,1,1,1,1,2,1] => 11111101 => 10111111 => 11011111
[1,1,1,1,1,3] => 11111100 => 00111111 => 10011111
[1,1,1,1,2,1,1] => 11111011 => 11011111 => 11101111
[1,1,1,1,2,2] => 11111010 => 01011111 => 10101111
[1,1,1,1,3,1] => 11111001 => 10011111 => 11001111
[1,1,1,1,4] => 11111000 => 00011111 => 10001111
[1,1,1,2,1,1,1] => 11110111 => 11101111 => 11110111
[1,1,1,2,1,2] => 11110110 => 01101111 => 10110111
[1,1,1,2,2,1] => 11110101 => 10101111 => 11010111
[1,1,1,2,3] => 11110100 => 00101111 => 10010111
[1,1,1,3,1,1] => 11110011 => 11001111 => 11100111
[1,1,1,3,2] => 11110010 => 01001111 => 10100111
[1,1,1,4,1] => 11110001 => 10001111 => 11000111
[1,1,1,5] => 11110000 => 00001111 => 10000111
[1,1,2,1,1,1,1] => 11101111 => 11110111 => 11111011
[1,1,2,1,1,2] => 11101110 => 01110111 => 10111011
[1,1,2,1,2,1] => 11101101 => 10110111 => 11011011
[1,1,2,1,3] => 11101100 => 00110111 => 10011011
[1,1,2,2,1,1] => 11101011 => 11010111 => 11101011
[1,1,2,2,2] => 11101010 => 01010111 => 10101011
[1,1,2,3,1] => 11101001 => 10010111 => 11001011
[1,1,2,4] => 11101000 => 00010111 => 10001011
[1,1,3,1,1,1] => 11100111 => 11100111 => 11110011
[1,1,3,1,2] => 11100110 => 01100111 => 10110011
[1,1,3,2,1] => 11100101 => 10100111 => 11010011
[1,1,3,3] => 11100100 => 00100111 => 10010011
[1,1,4,1,1] => 11100011 => 11000111 => 11100011
[1,1,4,2] => 11100010 => 01000111 => 10100011
[1,1,5,1] => 11100001 => 10000111 => 11000011
[1,1,6] => 11100000 => 00000111 => 10000011
[1,2,1,1,1,1,1] => 11011111 => 11111011 => 11111101
[1,2,1,1,1,2] => 11011110 => 01111011 => 10111101
[1,2,1,1,2,1] => 11011101 => 10111011 => 11011101
[1,2,1,1,3] => 11011100 => 00111011 => 10011101
[1,2,1,2,1,1] => 11011011 => 11011011 => 11101101
[1,2,1,2,2] => 11011010 => 01011011 => 10101101
[1,2,1,3,1] => 11011001 => 10011011 => 11001101
[1,2,1,4] => 11011000 => 00011011 => 10001101
[1,2,2,1,1,1] => 11010111 => 11101011 => 11110101
[1,2,2,1,2] => 11010110 => 01101011 => 10110101
[1,2,2,2,1] => 11010101 => 10101011 => 11010101
[1,2,2,3] => 11010100 => 00101011 => 10010101
[1,2,3,1,1] => 11010011 => 11001011 => 11100101
[1,2,3,2] => 11010010 => 01001011 => 10100101
[1,2,4,1] => 11010001 => 10001011 => 11000101
[1,2,5] => 11010000 => 00001011 => 10000101
[1,3,1,1,1,1] => 11001111 => 11110011 => 11111001
[1,3,1,1,2] => 11001110 => 01110011 => 10111001
[1,3,1,2,1] => 11001101 => 10110011 => 11011001
[1,3,1,3] => 11001100 => 00110011 => 10011001
[1,3,2,1,1] => 11001011 => 11010011 => 11101001
[1,3,2,2] => 11001010 => 01010011 => 10101001
[1,3,3,1] => 11001001 => 10010011 => 11001001
[1,3,4] => 11001000 => 00010011 => 10001001
[1,4,1,1,1] => 11000111 => 11100011 => 11110001
[1,4,1,2] => 11000110 => 01100011 => 10110001
[1,4,2,1] => 11000101 => 10100011 => 11010001
[1,4,3] => 11000100 => 00100011 => 10010001
[1,5,1,1] => 11000011 => 11000011 => 11100001
[1,5,2] => 11000010 => 01000011 => 10100001
[1,6,1] => 11000001 => 10000011 => 11000001
[1,7] => 11000000 => 00000011 => 10000001
[2,1,1,1,1,1,1] => 10111111 => 11111101 => 11111110
[2,1,1,1,1,2] => 10111110 => 01111101 => 10111110
[2,1,1,1,2,1] => 10111101 => 10111101 => 11011110
[2,1,1,1,3] => 10111100 => 00111101 => 10011110
[2,1,1,2,1,1] => 10111011 => 11011101 => 11101110
[2,1,1,2,2] => 10111010 => 01011101 => 10101110
[2,1,1,3,1] => 10111001 => 10011101 => 11001110
[2,1,1,4] => 10111000 => 00011101 => 10001110
[2,1,2,1,1,1] => 10110111 => 11101101 => 11110110
[2,1,2,1,2] => 10110110 => 01101101 => 10110110
[2,1,2,2,1] => 10110101 => 10101101 => 11010110
[2,1,2,3] => 10110100 => 00101101 => 10010110
[2,1,3,1,1] => 10110011 => 11001101 => 11100110
[2,1,3,2] => 10110010 => 01001101 => 10100110
[2,1,4,1] => 10110001 => 10001101 => 11000110
[2,1,5] => 10110000 => 00001101 => 10000110
[2,2,1,1,1,1] => 10101111 => 11110101 => 11111010
[2,2,1,1,2] => 10101110 => 01110101 => 10111010
[2,2,1,2,1] => 10101101 => 10110101 => 11011010
[2,2,1,3] => 10101100 => 00110101 => 10011010
[2,2,2,1,1] => 10101011 => 11010101 => 11101010
[2,2,2,2] => 10101010 => 01010101 => 10101010
[2,2,3,1] => 10101001 => 10010101 => 11001010
[2,2,4] => 10101000 => 00010101 => 10001010
[2,3,1,1,1] => 10100111 => 11100101 => 11110010
[2,3,1,2] => 10100110 => 01100101 => 10110010
[2,3,2,1] => 10100101 => 10100101 => 11010010
[2,3,3] => 10100100 => 00100101 => 10010010
[2,4,1,1] => 10100011 => 11000101 => 11100010
[2,4,2] => 10100010 => 01000101 => 10100010
[2,5,1] => 10100001 => 10000101 => 11000010
[2,6] => 10100000 => 00000101 => 10000010
[3,1,1,1,1,1] => 10011111 => 11111001 => 11111100
[3,1,1,1,2] => 10011110 => 01111001 => 10111100
[3,1,1,2,1] => 10011101 => 10111001 => 11011100
[3,1,1,3] => 10011100 => 00111001 => 10011100
[3,1,2,1,1] => 10011011 => 11011001 => 11101100
[3,1,2,2] => 10011010 => 01011001 => 10101100
[3,1,3,1] => 10011001 => 10011001 => 11001100
[3,1,4] => 10011000 => 00011001 => 10001100
[3,2,1,1,1] => 10010111 => 11101001 => 11110100
[3,2,1,2] => 10010110 => 01101001 => 10110100
[3,2,2,1] => 10010101 => 10101001 => 11010100
[3,2,3] => 10010100 => 00101001 => 10010100
[3,3,1,1] => 10010011 => 11001001 => 11100100
[3,3,2] => 10010010 => 01001001 => 10100100
[3,4,1] => 10010001 => 10001001 => 11000100
[3,5] => 10010000 => 00001001 => 10000100
[4,1,1,1,1] => 10001111 => 11110001 => 11111000
[4,1,1,2] => 10001110 => 01110001 => 10111000
[4,1,2,1] => 10001101 => 10110001 => 11011000
[4,1,3] => 10001100 => 00110001 => 10011000
[4,2,1,1] => 10001011 => 11010001 => 11101000
[4,2,2] => 10001010 => 01010001 => 10101000
[4,3,1] => 10001001 => 10010001 => 11001000
[4,4] => 10001000 => 00010001 => 10001000
[5,1,1,1] => 10000111 => 11100001 => 11110000
[5,1,2] => 10000110 => 01100001 => 10110000
[5,2,1] => 10000101 => 10100001 => 11010000
[5,3] => 10000100 => 00100001 => 10010000
[6,1,1] => 10000011 => 11000001 => 11100000
[6,2] => 10000010 => 01000001 => 10100000
[7,1] => 10000001 => 10000001 => 11000000
[8] => 10000000 => 00000001 => 10000000
[1,1,1,1,1,1,1,1,1] => 111111111 => 111111111 => 111111111
[1,1,1,1,1,1,1,2] => 111111110 => 011111111 => 101111111
[1,1,1,1,1,1,2,1] => 111111101 => 101111111 => 110111111
[1,1,1,1,1,1,3] => 111111100 => 001111111 => 100111111
[1,1,1,1,1,2,1,1] => 111111011 => 110111111 => 111011111
[1,1,1,1,1,2,2] => 111111010 => 010111111 => 101011111
[1,1,1,1,1,3,1] => 111111001 => 100111111 => 110011111
[1,1,1,1,1,4] => 111111000 => 000111111 => 100011111
[1,1,1,1,2,1,1,1] => 111110111 => 111011111 => 111101111
[1,1,1,1,2,1,2] => 111110110 => 011011111 => 101101111
[1,1,1,1,2,2,1] => 111110101 => 101011111 => 110101111
[1,1,1,1,2,3] => 111110100 => 001011111 => 100101111
[1,1,1,1,3,1,1] => 111110011 => 110011111 => 111001111
[1,1,1,1,3,2] => 111110010 => 010011111 => 101001111
[1,1,1,1,4,1] => 111110001 => 100011111 => 110001111
[1,1,1,1,5] => 111110000 => 000011111 => 100001111
[1,1,1,2,1,1,1,1] => 111101111 => 111101111 => 111110111
[1,1,1,2,1,1,2] => 111101110 => 011101111 => 101110111
[1,1,1,2,1,2,1] => 111101101 => 101101111 => 110110111
[1,1,1,2,1,3] => 111101100 => 001101111 => 100110111
[1,1,1,2,2,1,1] => 111101011 => 110101111 => 111010111
[1,1,1,2,2,2] => 111101010 => 010101111 => 101010111
[1,1,1,2,3,1] => 111101001 => 100101111 => 110010111
[1,1,1,2,4] => 111101000 => 000101111 => 100010111
[1,1,1,3,1,1,1] => 111100111 => 111001111 => 111100111
[1,1,1,3,1,2] => 111100110 => 011001111 => 101100111
[1,1,1,3,2,1] => 111100101 => 101001111 => 110100111
[1,1,1,3,3] => 111100100 => 001001111 => 100100111
[1,1,1,4,1,1] => 111100011 => 110001111 => 111000111
[1,1,1,4,2] => 111100010 => 010001111 => 101000111
[1,1,1,5,1] => 111100001 => 100001111 => 110000111
[1,1,1,6] => 111100000 => 000001111 => 100000111
[1,1,2,1,1,1,1,1] => 111011111 => 111110111 => 111111011
[1,1,2,1,1,1,2] => 111011110 => 011110111 => 101111011
[1,1,2,1,1,2,1] => 111011101 => 101110111 => 110111011
[1,1,2,1,1,3] => 111011100 => 001110111 => 100111011
[1,1,2,1,2,1,1] => 111011011 => 110110111 => 111011011
[1,1,2,1,2,2] => 111011010 => 010110111 => 101011011
[1,1,2,1,3,1] => 111011001 => 100110111 => 110011011
[1,1,2,1,4] => 111011000 => 000110111 => 100011011
[1,1,2,2,1,1,1] => 111010111 => 111010111 => 111101011
[1,1,2,2,1,2] => 111010110 => 011010111 => 101101011
[1,1,2,2,2,1] => 111010101 => 101010111 => 110101011
[1,1,2,2,3] => 111010100 => 001010111 => 100101011
[1,1,2,3,1,1] => 111010011 => 110010111 => 111001011
[1,1,2,3,2] => 111010010 => 010010111 => 101001011
[1,1,2,4,1] => 111010001 => 100010111 => 110001011
[1,1,2,5] => 111010000 => 000010111 => 100001011
[1,1,3,1,1,1,1] => 111001111 => 111100111 => 111110011
[1,1,3,1,1,2] => 111001110 => 011100111 => 101110011
[1,1,3,1,2,1] => 111001101 => 101100111 => 110110011
[1,1,3,1,3] => 111001100 => 001100111 => 100110011
[1,1,3,2,1,1] => 111001011 => 110100111 => 111010011
[1,1,3,2,2] => 111001010 => 010100111 => 101010011
[1,1,3,3,1] => 111001001 => 100100111 => 110010011
[1,1,3,4] => 111001000 => 000100111 => 100010011
[1,1,4,1,1,1] => 111000111 => 111000111 => 111100011
[1,1,4,1,2] => 111000110 => 011000111 => 101100011
[1,1,4,2,1] => 111000101 => 101000111 => 110100011
[1,1,4,3] => 111000100 => 001000111 => 100100011
[1,1,5,1,1] => 111000011 => 110000111 => 111000011
[1,1,5,2] => 111000010 => 010000111 => 101000011
[1,1,6,1] => 111000001 => 100000111 => 110000011
[1,1,7] => 111000000 => 000000111 => 100000011
[1,2,1,1,1,1,1,1] => 110111111 => 111111011 => 111111101
[1,2,1,1,1,1,2] => 110111110 => 011111011 => 101111101
[1,2,1,1,1,2,1] => 110111101 => 101111011 => 110111101
[1,2,1,1,1,3] => 110111100 => 001111011 => 100111101
[1,2,1,1,2,1,1] => 110111011 => 110111011 => 111011101
[1,2,1,1,2,2] => 110111010 => 010111011 => 101011101
[1,2,1,1,3,1] => 110111001 => 100111011 => 110011101
[1,2,1,1,4] => 110111000 => 000111011 => 100011101
[1,2,1,2,1,1,1] => 110110111 => 111011011 => 111101101
[1,2,1,2,1,2] => 110110110 => 011011011 => 101101101
[1,2,1,2,2,1] => 110110101 => 101011011 => 110101101
[1,2,1,2,3] => 110110100 => 001011011 => 100101101
[1,2,1,3,1,1] => 110110011 => 110011011 => 111001101
[1,2,1,3,2] => 110110010 => 010011011 => 101001101
[1,2,1,4,1] => 110110001 => 100011011 => 110001101
[1,2,1,5] => 110110000 => 000011011 => 100001101
[1,2,2,1,1,1,1] => 110101111 => 111101011 => 111110101
[1,2,2,1,1,2] => 110101110 => 011101011 => 101110101
[1,2,2,1,2,1] => 110101101 => 101101011 => 110110101
[1,2,2,1,3] => 110101100 => 001101011 => 100110101
[1,2,2,2,1,1] => 110101011 => 110101011 => 111010101
[1,2,2,2,2] => 110101010 => 010101011 => 101010101
[1,2,2,3,1] => 110101001 => 100101011 => 110010101
[1,2,2,4] => 110101000 => 000101011 => 100010101
[1,2,3,1,1,1] => 110100111 => 111001011 => 111100101
[1,2,3,1,2] => 110100110 => 011001011 => 101100101
[1,2,3,2,1] => 110100101 => 101001011 => 110100101
[1,2,3,3] => 110100100 => 001001011 => 100100101
[1,2,4,1,1] => 110100011 => 110001011 => 111000101
[1,2,4,2] => 110100010 => 010001011 => 101000101
[1,2,5,1] => 110100001 => 100001011 => 110000101
[1,2,6] => 110100000 => 000001011 => 100000101
[1,3,1,1,1,1,1] => 110011111 => 111110011 => 111111001
[1,3,1,1,1,2] => 110011110 => 011110011 => 101111001
[1,3,1,1,2,1] => 110011101 => 101110011 => 110111001
[1,3,1,1,3] => 110011100 => 001110011 => 100111001
[1,3,1,2,1,1] => 110011011 => 110110011 => 111011001
[1,3,1,2,2] => 110011010 => 010110011 => 101011001
[1,3,1,3,1] => 110011001 => 100110011 => 110011001
[1,3,1,4] => 110011000 => 000110011 => 100011001
[1,3,2,1,1,1] => 110010111 => 111010011 => 111101001
[1,3,2,1,2] => 110010110 => 011010011 => 101101001
[1,3,2,2,1] => 110010101 => 101010011 => 110101001
[1,3,2,3] => 110010100 => 001010011 => 100101001
[1,3,3,1,1] => 110010011 => 110010011 => 111001001
[1,3,3,2] => 110010010 => 010010011 => 101001001
[1,3,4,1] => 110010001 => 100010011 => 110001001
[1,3,5] => 110010000 => 000010011 => 100001001
[1,4,1,1,1,1] => 110001111 => 111100011 => 111110001
[1,4,1,1,2] => 110001110 => 011100011 => 101110001
[1,4,1,2,1] => 110001101 => 101100011 => 110110001
[1,4,1,3] => 110001100 => 001100011 => 100110001
[1,4,2,1,1] => 110001011 => 110100011 => 111010001
[1,4,2,2] => 110001010 => 010100011 => 101010001
[1,4,3,1] => 110001001 => 100100011 => 110010001
[1,4,4] => 110001000 => 000100011 => 100010001
[1,5,1,1,1] => 110000111 => 111000011 => 111100001
[1,5,1,2] => 110000110 => 011000011 => 101100001
[1,5,2,1] => 110000101 => 101000011 => 110100001
[1,5,3] => 110000100 => 001000011 => 100100001
[1,6,1,1] => 110000011 => 110000011 => 111000001
[1,6,2] => 110000010 => 010000011 => 101000001
[1,7,1] => 110000001 => 100000011 => 110000001
[1,8] => 110000000 => 000000011 => 100000001
[2,1,1,1,1,1,1,1] => 101111111 => 111111101 => 111111110
[2,1,1,1,1,1,2] => 101111110 => 011111101 => 101111110
[2,1,1,1,1,2,1] => 101111101 => 101111101 => 110111110
[2,1,1,1,1,3] => 101111100 => 001111101 => 100111110
[2,1,1,1,2,1,1] => 101111011 => 110111101 => 111011110
[2,1,1,1,2,2] => 101111010 => 010111101 => 101011110
[2,1,1,1,3,1] => 101111001 => 100111101 => 110011110
[2,1,1,1,4] => 101111000 => 000111101 => 100011110
[2,1,1,2,1,1,1] => 101110111 => 111011101 => 111101110
[2,1,1,2,1,2] => 101110110 => 011011101 => 101101110
[2,1,1,2,2,1] => 101110101 => 101011101 => 110101110
[2,1,1,2,3] => 101110100 => 001011101 => 100101110
[2,1,1,3,1,1] => 101110011 => 110011101 => 111001110
[2,1,1,3,2] => 101110010 => 010011101 => 101001110
[2,1,1,4,1] => 101110001 => 100011101 => 110001110
[2,1,1,5] => 101110000 => 000011101 => 100001110
[2,1,2,1,1,1,1] => 101101111 => 111101101 => 111110110
[2,1,2,1,1,2] => 101101110 => 011101101 => 101110110
[2,1,2,1,2,1] => 101101101 => 101101101 => 110110110
[2,1,2,1,3] => 101101100 => 001101101 => 100110110
[2,1,2,2,1,1] => 101101011 => 110101101 => 111010110
[2,1,2,2,2] => 101101010 => 010101101 => 101010110
[2,1,2,3,1] => 101101001 => 100101101 => 110010110
[2,1,2,4] => 101101000 => 000101101 => 100010110
[2,1,3,1,1,1] => 101100111 => 111001101 => 111100110
[2,1,3,1,2] => 101100110 => 011001101 => 101100110
[2,1,3,2,1] => 101100101 => 101001101 => 110100110
[2,1,3,3] => 101100100 => 001001101 => 100100110
[2,1,4,1,1] => 101100011 => 110001101 => 111000110
[2,1,4,2] => 101100010 => 010001101 => 101000110
[2,1,5,1] => 101100001 => 100001101 => 110000110
[2,1,6] => 101100000 => 000001101 => 100000110
[2,2,1,1,1,1,1] => 101011111 => 111110101 => 111111010
[2,2,1,1,1,2] => 101011110 => 011110101 => 101111010
[2,2,1,1,2,1] => 101011101 => 101110101 => 110111010
[2,2,1,1,3] => 101011100 => 001110101 => 100111010
[2,2,1,2,1,1] => 101011011 => 110110101 => 111011010
[2,2,1,2,2] => 101011010 => 010110101 => 101011010
[2,2,1,3,1] => 101011001 => 100110101 => 110011010
[2,2,1,4] => 101011000 => 000110101 => 100011010
[2,2,2,1,1,1] => 101010111 => 111010101 => 111101010
[2,2,2,1,2] => 101010110 => 011010101 => 101101010
[2,2,2,2,1] => 101010101 => 101010101 => 110101010
[2,2,2,3] => 101010100 => 001010101 => 100101010
[2,2,3,1,1] => 101010011 => 110010101 => 111001010
[2,2,3,2] => 101010010 => 010010101 => 101001010
[2,2,4,1] => 101010001 => 100010101 => 110001010
[2,2,5] => 101010000 => 000010101 => 100001010
[2,3,1,1,1,1] => 101001111 => 111100101 => 111110010
[2,3,1,1,2] => 101001110 => 011100101 => 101110010
[2,3,1,2,1] => 101001101 => 101100101 => 110110010
[2,3,1,3] => 101001100 => 001100101 => 100110010
[2,3,2,1,1] => 101001011 => 110100101 => 111010010
[2,3,2,2] => 101001010 => 010100101 => 101010010
[2,3,3,1] => 101001001 => 100100101 => 110010010
[2,3,4] => 101001000 => 000100101 => 100010010
[2,4,1,1,1] => 101000111 => 111000101 => 111100010
[2,4,1,2] => 101000110 => 011000101 => 101100010
[2,4,2,1] => 101000101 => 101000101 => 110100010
[2,4,3] => 101000100 => 001000101 => 100100010
[2,5,1,1] => 101000011 => 110000101 => 111000010
[2,5,2] => 101000010 => 010000101 => 101000010
[2,6,1] => 101000001 => 100000101 => 110000010
[2,7] => 101000000 => 000000101 => 100000010
[3,1,1,1,1,1,1] => 100111111 => 111111001 => 111111100
[3,1,1,1,1,2] => 100111110 => 011111001 => 101111100
[3,1,1,1,2,1] => 100111101 => 101111001 => 110111100
[3,1,1,1,3] => 100111100 => 001111001 => 100111100
[3,1,1,2,1,1] => 100111011 => 110111001 => 111011100
[3,1,1,2,2] => 100111010 => 010111001 => 101011100
[3,1,1,3,1] => 100111001 => 100111001 => 110011100
[3,1,1,4] => 100111000 => 000111001 => 100011100
[3,1,2,1,1,1] => 100110111 => 111011001 => 111101100
[3,1,2,1,2] => 100110110 => 011011001 => 101101100
[3,1,2,2,1] => 100110101 => 101011001 => 110101100
[3,1,2,3] => 100110100 => 001011001 => 100101100
[3,1,3,1,1] => 100110011 => 110011001 => 111001100
[3,1,3,2] => 100110010 => 010011001 => 101001100
[3,1,4,1] => 100110001 => 100011001 => 110001100
[3,1,5] => 100110000 => 000011001 => 100001100
[3,2,1,1,1,1] => 100101111 => 111101001 => 111110100
[3,2,1,1,2] => 100101110 => 011101001 => 101110100
[3,2,1,2,1] => 100101101 => 101101001 => 110110100
[3,2,1,3] => 100101100 => 001101001 => 100110100
[3,2,2,1,1] => 100101011 => 110101001 => 111010100
[3,2,2,2] => 100101010 => 010101001 => 101010100
[3,2,3,1] => 100101001 => 100101001 => 110010100
[3,2,4] => 100101000 => 000101001 => 100010100
[3,3,1,1,1] => 100100111 => 111001001 => 111100100
[3,3,1,2] => 100100110 => 011001001 => 101100100
[3,3,2,1] => 100100101 => 101001001 => 110100100
[3,3,3] => 100100100 => 001001001 => 100100100
[3,4,1,1] => 100100011 => 110001001 => 111000100
[3,4,2] => 100100010 => 010001001 => 101000100
[3,5,1] => 100100001 => 100001001 => 110000100
[3,6] => 100100000 => 000001001 => 100000100
[4,1,1,1,1,1] => 100011111 => 111110001 => 111111000
[4,1,1,1,2] => 100011110 => 011110001 => 101111000
[4,1,1,2,1] => 100011101 => 101110001 => 110111000
[4,1,1,3] => 100011100 => 001110001 => 100111000
[4,1,2,1,1] => 100011011 => 110110001 => 111011000
[4,1,2,2] => 100011010 => 010110001 => 101011000
[4,1,3,1] => 100011001 => 100110001 => 110011000
[4,1,4] => 100011000 => 000110001 => 100011000
[4,2,1,1,1] => 100010111 => 111010001 => 111101000
[4,2,1,2] => 100010110 => 011010001 => 101101000
[4,2,2,1] => 100010101 => 101010001 => 110101000
[4,2,3] => 100010100 => 001010001 => 100101000
[4,3,1,1] => 100010011 => 110010001 => 111001000
[4,3,2] => 100010010 => 010010001 => 101001000
[4,4,1] => 100010001 => 100010001 => 110001000
[4,5] => 100010000 => 000010001 => 100001000
[5,1,1,1,1] => 100001111 => 111100001 => 111110000
[5,1,1,2] => 100001110 => 011100001 => 101110000
[5,1,2,1] => 100001101 => 101100001 => 110110000
[5,1,3] => 100001100 => 001100001 => 100110000
[5,2,1,1] => 100001011 => 110100001 => 111010000
[5,2,2] => 100001010 => 010100001 => 101010000
[5,3,1] => 100001001 => 100100001 => 110010000
[5,4] => 100001000 => 000100001 => 100010000
[6,1,1,1] => 100000111 => 111000001 => 111100000
[6,1,2] => 100000110 => 011000001 => 101100000
[6,2,1] => 100000101 => 101000001 => 110100000
[6,3] => 100000100 => 001000001 => 100100000
[7,1,1] => 100000011 => 110000001 => 111000000
[7,2] => 100000010 => 010000001 => 101000000
[8,1] => 100000001 => 100000001 => 110000000
[9] => 100000000 => 000000001 => 100000000
[1,1,1,1,1,1,1,1,1,1] => 1111111111 => 1111111111 => 1111111111
[1,1,1,1,1,1,1,1,2] => 1111111110 => 0111111111 => 1011111111
[1,1,1,1,1,1,1,2,1] => 1111111101 => 1011111111 => 1101111111
[1,1,1,1,1,1,1,3] => 1111111100 => 0011111111 => 1001111111
[1,1,1,1,1,1,2,1,1] => 1111111011 => 1101111111 => 1110111111
[1,1,1,1,1,1,2,2] => 1111111010 => 0101111111 => 1010111111
[1,1,1,1,1,1,3,1] => 1111111001 => 1001111111 => 1100111111
[1,1,1,1,1,1,4] => 1111111000 => 0001111111 => 1000111111
[1,1,1,1,1,2,1,1,1] => 1111110111 => 1110111111 => 1111011111
[1,1,1,1,1,2,1,2] => 1111110110 => 0110111111 => 1011011111
[1,1,1,1,1,2,2,1] => 1111110101 => 1010111111 => 1101011111
[1,1,1,1,1,2,3] => 1111110100 => 0010111111 => 1001011111
[1,1,1,1,1,3,1,1] => 1111110011 => 1100111111 => 1110011111
[1,1,1,1,1,3,2] => 1111110010 => 0100111111 => 1010011111
[1,1,1,1,1,5] => 1111110000 => 0000111111 => 1000011111
[1,1,1,1,2,1,1,2] => 1111101110 => 0111011111 => 1011101111
[1,1,1,1,2,1,2,1] => 1111101101 => 1011011111 => 1101101111
[1,1,1,1,2,1,3] => 1111101100 => 0011011111 => 1001101111
[1,1,1,1,2,2,1,1] => 1111101011 => 1101011111 => 1110101111
[1,1,1,1,2,2,2] => 1111101010 => 0101011111 => 1010101111
[1,1,1,1,2,3,1] => 1111101001 => 1001011111 => 1100101111
[1,1,1,1,2,4] => 1111101000 => 0001011111 => 1000101111
[1,1,1,1,3,1,1,1] => 1111100111 => 1110011111 => 1111001111
[1,1,1,1,3,1,2] => 1111100110 => 0110011111 => 1011001111
[1,1,1,1,3,3] => 1111100100 => 0010011111 => 1001001111
[1,1,1,1,4,2] => 1111100010 => 0100011111 => 1010001111
[1,1,1,1,5,1] => 1111100001 => 1000011111 => 1100001111
[1,1,1,1,6] => 1111100000 => 0000011111 => 1000001111
[1,1,1,2,1,1,1,2] => 1111011110 => 0111101111 => 1011110111
[1,1,1,2,1,2,1,1] => 1111011011 => 1101101111 => 1110110111
[1,1,1,2,1,2,2] => 1111011010 => 0101101111 => 1010110111
[1,1,1,2,1,4] => 1111011000 => 0001101111 => 1000110111
[1,1,1,2,2,1,1,1] => 1111010111 => 1110101111 => 1111010111
[1,1,1,2,2,1,2] => 1111010110 => 0110101111 => 1011010111
[1,1,1,2,2,2,1] => 1111010101 => 1010101111 => 1101010111
[1,1,1,2,3,2] => 1111010010 => 0100101111 => 1010010111
[1,1,1,2,4,1] => 1111010001 => 1000101111 => 1100010111
[1,1,1,2,5] => 1111010000 => 0000101111 => 1000010111
[1,1,1,3,1,1,1,1] => 1111001111 => 1111001111 => 1111100111
[1,1,1,3,1,3] => 1111001100 => 0011001111 => 1001100111
[1,1,1,3,2,1,1] => 1111001011 => 1101001111 => 1110100111
[1,1,1,3,2,2] => 1111001010 => 0101001111 => 1010100111
[1,1,1,3,3,1] => 1111001001 => 1001001111 => 1100100111
[1,1,1,3,4] => 1111001000 => 0001001111 => 1000100111
[1,1,1,4,2,1] => 1111000101 => 1010001111 => 1101000111
[1,1,1,4,3] => 1111000100 => 0010001111 => 1001000111
[1,1,1,5,1,1] => 1111000011 => 1100001111 => 1110000111
[1,1,1,5,2] => 1111000010 => 0100001111 => 1010000111
[1,1,1,6,1] => 1111000001 => 1000001111 => 1100000111
[1,1,1,7] => 1111000000 => 0000001111 => 1000000111
[1,1,2,1,1,1,1,2] => 1110111110 => 0111110111 => 1011111011
[1,1,2,1,1,1,2,1] => 1110111101 => 1011110111 => 1101111011
[1,1,2,1,1,1,3] => 1110111100 => 0011110111 => 1001111011
[1,1,2,1,1,2,1,1] => 1110111011 => 1101110111 => 1110111011
[1,1,2,1,1,2,2] => 1110111010 => 0101110111 => 1010111011
[1,1,2,1,1,4] => 1110111000 => 0001110111 => 1000111011
[1,1,2,1,2,1,1,1] => 1110110111 => 1110110111 => 1111011011
[1,1,2,1,2,1,2] => 1110110110 => 0110110111 => 1011011011
[1,1,2,1,2,3] => 1110110100 => 0010110111 => 1001011011
[1,1,2,1,3,2] => 1110110010 => 0100110111 => 1010011011
[1,1,2,1,4,1] => 1110110001 => 1000110111 => 1100011011
[1,1,2,1,5] => 1110110000 => 0000110111 => 1000011011
[1,1,2,2,1,1,1,1] => 1110101111 => 1111010111 => 1111101011
[1,1,2,2,1,3] => 1110101100 => 0011010111 => 1001101011
[1,1,2,2,2,1,1] => 1110101011 => 1101010111 => 1110101011
[1,1,2,2,2,2] => 1110101010 => 0101010111 => 1010101011
[1,1,2,2,3,1] => 1110101001 => 1001010111 => 1100101011
[1,1,2,2,4] => 1110101000 => 0001010111 => 1000101011
[1,1,2,3,1,2] => 1110100110 => 0110010111 => 1011001011
[1,1,2,3,2,1] => 1110100101 => 1010010111 => 1101001011
[1,1,2,3,3] => 1110100100 => 0010010111 => 1001001011
[1,1,2,4,1,1] => 1110100011 => 1100010111 => 1110001011
[1,1,2,4,2] => 1110100010 => 0100010111 => 1010001011
[1,1,2,5,1] => 1110100001 => 1000010111 => 1100001011
[1,1,2,6] => 1110100000 => 0000010111 => 1000001011
[1,1,3,1,1,1,1,1] => 1110011111 => 1111100111 => 1111110011
[1,1,3,1,1,1,2] => 1110011110 => 0111100111 => 1011110011
[1,1,3,1,1,3] => 1110011100 => 0011100111 => 1001110011
[1,1,3,1,2,2] => 1110011010 => 0101100111 => 1010110011
[1,1,3,1,3,1] => 1110011001 => 1001100111 => 1100110011
[1,1,3,1,4] => 1110011000 => 0001100111 => 1000110011
[1,1,3,2,1,2] => 1110010110 => 0110100111 => 1011010011
[1,1,3,2,2,1] => 1110010101 => 1010100111 => 1101010011
[1,1,3,2,3] => 1110010100 => 0010100111 => 1001010011
[1,1,3,3,1,1] => 1110010011 => 1100100111 => 1110010011
[1,1,3,3,2] => 1110010010 => 0100100111 => 1010010011
[1,1,3,4,1] => 1110010001 => 1000100111 => 1100010011
[1,1,3,5] => 1110010000 => 0000100111 => 1000010011
[1,1,4,1,1,2] => 1110001110 => 0111000111 => 1011100011
[1,1,4,1,2,1] => 1110001101 => 1011000111 => 1101100011
[1,1,4,1,3] => 1110001100 => 0011000111 => 1001100011
[1,1,4,2,1,1] => 1110001011 => 1101000111 => 1110100011
[1,1,4,2,2] => 1110001010 => 0101000111 => 1010100011
[1,1,4,3,1] => 1110001001 => 1001000111 => 1100100011
[1,1,5,1,1,1] => 1110000111 => 1110000111 => 1111000011
[1,1,5,1,2] => 1110000110 => 0110000111 => 1011000011
[1,1,5,2,1] => 1110000101 => 1010000111 => 1101000011
[1,1,5,3] => 1110000100 => 0010000111 => 1001000011
[1,1,6,1,1] => 1110000011 => 1100000111 => 1110000011
[1,1,6,2] => 1110000010 => 0100000111 => 1010000011
[1,1,7,1] => 1110000001 => 1000000111 => 1100000011
[1,1,8] => 1110000000 => 0000000111 => 1000000011
[1,2,1,1,1,1,1,1,1] => 1101111111 => 1111111011 => 1111111101
[1,2,1,1,1,1,1,2] => 1101111110 => 0111111011 => 1011111101
[1,2,1,1,1,1,2,1] => 1101111101 => 1011111011 => 1101111101
[1,2,1,1,1,2,1,1] => 1101111011 => 1101111011 => 1110111101
[1,2,1,1,1,2,2] => 1101111010 => 0101111011 => 1010111101
[1,2,1,1,1,3,1] => 1101111001 => 1001111011 => 1100111101
[1,2,1,1,2,1,1,1] => 1101110111 => 1110111011 => 1111011101
[1,2,1,1,2,1,2] => 1101110110 => 0110111011 => 1011011101
[1,2,1,1,3,2] => 1101110010 => 0100111011 => 1010011101
[1,2,1,1,4,1] => 1101110001 => 1000111011 => 1100011101
[1,2,1,1,5] => 1101110000 => 0000111011 => 1000011101
[1,2,1,2,1,1,1,1] => 1101101111 => 1111011011 => 1111101101
[1,2,1,2,2,1,1] => 1101101011 => 1101011011 => 1110101101
[1,2,1,2,2,2] => 1101101010 => 0101011011 => 1010101101
[1,2,1,2,3,1] => 1101101001 => 1001011011 => 1100101101
[1,2,1,2,4] => 1101101000 => 0001011011 => 1000101101
[1,2,1,3,1,2] => 1101100110 => 0110011011 => 1011001101
[1,2,1,3,2,1] => 1101100101 => 1010011011 => 1101001101
[1,2,1,3,3] => 1101100100 => 0010011011 => 1001001101
[1,2,1,4,1,1] => 1101100011 => 1100011011 => 1110001101
[1,2,1,4,2] => 1101100010 => 0100011011 => 1010001101
[1,2,1,5,1] => 1101100001 => 1000011011 => 1100001101
[1,2,1,6] => 1101100000 => 0000011011 => 1000001101
[1,2,2,1,1,1,1,1] => 1101011111 => 1111101011 => 1111110101
[1,2,2,1,1,1,2] => 1101011110 => 0111101011 => 1011110101
[1,2,2,1,1,2,1] => 1101011101 => 1011101011 => 1101110101
[1,2,2,1,2,1,1] => 1101011011 => 1101101011 => 1110110101
[1,2,2,1,2,2] => 1101011010 => 0101101011 => 1010110101
[1,2,2,1,3,1] => 1101011001 => 1001101011 => 1100110101
[1,2,2,1,4] => 1101011000 => 0001101011 => 1000110101
[1,2,2,2,1,1,1] => 1101010111 => 1110101011 => 1111010101
[1,2,2,2,1,2] => 1101010110 => 0110101011 => 1011010101
[1,2,2,2,2,1] => 1101010101 => 1010101011 => 1101010101
[1,2,2,2,3] => 1101010100 => 0010101011 => 1001010101
[1,2,2,3,1,1] => 1101010011 => 1100101011 => 1110010101
[1,2,2,3,2] => 1101010010 => 0100101011 => 1010010101
[1,2,2,4,1] => 1101010001 => 1000101011 => 1100010101
[1,2,2,5] => 1101010000 => 0000101011 => 1000010101
[1,2,3,1,1,1,1] => 1101001111 => 1111001011 => 1111100101
[1,2,3,1,1,2] => 1101001110 => 0111001011 => 1011100101
[1,2,3,1,2,1] => 1101001101 => 1011001011 => 1101100101
[1,2,3,1,3] => 1101001100 => 0011001011 => 1001100101
[1,2,3,2,1,1] => 1101001011 => 1101001011 => 1110100101
[1,2,3,2,2] => 1101001010 => 0101001011 => 1010100101
[1,2,3,3,1] => 1101001001 => 1001001011 => 1100100101
[1,2,3,4] => 1101001000 => 0001001011 => 1000100101
[1,2,4,1,2] => 1101000110 => 0110001011 => 1011000101
[1,2,4,2,1] => 1101000101 => 1010001011 => 1101000101
[1,2,5,1,1] => 1101000011 => 1100001011 => 1110000101
[1,2,5,2] => 1101000010 => 0100001011 => 1010000101
[1,2,6,1] => 1101000001 => 1000001011 => 1100000101
[1,2,7] => 1101000000 => 0000001011 => 1000000101
[1,3,1,1,1,1,1,1] => 1100111111 => 1111110011 => 1111111001
[1,3,1,1,1,3] => 1100111100 => 0011110011 => 1001111001
[1,3,1,1,2,2] => 1100111010 => 0101110011 => 1010111001
[1,3,1,1,3,1] => 1100111001 => 1001110011 => 1100111001
[1,3,1,1,4] => 1100111000 => 0001110011 => 1000111001
[1,3,1,2,1,2] => 1100110110 => 0110110011 => 1011011001
[1,3,1,2,2,1] => 1100110101 => 1010110011 => 1101011001
[1,3,1,2,3] => 1100110100 => 0010110011 => 1001011001
[1,3,1,3,1,1] => 1100110011 => 1100110011 => 1110011001
[1,3,1,3,2] => 1100110010 => 0100110011 => 1010011001
[1,3,1,4,1] => 1100110001 => 1000110011 => 1100011001
[1,3,1,5] => 1100110000 => 0000110011 => 1000011001
[1,3,2,1,1,2] => 1100101110 => 0111010011 => 1011101001
[1,3,2,1,2,1] => 1100101101 => 1011010011 => 1101101001
[1,3,2,1,3] => 1100101100 => 0011010011 => 1001101001
[1,3,2,2,1,1] => 1100101011 => 1101010011 => 1110101001
[1,3,2,2,2] => 1100101010 => 0101010011 => 1010101001
[1,3,2,3,1] => 1100101001 => 1001010011 => 1100101001
[1,3,3,1,1,1] => 1100100111 => 1110010011 => 1111001001
[1,3,3,1,2] => 1100100110 => 0110010011 => 1011001001
[1,3,3,2,1] => 1100100101 => 1010010011 => 1101001001
[1,3,3,3] => 1100100100 => 0010010011 => 1001001001
[1,3,4,1,1] => 1100100011 => 1100010011 => 1110001001
[1,3,4,2] => 1100100010 => 0100010011 => 1010001001
[1,4,1,1,1,1,1] => 1100011111 => 1111100011 => 1111110001
[1,4,1,1,1,2] => 1100011110 => 0111100011 => 1011110001
[1,4,1,1,2,1] => 1100011101 => 1011100011 => 1101110001
[1,4,1,2,1,1] => 1100011011 => 1101100011 => 1110110001
[1,4,1,2,2] => 1100011010 => 0101100011 => 1010110001
[1,4,1,3,1] => 1100011001 => 1001100011 => 1100110001
[1,4,1,4] => 1100011000 => 0001100011 => 1000110001
[1,4,2,1,1,1] => 1100010111 => 1110100011 => 1111010001
[1,4,2,1,2] => 1100010110 => 0110100011 => 1011010001
[1,4,2,2,1] => 1100010101 => 1010100011 => 1101010001
[1,4,3,1,1] => 1100010011 => 1100100011 => 1110010001
[1,4,3,2] => 1100010010 => 0100100011 => 1010010001
[1,5,1,1,1,1] => 1100001111 => 1111000011 => 1111100001
[1,5,1,1,2] => 1100001110 => 0111000011 => 1011100001
[1,5,1,2,1] => 1100001101 => 1011000011 => 1101100001
[1,5,1,3] => 1100001100 => 0011000011 => 1001100001
[1,5,2,1,1] => 1100001011 => 1101000011 => 1110100001
[1,5,2,2] => 1100001010 => 0101000011 => 1010100001
[1,5,4] => 1100001000 => 0001000011 => 1000100001
[1,6,1,1,1] => 1100000111 => 1110000011 => 1111000001
[1,6,1,2] => 1100000110 => 0110000011 => 1011000001
[1,7,1,1] => 1100000011 => 1100000011 => 1110000001
[1,7,2] => 1100000010 => 0100000011 => 1010000001
[1,8,1] => 1100000001 => 1000000011 => 1100000001
[1,9] => 1100000000 => 0000000011 => 1000000001
[2,1,1,1,1,1,1,1,1] => 1011111111 => 1111111101 => 1111111110
[2,1,1,1,1,1,1,2] => 1011111110 => 0111111101 => 1011111110
[2,1,1,1,1,1,2,1] => 1011111101 => 1011111101 => 1101111110
[2,1,1,1,1,1,3] => 1011111100 => 0011111101 => 1001111110
[2,1,1,1,1,2,1,1] => 1011111011 => 1101111101 => 1110111110
[2,1,1,1,1,2,2] => 1011111010 => 0101111101 => 1010111110
[2,1,1,1,1,4] => 1011111000 => 0001111101 => 1000111110
[2,1,1,1,2,1,1,1] => 1011110111 => 1110111101 => 1111011110
[2,1,1,1,2,1,2] => 1011110110 => 0110111101 => 1011011110
[2,1,1,1,2,3] => 1011110100 => 0010111101 => 1001011110
[2,1,1,1,4,1] => 1011110001 => 1000111101 => 1100011110
[2,1,1,1,5] => 1011110000 => 0000111101 => 1000011110
[2,1,1,2,1,1,1,1] => 1011101111 => 1111011101 => 1111101110
[2,1,1,2,1,3] => 1011101100 => 0011011101 => 1001101110
[2,1,1,2,2,2] => 1011101010 => 0101011101 => 1010101110
[2,1,1,2,3,1] => 1011101001 => 1001011101 => 1100101110
[2,1,1,2,4] => 1011101000 => 0001011101 => 1000101110
[2,1,1,3,2,1] => 1011100101 => 1010011101 => 1101001110
[2,1,1,3,3] => 1011100100 => 0010011101 => 1001001110
[2,1,1,4,1,1] => 1011100011 => 1100011101 => 1110001110
[2,1,1,4,2] => 1011100010 => 0100011101 => 1010001110
[2,1,1,5,1] => 1011100001 => 1000011101 => 1100001110
[2,1,1,6] => 1011100000 => 0000011101 => 1000001110
[2,1,2,1,1,1,1,1] => 1011011111 => 1111101101 => 1111110110
[2,1,2,1,1,1,2] => 1011011110 => 0111101101 => 1011110110
[2,1,2,1,1,3] => 1011011100 => 0011101101 => 1001110110
[2,1,2,1,3,1] => 1011011001 => 1001101101 => 1100110110
[2,1,2,1,4] => 1011011000 => 0001101101 => 1000110110
[2,1,2,2,1,1,1] => 1011010111 => 1110101101 => 1111010110
[2,1,2,2,1,2] => 1011010110 => 0110101101 => 1011010110
[2,1,2,2,2,1] => 1011010101 => 1010101101 => 1101010110
[2,1,2,2,3] => 1011010100 => 0010101101 => 1001010110
[2,1,2,3,1,1] => 1011010011 => 1100101101 => 1110010110
[2,1,2,3,2] => 1011010010 => 0100101101 => 1010010110
[2,1,2,4,1] => 1011010001 => 1000101101 => 1100010110
[2,1,2,5] => 1011010000 => 0000101101 => 1000010110
[2,1,3,1,1,2] => 1011001110 => 0111001101 => 1011100110
[2,1,3,1,2,1] => 1011001101 => 1011001101 => 1101100110
[2,1,3,1,3] => 1011001100 => 0011001101 => 1001100110
[2,1,3,2,1,1] => 1011001011 => 1101001101 => 1110100110
[2,1,3,2,2] => 1011001010 => 0101001101 => 1010100110
[2,1,3,3,1] => 1011001001 => 1001001101 => 1100100110
[2,1,4,1,1,1] => 1011000111 => 1110001101 => 1111000110
[2,1,4,1,2] => 1011000110 => 0110001101 => 1011000110
[2,1,4,2,1] => 1011000101 => 1010001101 => 1101000110
[2,1,4,3] => 1011000100 => 0010001101 => 1001000110
[2,1,5,1,1] => 1011000011 => 1100001101 => 1110000110
[2,1,6,1] => 1011000001 => 1000001101 => 1100000110
[2,1,7] => 1011000000 => 0000001101 => 1000000110
[2,2,1,1,1,1,1,1] => 1010111111 => 1111110101 => 1111111010
[2,2,1,1,1,1,2] => 1010111110 => 0111110101 => 1011111010
[2,2,1,1,1,3] => 1010111100 => 0011110101 => 1001111010
[2,2,1,1,2,2] => 1010111010 => 0101110101 => 1010111010
[2,2,1,1,3,1] => 1010111001 => 1001110101 => 1100111010
[2,2,1,1,4] => 1010111000 => 0001110101 => 1000111010
[2,2,1,2,1,1,1] => 1010110111 => 1110110101 => 1111011010
[2,2,1,2,1,2] => 1010110110 => 0110110101 => 1011011010
[2,2,1,2,2,1] => 1010110101 => 1010110101 => 1101011010
[2,2,1,2,3] => 1010110100 => 0010110101 => 1001011010
[2,2,1,3,1,1] => 1010110011 => 1100110101 => 1110011010
[2,2,1,3,2] => 1010110010 => 0100110101 => 1010011010
[2,2,1,4,1] => 1010110001 => 1000110101 => 1100011010
[2,2,1,5] => 1010110000 => 0000110101 => 1000011010
[2,2,2,1,1,1,1] => 1010101111 => 1111010101 => 1111101010
[2,2,2,1,1,2] => 1010101110 => 0111010101 => 1011101010
[2,2,2,1,2,1] => 1010101101 => 1011010101 => 1101101010
[2,2,2,1,3] => 1010101100 => 0011010101 => 1001101010
[2,2,2,2,1,1] => 1010101011 => 1101010101 => 1110101010
[2,2,2,2,2] => 1010101010 => 0101010101 => 1010101010
[2,2,2,3,1] => 1010101001 => 1001010101 => 1100101010
[2,2,2,4] => 1010101000 => 0001010101 => 1000101010
[2,2,3,1,1,1] => 1010100111 => 1110010101 => 1111001010
[2,2,3,1,2] => 1010100110 => 0110010101 => 1011001010
[2,2,3,2,1] => 1010100101 => 1010010101 => 1101001010
[2,2,3,3] => 1010100100 => 0010010101 => 1001001010
[2,2,4,1,1] => 1010100011 => 1100010101 => 1110001010
[2,2,4,2] => 1010100010 => 0100010101 => 1010001010
[2,2,5,1] => 1010100001 => 1000010101 => 1100001010
[2,2,6] => 1010100000 => 0000010101 => 1000001010
[2,3,1,1,1,2] => 1010011110 => 0111100101 => 1011110010
[2,3,1,1,2,1] => 1010011101 => 1011100101 => 1101110010
[2,3,1,1,3] => 1010011100 => 0011100101 => 1001110010
[2,3,1,2,1,1] => 1010011011 => 1101100101 => 1110110010
[2,3,1,2,2] => 1010011010 => 0101100101 => 1010110010
[2,3,1,3,1] => 1010011001 => 1001100101 => 1100110010
[2,3,2,1,1,1] => 1010010111 => 1110100101 => 1111010010
[2,3,2,1,2] => 1010010110 => 0110100101 => 1011010010
[2,3,2,2,1] => 1010010101 => 1010100101 => 1101010010
[2,3,2,3] => 1010010100 => 0010100101 => 1001010010
[2,3,3,1,1] => 1010010011 => 1100100101 => 1110010010
[2,3,4,1] => 1010010001 => 1000100101 => 1100010010
[2,3,5] => 1010010000 => 0000100101 => 1000010010
[2,4,1,1,1,1] => 1010001111 => 1111000101 => 1111100010
[2,4,1,1,2] => 1010001110 => 0111000101 => 1011100010
[2,4,1,2,1] => 1010001101 => 1011000101 => 1101100010
[2,4,2,1,1] => 1010001011 => 1101000101 => 1110100010
[2,4,2,2] => 1010001010 => 0101000101 => 1010100010
[2,5,1,1,1] => 1010000111 => 1110000101 => 1111000010
[2,5,2,1] => 1010000101 => 1010000101 => 1101000010
[2,5,3] => 1010000100 => 0010000101 => 1001000010
[2,6,2] => 1010000010 => 0100000101 => 1010000010
[2,7,1] => 1010000001 => 1000000101 => 1100000010
[2,8] => 1010000000 => 0000000101 => 1000000010
[3,1,1,1,1,1,1,1] => 1001111111 => 1111111001 => 1111111100
[3,1,1,1,1,1,2] => 1001111110 => 0111111001 => 1011111100
[3,1,1,1,1,3] => 1001111100 => 0011111001 => 1001111100
[3,1,1,1,2,1,1] => 1001111011 => 1101111001 => 1110111100
[3,1,1,1,2,2] => 1001111010 => 0101111001 => 1010111100
[3,1,1,1,3,1] => 1001111001 => 1001111001 => 1100111100
[3,1,1,1,4] => 1001111000 => 0001111001 => 1000111100
[3,1,1,2,1,2] => 1001110110 => 0110111001 => 1011011100
[3,1,1,2,3] => 1001110100 => 0010111001 => 1001011100
[3,1,1,3,1,1] => 1001110011 => 1100111001 => 1110011100
[3,1,1,3,2] => 1001110010 => 0100111001 => 1010011100
[3,1,1,4,1] => 1001110001 => 1000111001 => 1100011100
[3,1,1,5] => 1001110000 => 0000111001 => 1000011100
[3,1,2,1,1,2] => 1001101110 => 0111011001 => 1011101100
[3,1,2,1,2,1] => 1001101101 => 1011011001 => 1101101100
[3,1,2,1,3] => 1001101100 => 0011011001 => 1001101100
[3,1,2,2,1,1] => 1001101011 => 1101011001 => 1110101100
[3,1,2,2,2] => 1001101010 => 0101011001 => 1010101100
[3,1,2,3,1] => 1001101001 => 1001011001 => 1100101100
[3,1,3,1,1,1] => 1001100111 => 1110011001 => 1111001100
[3,1,3,1,2] => 1001100110 => 0110011001 => 1011001100
[3,1,3,2,1] => 1001100101 => 1010011001 => 1101001100
[3,1,3,3] => 1001100100 => 0010011001 => 1001001100
[3,1,4,1,1] => 1001100011 => 1100011001 => 1110001100
[3,1,4,2] => 1001100010 => 0100011001 => 1010001100
[3,1,5,1] => 1001100001 => 1000011001 => 1100001100
[3,1,6] => 1001100000 => 0000011001 => 1000001100
[3,2,1,1,1,1,1] => 1001011111 => 1111101001 => 1111110100
[3,2,1,1,1,2] => 1001011110 => 0111101001 => 1011110100
[3,2,1,2,1,1] => 1001011011 => 1101101001 => 1110110100
[3,2,1,2,2] => 1001011010 => 0101101001 => 1010110100
[3,2,1,3,1] => 1001011001 => 1001101001 => 1100110100
[3,2,1,4] => 1001011000 => 0001101001 => 1000110100
[3,2,2,1,1,1] => 1001010111 => 1110101001 => 1111010100
[3,2,2,1,2] => 1001010110 => 0110101001 => 1011010100
[3,2,2,2,1] => 1001010101 => 1010101001 => 1101010100
[3,2,3,2] => 1001010010 => 0100101001 => 1010010100
[3,3,1,1,1,1] => 1001001111 => 1111001001 => 1111100100
[3,3,1,1,2] => 1001001110 => 0111001001 => 1011100100
[3,3,1,2,1] => 1001001101 => 1011001001 => 1101100100
[3,3,1,3] => 1001001100 => 0011001001 => 1001100100
[3,3,2,1,1] => 1001001011 => 1101001001 => 1110100100
[3,4,1,1,1] => 1001000111 => 1110001001 => 1111000100
[3,4,1,2] => 1001000110 => 0110001001 => 1011000100
[3,6,1] => 1001000001 => 1000001001 => 1100000100
[3,7] => 1001000000 => 0000001001 => 1000000100
[4,1,1,1,1,1,1] => 1000111111 => 1111110001 => 1111111000
[4,1,1,1,1,2] => 1000111110 => 0111110001 => 1011111000
[4,1,1,1,2,1] => 1000111101 => 1011110001 => 1101111000
[4,1,1,1,3] => 1000111100 => 0011110001 => 1001111000
[4,1,1,2,1,1] => 1000111011 => 1101110001 => 1110111000
[4,1,1,2,2] => 1000111010 => 0101110001 => 1010111000
[4,1,2,1,1,1] => 1000110111 => 1110110001 => 1111011000
[4,1,2,1,2] => 1000110110 => 0110110001 => 1011011000
[4,1,2,3] => 1000110100 => 0010110001 => 1001011000
[4,1,3,1,1] => 1000110011 => 1100110001 => 1110011000
[4,1,3,2] => 1000110010 => 0100110001 => 1010011000
[4,1,4,1] => 1000110001 => 1000110001 => 1100011000
[4,1,5] => 1000110000 => 0000110001 => 1000011000
[4,2,1,1,1,1] => 1000101111 => 1111010001 => 1111101000
[4,2,1,1,2] => 1000101110 => 0111010001 => 1011101000
[4,2,2,1,1] => 1000101011 => 1101010001 => 1110101000
[4,2,2,2] => 1000101010 => 0101010001 => 1010101000
[4,2,4] => 1000101000 => 0001010001 => 1000101000
[4,3,1,1,1] => 1000100111 => 1110010001 => 1111001000
[4,3,1,2] => 1000100110 => 0110010001 => 1011001000
[4,3,2,1] => 1000100101 => 1010010001 => 1101001000
[4,3,3] => 1000100100 => 0010010001 => 1001001000
[4,4,2] => 1000100010 => 0100010001 => 1010001000
[4,6] => 1000100000 => 0000010001 => 1000001000
[5,1,1,1,1,1] => 1000011111 => 1111100001 => 1111110000
[5,1,1,1,2] => 1000011110 => 0111100001 => 1011110000
[5,1,1,2,1] => 1000011101 => 1011100001 => 1101110000
[5,1,1,3] => 1000011100 => 0011100001 => 1001110000
[5,1,2,1,1] => 1000011011 => 1101100001 => 1110110000
[5,1,2,2] => 1000011010 => 0101100001 => 1010110000
[5,1,3,1] => 1000011001 => 1001100001 => 1100110000
[5,1,4] => 1000011000 => 0001100001 => 1000110000
[5,2,1,1,1] => 1000010111 => 1110100001 => 1111010000
[5,2,1,2] => 1000010110 => 0110100001 => 1011010000
[5,3,1,1] => 1000010011 => 1100100001 => 1110010000
[5,3,2] => 1000010010 => 0100100001 => 1010010000
[5,5] => 1000010000 => 0000100001 => 1000010000
[6,1,1,1,1] => 1000001111 => 1111000001 => 1111100000
[6,1,1,2] => 1000001110 => 0111000001 => 1011100000
[6,1,2,1] => 1000001101 => 1011000001 => 1101100000
[6,1,3] => 1000001100 => 0011000001 => 1001100000
[6,2,1,1] => 1000001011 => 1101000001 => 1110100000
[6,2,2] => 1000001010 => 0101000001 => 1010100000
[6,4] => 1000001000 => 0001000001 => 1000100000
[7,1,1,1] => 1000000111 => 1110000001 => 1111000000
[7,1,2] => 1000000110 => 0110000001 => 1011000000
[7,2,1] => 1000000101 => 1010000001 => 1101000000
[7,3] => 1000000100 => 0010000001 => 1001000000
[8,1,1] => 1000000011 => 1100000001 => 1110000000
[8,2] => 1000000010 => 0100000001 => 1010000000
[9,1] => 1000000001 => 1000000001 => 1100000000
[10] => 1000000000 => 0000000001 => 1000000000
[1,10] => 11000000000 => 00000000011 => 10000000001
[1,8,1,1] => 11000000011 => 11000000011 => 11100000001
[1,2,7,1] => 11010000001 => 10000001011 => 11000000101
[10,1] => 10000000001 => 10000000001 => 11000000000
[1,1,1,1,1,1,1,1,1,1,1,1] => 111111111111 => 111111111111 => 111111111111
[1,1,1,1,1,1,1,1,2,2] => 111111111010 => 010111111111 => 101011111111
[1,1,1,1,1,1,2,2,1,1] => 111111101011 => 110101111111 => 111010111111
[1,1,1,1,1,1,2,1,1,2] => 111111101110 => 011101111111 => 101110111111
[1,1,1,1,1,1,3,3] => 111111100100 => 001001111111 => 100100111111
[1,1,1,1,2,2,1,1,1,1] => 111110101111 => 111101011111 => 111110101111
[1,1,1,1,2,2,2,2] => 111110101010 => 010101011111 => 101010101111
[1,1,1,1,2,1,1,2,1,1] => 111110111011 => 110111011111 => 111011101111
[1,1,1,1,2,1,1,1,1,2] => 111110111110 => 011111011111 => 101111101111
[1,1,1,1,2,1,2,3] => 111110110100 => 001011011111 => 100101101111
[1,1,1,1,3,2,1,2] => 111110010110 => 011010011111 => 101101001111
[1,1,1,1,3,1,1,3] => 111110011100 => 001110011111 => 100111001111
[1,1,1,1,4,4] => 111110001000 => 000100011111 => 100010001111
[1,1,2,2,1,1,1,1,1,1] => 111010111111 => 111111010111 => 111111101011
[1,1,2,2,1,1,2,2] => 111010111010 => 010111010111 => 101011101011
[1,1,2,2,2,2,1,1] => 111010101011 => 110101010111 => 111010101011
[1,1,2,2,2,1,1,2] => 111010101110 => 011101010111 => 101110101011
[1,1,2,2,3,3] => 111010100100 => 001001010111 => 100100101011
[1,1,2,1,1,2,1,1,1,1] => 111011101111 => 111101110111 => 111110111011
[1,1,2,1,1,2,2,2] => 111011101010 => 010101110111 => 101010111011
[1,1,2,1,1,1,1,2,1,1] => 111011111011 => 110111110111 => 111011111011
[1,1,2,1,1,1,1,1,1,2] => 111011111110 => 011111110111 => 101111111011
[1,1,2,1,1,1,2,3] => 111011110100 => 001011110111 => 100101111011
[1,1,2,1,2,2,1,2] => 111011010110 => 011010110111 => 101101011011
[1,1,2,1,2,1,1,3] => 111011011100 => 001110110111 => 100111011011
[1,1,2,1,3,4] => 111011001000 => 000100110111 => 100010011011
[1,1,3,3,1,1,1,1] => 111001001111 => 111100100111 => 111110010011
[1,1,3,3,2,2] => 111001001010 => 010100100111 => 101010010011
[1,1,3,2,1,1,1,2] => 111001011110 => 011110100111 => 101111010011
[1,1,3,2,2,3] => 111001010100 => 001010100111 => 100101010011
[1,1,3,1,1,1,1,3] => 111001111100 => 001111100111 => 100111110011
[1,1,3,1,2,4] => 111001101000 => 000101100111 => 100010110011
[1,1,4,4,1,1] => 111000100011 => 110001000111 => 111000100011
[1,1,4,3,1,2] => 111000100110 => 011001000111 => 101100100011
[1,1,4,2,1,3] => 111000101100 => 001101000111 => 100110100011
[1,1,4,1,1,4] => 111000111000 => 000111000111 => 100011100011
[1,1,5,5] => 111000010000 => 000010000111 => 100001000011
[2,2,1,1,1,1,1,1,1,1] => 101011111111 => 111111110101 => 111111111010
[2,2,1,1,1,1,2,2] => 101011111010 => 010111110101 => 101011111010
[2,2,1,1,2,2,1,1] => 101011101011 => 110101110101 => 111010111010
[2,2,1,1,2,1,1,2] => 101011101110 => 011101110101 => 101110111010
[2,2,1,1,3,3] => 101011100100 => 001001110101 => 100100111010
[2,2,2,2,1,1,1,1] => 101010101111 => 111101010101 => 111110101010
[2,2,2,2,2,2] => 101010101010 => 010101010101 => 101010101010
[2,2,2,1,1,2,1,1] => 101010111011 => 110111010101 => 111011101010
[2,2,2,1,1,1,1,2] => 101010111110 => 011111010101 => 101111101010
[2,2,2,1,2,3] => 101010110100 => 001011010101 => 100101101010
[2,2,3,3,1,1] => 101010010011 => 110010010101 => 111001001010
[2,2,3,2,1,2] => 101010010110 => 011010010101 => 101101001010
[2,2,4,4] => 101010001000 => 000100010101 => 100010001010
[2,1,1,2,1,1,1,1,1,1] => 101110111111 => 111111011101 => 111111101110
[2,1,1,2,1,1,2,2] => 101110111010 => 010111011101 => 101011101110
[2,1,1,2,2,2,1,1] => 101110101011 => 110101011101 => 111010101110
[2,1,1,2,2,1,1,2] => 101110101110 => 011101011101 => 101110101110
[2,1,1,2,3,3] => 101110100100 => 001001011101 => 100100101110
[2,1,1,1,1,2,1,1,1,1] => 101111101111 => 111101111101 => 111110111110
[2,1,1,1,1,2,2,2] => 101111101010 => 010101111101 => 101010111110
[2,1,1,1,1,1,1,2,1,1] => 101111111011 => 110111111101 => 111011111110
[2,1,1,1,1,1,1,1,1,2] => 101111111110 => 011111111101 => 101111111110
[2,1,1,1,1,1,2,3] => 101111110100 => 001011111101 => 100101111110
[2,1,1,1,2,3,1,1] => 101111010011 => 110010111101 => 111001011110
[2,1,1,1,2,2,1,2] => 101111010110 => 011010111101 => 101101011110
[2,1,1,1,2,1,1,3] => 101111011100 => 001110111101 => 100111011110
[2,1,1,1,3,4] => 101111001000 => 000100111101 => 100010011110
[2,1,2,3,1,1,1,1] => 101101001111 => 111100101101 => 111110010110
[2,1,2,3,2,2] => 101101001010 => 010100101101 => 101010010110
[2,1,2,2,1,2,1,1] => 101101011011 => 110110101101 => 111011010110
[2,1,2,2,1,1,1,2] => 101101011110 => 011110101101 => 101111010110
[2,1,2,2,2,3] => 101101010100 => 001010101101 => 100101010110
[2,1,2,1,1,1,1,3] => 101101111100 => 001111101101 => 100111110110
[2,1,2,1,2,4] => 101101101000 => 000101101101 => 100010110110
[2,1,3,4,1,1] => 101100100011 => 110001001101 => 111000100110
[2,1,3,2,1,3] => 101100101100 => 001101001101 => 100110100110
[2,1,3,1,1,4] => 101100111000 => 000111001101 => 100011100110
[2,1,4,5] => 101100010000 => 000010001101 => 100001000110
[3,3,1,1,1,1,1,1] => 100100111111 => 111111001001 => 111111100100
[3,3,1,1,2,2] => 100100111010 => 010111001001 => 101011100100
[3,3,2,2,1,1] => 100100101011 => 110101001001 => 111010100100
[3,3,2,1,1,2] => 100100101110 => 011101001001 => 101110100100
[3,3,3,3] => 100100100100 => 001001001001 => 100100100100
[3,2,1,2,1,1,1,1] => 100101101111 => 111101101001 => 111110110100
[3,2,1,2,2,2] => 100101101010 => 010101101001 => 101010110100
[3,2,1,1,2,3] => 100101110100 => 001011101001 => 100101110100
[3,2,2,2,1,2] => 100101010110 => 011010101001 => 101101010100
[3,2,3,4] => 100101001000 => 000100101001 => 100010010100
[3,1,1,3,1,1,1,1] => 100111001111 => 111100111001 => 111110011100
[3,1,1,2,1,2,1,1] => 100111011011 => 110110111001 => 111011011100
[3,1,1,2,1,1,1,2] => 100111011110 => 011110111001 => 101111011100
[3,1,1,2,2,3] => 100111010100 => 001010111001 => 100101011100
[3,1,1,1,1,1,1,3] => 100111111100 => 001111111001 => 100111111100
[3,1,1,1,2,4] => 100111101000 => 000101111001 => 100010111100
[3,1,2,3,1,2] => 100110100110 => 011001011001 => 101100101100
[3,1,2,1,1,4] => 100110111000 => 000111011001 => 100011101100
[3,1,3,5] => 100110010000 => 000010011001 => 100001001100
[4,4,1,1,1,1] => 100010001111 => 111100010001 => 111110001000
[4,4,2,2] => 100010001010 => 010100010001 => 101010001000
[4,3,1,2,1,1] => 100010011011 => 110110010001 => 111011001000
[4,3,1,1,1,2] => 100010011110 => 011110010001 => 101111001000
[4,3,2,3] => 100010010100 => 001010010001 => 100101001000
[4,2,1,3,1,1] => 100010110011 => 110011010001 => 111001101000
[4,2,1,2,1,2] => 100010110110 => 011011010001 => 101101101000
[4,2,1,1,1,3] => 100010111100 => 001111010001 => 100111101000
[4,2,2,4] => 100010101000 => 000101010001 => 100010101000
[4,1,1,4,1,1] => 100011100011 => 110001110001 => 111000111000
[4,1,1,3,1,2] => 100011100110 => 011001110001 => 101100111000
[4,1,1,2,1,3] => 100011101100 => 001101110001 => 100110111000
[4,1,1,1,1,4] => 100011111000 => 000111110001 => 100011111000
[4,1,2,5] => 100011010000 => 000010110001 => 100001011000
[5,5,1,1] => 100001000011 => 110000100001 => 111000010000
[5,4,1,2] => 100001000110 => 011000100001 => 101100010000
[5,3,1,3] => 100001001100 => 001100100001 => 100110010000
[5,2,1,4] => 100001011000 => 000110100001 => 100011010000
[5,1,1,5] => 100001110000 => 000011100001 => 100001110000
[6,6] => 100000100000 => 000001000001 => 100000100000
[1,2,2,2,2,2,1] => 110101010101 => 101010101011 => 110101010101
[1,2,2,2,3,2] => 110101010010 => 010010101011 => 101001010101
[1,2,2,3,3,1] => 110101001001 => 100100101011 => 110010010101
[1,2,2,3,2,2] => 110101001010 => 010100101011 => 101010010101
[1,2,3,3,2,1] => 110100100101 => 101001001011 => 110100100101
[1,2,3,2,3,1] => 110100101001 => 100101001011 => 110010100101
[1,2,3,2,2,2] => 110100101010 => 010101001011 => 101010100101
[1,2,5,4] => 110100001000 => 000100001011 => 100010000101
[1,3,3,2,2,1] => 110010010101 => 101010010011 => 110101001001
[1,3,4,3,1] => 110010001001 => 100100010011 => 110010001001
[1,3,5,3] => 110010000100 => 001000010011 => 100100001001
[1,3,2,3,2,1] => 110010100101 => 101001010011 => 110100101001
[1,3,2,2,3,1] => 110010101001 => 100101010011 => 110010101001
[1,3,2,2,2,2] => 110010101010 => 010101010011 => 101010101001
[1,4,4,2,1] => 110001000101 => 101000100011 => 110100010001
[1,4,5,2] => 110001000010 => 010000100011 => 101000010001
[1,4,3,3,1] => 110001001001 => 100100100011 => 110010010001
[1,4,3,4] => 110001001000 => 000100100011 => 100010010001
[1,5,3,3] => 110000100100 => 001001000011 => 100100100001
[2,3,2,2,2,1] => 101001010101 => 101010100101 => 110101010010
[2,3,4,3] => 101001000100 => 001000100101 => 100100010010
[2,4,4,2] => 101000100010 => 010001000101 => 101000100010
[2,5,4,1] => 101000010001 => 100010000101 => 110001000010
[2,5,2,3] => 101000010100 => 001010000101 => 100101000010
[2,2,3,2,2,1] => 101010010101 => 101010010101 => 110101001010
[2,2,5,3] => 101010000100 => 001000010101 => 100100001010
[2,2,2,3,2,1] => 101010100101 => 101001010101 => 110100101010
[2,2,2,2,3,1] => 101010101001 => 100101010101 => 110010101010
[2,2,3,2,3] => 101010010100 => 001010010101 => 100101001010
[2,4,2,4] => 101000101000 => 000101000101 => 100010100010
[2,5,5] => 101000010000 => 000010000101 => 100001000010
[3,4,3,2] => 100100010010 => 010010001001 => 101001000100
[3,2,5,2] => 100101000010 => 010000101001 => 101000010100
[4,5,2,1] => 100010000101 => 101000010001 => 110100001000
[4,4,3,1] => 100010001001 => 100100010001 => 110010001000
[4,5,3] => 100010000100 => 001000010001 => 100100001000
[4,3,4,1] => 100010010001 => 100010010001 => 110001001000
[4,2,4,2] => 100010100010 => 010001010001 => 101000101000
[4,3,5] => 100010010000 => 000010010001 => 100001001000
[1,8,2] => 11000000010 => 01000000011 => 10100000001
[1,6,1,1,2] => 11000001110 => 01110000011 => 10111000001
[1,4,1,1,1,1,2] => 11000111110 => 01111100011 => 10111110001
[1,2,1,1,1,1,1,1,2] => 11011111110 => 01111111011 => 10111111101
[1,1,1,1,1,1,1,1,1,2] => 11111111110 => 01111111111 => 10111111111
[1,11] => 110000000000 => 000000000011 => 100000000001
[1,8,1,2] => 110000000110 => 011000000011 => 101100000001
[1,6,1,1,1,2] => 110000011110 => 011110000011 => 101111000001
[1,4,2,1,1,2] => 11000101110 => 01110100011 => 10111010001
[1,5,1,1,1,1,2] => 110000111110 => 011111000011 => 101111100001
[1,1,1,1,1,1,1,1,1,1,2] => 111111111110 => 011111111111 => 101111111111
[1,2,2,2,2,2] => 11010101010 => 01010101011 => 10101010101
[1,2,2,2,1,3] => 11010101100 => 00110101011 => 10011010101
[1,2,2,1,2,3] => 11010110100 => 00101101011 => 10010110101
[1,2,1,2,2,3] => 11011010100 => 00101011011 => 10010101101
[1,2,1,1,4,2] => 11011100010 => 01000111011 => 10100011101
[1,2,1,1,2,4] => 11011101000 => 00010111011 => 10001011101
[1,1,3,2,2,2] => 11100101010 => 01010100111 => 10101010011
[1,1,2,3,2,2] => 11101001010 => 01010010111 => 10101001011
[1,1,2,2,3,2] => 11101010010 => 01001010111 => 10100101011
[1,1,2,2,2,3] => 11101010100 => 00101010111 => 10010101011
[1,1,1,3,1,4] => 11110011000 => 00011001111 => 10001100111
[1,1,1,2,4,2] => 11110100010 => 01000101111 => 10100010111
[1,1,1,2,1,5] => 11110110000 => 00001101111 => 10000110111
[1,1,1,1,5,2] => 11111000010 => 01000011111 => 10100001111
[1,1,1,1,1,6] => 11111100000 => 00000111111 => 10000011111
[12] => 100000000000 => 000000000001 => 100000000000
[1,1,2,1,7] => 111011000000 => 000000110111 => 100000011011
[1,1,2,3,5] => 111010010000 => 000010010111 => 100001001011
[3,1,2,1,5] => 100110110000 => 000011011001 => 100001101100
[1,1,4,1,5] => 111000110000 => 000011000111 => 100001100011
[1,1,2,5,3] => 111010000100 => 001000010111 => 100100001011
[3,1,2,3,3] => 100110100100 => 001001011001 => 100100101100
[1,1,4,3,3] => 111000100100 => 001001000111 => 100100100011
[5,1,2,1,3] => 100001101100 => 001101100001 => 100110110000
[3,1,4,1,3] => 100110001100 => 001100011001 => 100110001100
[1,1,6,1,3] => 111000001100 => 001100000111 => 100110000011
[1,1,1,1,2,1,1,1,3] => 111110111100 => 001111011111 => 100111101111
[1,1,2,1,4,2,1] => 111011000101 => 101000110111 => 110100011011
[1,6,2,2,1] => 110000010101 => 101010000011 => 110101000001
[1,1,2,3,2,2,1] => 111010010101 => 101010010111 => 110101001011
[1,3,2,1,2,2,1] => 110010110101 => 101011010011 => 110101101001
[1,1,4,1,2,2,1] => 111000110101 => 101011000111 => 110101100011
[1,1,1,2,1,1,2,2,1] => 111101110101 => 101011101111 => 110101110111
[1,1,2,1,2,4,1] => 111011010001 => 100010110111 => 110001011011
[1,1,1,2,1,5,1] => 111101100001 => 100001101111 => 110000110111
[5,1,2,3,1] => 100001101001 => 100101100001 => 110010110000
[1,2,2,1,2,3,1] => 110101101001 => 100101101011 => 110010110101
[1,5,2,3,1] => 110000101001 => 100101000011 => 110010100001
[1,1,2,2,2,3,1] => 111010101001 => 100101010111 => 110010101011
[3,1,4,3,1] => 100110001001 => 100100011001 => 110010001100
[1,1,1,2,3,3,1] => 111101001001 => 100100101111 => 110010010111
[3,1,1,2,1,3,1] => 100111011001 => 100110111001 => 110011011100
[1,3,1,2,1,3,1] => 110011011001 => 100110110011 => 110011011001
[1,1,3,2,1,3,1] => 111001011001 => 100110100111 => 110011010011
[1,1,1,4,1,3,1] => 111100011001 => 100110001111 => 110011000111
[3,2,2,1,2,1,1] => 100101011011 => 110110101001 => 111011010100
[1,4,2,1,2,1,1] => 110001011011 => 110110100011 => 111011010001
[1,2,2,3,2,1,1] => 110101001011 => 110100101011 => 111010010101
[1,1,2,4,2,1,1] => 111010001011 => 110100010111 => 111010001011
[3,1,2,2,2,1,1] => 100110101011 => 110101011001 => 111010101100
[1,3,2,2,2,1,1] => 110010101011 => 110101010011 => 111010101001
[1,1,4,2,2,1,1] => 111000101011 => 110101000111 => 111010100011
[1,2,2,1,4,1,1] => 110101100011 => 110001101011 => 111000110101
[1,1,2,2,4,1,1] => 111010100011 => 110001010111 => 111000101011
[1,1,1,2,5,1,1] => 111101000011 => 110000101111 => 111000010111
[1,3,1,2,3,1,1] => 110011010011 => 110010110011 => 111001011001
[1,1,3,2,3,1,1] => 111001010011 => 110010100111 => 111001010011
[1,1,1,4,3,1,1] => 111100010011 => 110010001111 => 111001000111
[5,1,1,2,1,1,1] => 100001110111 => 111011100001 => 111101110000
[3,3,1,2,1,1,1] => 100100110111 => 111011001001 => 111101100100
[1,5,1,2,1,1,1] => 110000110111 => 111011000011 => 111101100001
[3,1,3,2,1,1,1] => 100110010111 => 111010011001 => 111101001100
[1,3,3,2,1,1,1] => 110010010111 => 111010010011 => 111101001001
[1,1,5,2,1,1,1] => 111000010111 => 111010000111 => 111101000011
[3,1,1,4,1,1,1] => 100111000111 => 111000111001 => 111100011100
[1,3,1,4,1,1,1] => 110011000111 => 111000110011 => 111100011001
[1,1,1,6,1,1,1] => 111100000111 => 111000001111 => 111100000111
[2,2,2,2,1,2,1] => 101010101101 => 101101010101 => 110110101010
[2,2,2,1,2,2,1] => 101010110101 => 101011010101 => 110101101010
[2,2,1,2,1,1,2,1] => 101011011101 => 101110110101 => 110111011010
[2,2,1,2,2,1,2] => 101011010110 => 011010110101 => 101101011010
[2,2,1,2,2,2,1] => 101011010101 => 101010110101 => 110101011010
[2,2,1,1,2,1,2,1] => 101011101101 => 101101110101 => 110110111010
[2,2,1,1,1,2,2,1] => 101011110101 => 101011110101 => 110101111010
[2,1,2,1,2,1,2,1] => 101101101101 => 101101101101 => 110110110110
[2,1,2,2,2,2,1] => 101101010101 => 101010101101 => 110101010110
[2,1,1,2,2,1,2,1] => 101110101101 => 101101011101 => 110110101110
[2,1,1,2,1,2,2,1] => 101110110101 => 101011011101 => 110101101110
[1,2,1,2,1,2,1,2] => 110110110110 => 011011011011 => 101101101101
[1,2,1,1,2,1,2,2] => 110111011010 => 010110111011 => 101011011101
[1,2,1,1,2,1,1,2,1] => 110111011101 => 101110111011 => 110111011101
[1,2,1,1,1,2,1,2,1] => 110111101101 => 101101111011 => 110110111101
[1,2,1,1,1,1,2,2,1] => 110111110101 => 101011111011 => 110101111101
[1,1,2,2,2,1,2,1] => 111010101101 => 101101010111 => 110110101011
[1,1,2,2,1,2,2,1] => 111010110101 => 101011010111 => 110101101011
[1,1,2,1,2,1,1,2,1] => 111011011101 => 101110110111 => 110111011011
[1,1,2,1,1,2,1,2,1] => 111011101101 => 101101110111 => 110110111011
[1,1,2,1,1,1,2,2,1] => 111011110101 => 101011110111 => 110101111011
[1,1,1,2,2,1,2,2] => 111101011010 => 010110101111 => 101011010111
[1,1,1,2,2,1,1,2,1] => 111101011101 => 101110101111 => 110111010111
[1,1,1,2,1,2,1,2,1] => 111101101101 => 101101101111 => 110110110111
[1,1,1,1,2,2,1,2,1] => 111110101101 => 101101011111 => 110110101111
[1,1,1,1,2,1,2,2,1] => 111110110101 => 101011011111 => 110101101111
[1,1,1,1,1,2,2,2,1] => 111111010101 => 101010111111 => 110101011111
[3,3,3,2] => 10010010010 => 01001001001 => 10100100100
[3,4,4] => 10010001000 => 00010001001 => 10001000100
[2,3,3,3] => 10100100100 => 00100100101 => 10010010010
[4,4,3] => 10001000100 => 00100010001 => 10010001000
[2,1,1,1,1,1,1,1,1,1] => 10111111111 => 11111111101 => 11111111110
[3,2,2,2,2,1] => 100101010101 => 101010101001 => 110101010100
[5,3,3,1] => 100001001001 => 100100100001 => 110010010000
[5,2,3,2] => 100001010010 => 010010100001 => 101001010000
[6,3,3] => 100000100100 => 001001000001 => 100100100000
[7,5] => 100000010000 => 000010000001 => 100001000000
[2,8,1] => 10100000001 => 10000000101 => 11000000010
[2,1,1,1,1,1,1,2,1] => 10111111101 => 10111111101 => 11011111110
[11,1] => 100000000001 => 100000000001 => 110000000000
[2,1,8,1] => 101100000001 => 100000001101 => 110000000110
[2,2,6,1] => 10101000001 => 10000010101 => 11000001010
[2,1,1,1,6,1] => 101111000001 => 100000111101 => 110000011110
[2,1,1,1,1,5,1] => 101111100001 => 100001111101 => 110000111110
[2,1,1,1,1,1,4,1] => 101111110001 => 100011111101 => 110001111110
[2,1,1,1,1,1,1,1,2,1] => 101111111101 => 101111111101 => 110111111110
[2,2,2,2,2,1] => 10101010101 => 10101010101 => 11010101010
[6,1,1,1,1,1] => 10000011111 => 11111000001 => 11111100000
[2,1,1,1,2,1,1,1,2] => 101111011110 => 011110111101 => 101111011110
[1,2,2,1,2,1,1,2] => 110101101110 => 011101101011 => 101110110101
[1,2,2,1,2,2,1,1] => 110101101011 => 110101101011 => 111010110101
[1,2,1,1,1,2,1,1,1,1] => 110111101111 => 111101111011 => 111110111101
[1,1,2,1,1,1,2,1,2] => 111011110110 => 011011110111 => 101101111011
[1,1,2,1,1,1,2,1,1,1] => 111011110111 => 111011110111 => 111101111011
[1,1,2,1,2,1,1,1,2] => 111011011110 => 011110110111 => 101111011011
[1,1,1,2,1,1,1,2,1,1] => 111101111011 => 110111101111 => 111011110111
[1,1,1,2,1,2,1,1,1,1] => 111101101111 => 111101101111 => 111110110111
[1,1,1,1,2,1,1,1,2,1] => 111110111101 => 101111011111 => 110111101111
[1,1,1,1,2,1,2,1,1,1] => 111110110111 => 111011011111 => 111101101111
[2,1,1,1,1,1,2,2] => 10111111010 => 01011111101 => 10101111110
[2,1,1,1,2,1,1,2] => 10111101110 => 01110111101 => 10111011110
[2,1,1,2,1,1,1,2] => 10111011110 => 01111011101 => 10111101110
[2,2,1,1,1,1,1,2] => 10101111110 => 01111110101 => 10111111010
[3,1,1,1,1,1,1,2] => 10011111110 => 01111111001 => 10111111100
[1,2,2,4,2,1] => 110101000101 => 101000101011 => 110100010101
[1,2,4,2,2,1] => 110100010101 => 101010001011 => 110101000101
[1,3,5,2,1] => 110010000101 => 101000010011 => 110100001001
[1,4,2,2,2,1] => 110001010101 => 101010100011 => 110101010001
[1,5,3,2,1] => 110000100101 => 101001000011 => 110100100001
[2,6,2,2] => 101000001010 => 010100000101 => 101010000010
[6,2,2,2] => 100000101010 => 010101000001 => 101010100000
[2,2,2,2,2,1,1] => 101010101011 => 110101010101 => 111010101010
[2,2,1,2,2,1,1,1] => 101011010111 => 111010110101 => 111101011010
[1,1,2,1,2,1,1,1,1,1] => 111011011111 => 111110110111 => 111111011011
[9,2] => 10000000010 => 01000000001 => 10100000000
[10,2] => 100000000010 => 010000000001 => 101000000000
[1,2,2,2,3,1,1] => 110101010011 => 110010101011 => 111001010101
[1,2,2,3,1,2,1] => 110101001101 => 101100101011 => 110110010101
[1,2,3,1,2,2,1] => 110100110101 => 101011001011 => 110101100101
[1,2,3,1,3,1,1] => 110100110011 => 110011001011 => 111001100101
[1,2,3,2,1,2,1] => 110100101101 => 101101001011 => 110110100101
[1,2,3,2,2,1,1] => 110100101011 => 110101001011 => 111010100101
[1,3,1,2,2,2,1] => 110011010101 => 101010110011 => 110101011001
[1,3,1,3,1,2,1] => 110011001101 => 101100110011 => 110110011001
[1,3,1,3,2,1,1] => 110011001011 => 110100110011 => 111010011001
[1,3,2,1,3,1,1] => 110010110011 => 110011010011 => 111001101001
[1,4,1,1,2,2,1] => 110001110101 => 101011100011 => 110101110001
[1,4,1,1,3,1,1] => 110001110011 => 110011100011 => 111001110001
[1,3,2,2,1,2,1] => 110010101101 => 101101010011 => 110110101001
[1,3,3,1,1,2,1] => 110010011101 => 101110010011 => 110111001001
[1,4,1,2,1,2,1] => 110001101101 => 101101100011 => 110110110001
[1,4,2,1,1,2,1] => 110001011101 => 101110100011 => 110111010001
[1,3,2,3,1,1,1] => 110010100111 => 111001010011 => 111100101001
[1,3,3,1,2,1,1] => 110010011011 => 110110010011 => 111011001001
[1,3,4,1,1,1,1] => 110010001111 => 111100010011 => 111110001001
[1,4,1,2,2,1,1] => 110001101011 => 110101100011 => 111010110001
[1,4,1,3,1,1,1] => 110001100111 => 111001100011 => 111100110001
[1,5,1,1,2,1,1] => 110000111011 => 110111000011 => 111011100001
[1,4,2,2,1,1,1] => 110001010111 => 111010100011 => 111101010001
[1,4,3,1,1,1,1] => 110001001111 => 111100100011 => 111110010001
[1,5,2,1,1,1,1] => 110000101111 => 111101000011 => 111110100001
[1,6,1,1,1,1,1] => 110000011111 => 111110000011 => 111111000001
[2,1,2,2,3,1,1] => 101101010011 => 110010101101 => 111001010110
[2,1,2,3,1,2,1] => 101101001101 => 101100101101 => 110110010110
[2,1,2,3,2,1,1] => 101101001011 => 110100101101 => 111010010110
[2,1,3,1,2,2,1] => 101100110101 => 101011001101 => 110101100110
[2,1,3,1,3,1,1] => 101100110011 => 110011001101 => 111001100110
[2,1,3,2,1,2,1] => 101100101101 => 101101001101 => 110110100110
[2,1,3,2,2,1,1] => 101100101011 => 110101001101 => 111010100110
[2,1,3,3,1,1,1] => 101100100111 => 111001001101 => 111100100110
[2,1,4,1,2,1,1] => 101100011011 => 110110001101 => 111011000110
[2,1,4,2,1,1,1] => 101100010111 => 111010001101 => 111101000110
[2,1,5,1,1,1,1] => 101100001111 => 111100001101 => 111110000110
[2,2,1,2,3,1,1] => 101011010011 => 110010110101 => 111001011010
[2,2,1,3,1,2,1] => 101011001101 => 101100110101 => 110110011010
[2,2,1,3,2,1,1] => 101011001011 => 110100110101 => 111010011010
[2,2,1,4,1,1,1] => 101011000111 => 111000110101 => 111100011010
[3,1,1,3,1,2,1] => 100111001101 => 101100111001 => 110110011100
[3,1,1,3,2,1,1] => 100111001011 => 110100111001 => 111010011100
[2,2,2,1,3,1,1] => 101010110011 => 110011010101 => 111001101010
[2,3,1,1,3,1,1] => 101001110011 => 110011100101 => 111001110010
[3,1,2,1,3,1,1] => 100110110011 => 110011011001 => 111001101100
[3,2,1,1,3,1,1] => 100101110011 => 110011101001 => 111001110100
[4,1,1,1,2,2,1] => 100011110101 => 101011110001 => 110101111000
[4,1,1,1,3,1,1] => 100011110011 => 110011110001 => 111001111000
[3,1,3,1,1,2,1] => 100110011101 => 101110011001 => 110111001100
[4,1,1,2,1,2,1] => 100011101101 => 101101110001 => 110110111000
[4,1,2,1,1,2,1] => 100011011101 => 101110110001 => 110111011000
[2,2,2,3,1,1,1] => 101010100111 => 111001010101 => 111100101010
[2,2,3,1,2,1,1] => 101010011011 => 110110010101 => 111011001010
[2,2,3,2,1,1,1] => 101010010111 => 111010010101 => 111101001010
[2,2,4,1,1,1,1] => 101010001111 => 111100010101 => 111110001010
[2,3,1,2,2,1,1] => 101001101011 => 110101100101 => 111010110010
[2,3,1,3,1,1,1] => 101001100111 => 111001100101 => 111100110010
[2,3,2,1,2,1,1] => 101001011011 => 110110100101 => 111011010010
[2,4,1,1,2,1,1] => 101000111011 => 110111000101 => 111011100010
[2,3,2,2,1,1,1] => 101001010111 => 111010100101 => 111101010010
[2,3,3,1,1,1,1] => 101001001111 => 111100100101 => 111110010010
[2,4,1,2,1,1,1] => 101000110111 => 111011000101 => 111101100010
[2,4,2,1,1,1,1] => 101000101111 => 111101000101 => 111110100010
[2,5,1,1,1,1,1] => 101000011111 => 111110000101 => 111111000010
[3,1,2,3,1,1,1] => 100110100111 => 111001011001 => 111100101100
[3,1,3,1,2,1,1] => 100110011011 => 110110011001 => 111011001100
[3,1,4,1,1,1,1] => 100110001111 => 111100011001 => 111110001100
[3,2,1,2,2,1,1] => 100101101011 => 110101101001 => 111010110100
[3,2,1,3,1,1,1] => 100101100111 => 111001101001 => 111100110100
[4,1,1,2,2,1,1] => 100011101011 => 110101110001 => 111010111000
[4,1,1,3,1,1,1] => 100011100111 => 111001110001 => 111100111000
[3,3,1,1,2,1,1] => 100100111011 => 110111001001 => 111011100100
[4,1,2,1,2,1,1] => 100011011011 => 110110110001 => 111011011000
[4,2,1,1,2,1,1] => 100010111011 => 110111010001 => 111011101000
[5,1,1,1,2,1,1] => 100001111011 => 110111100001 => 111011110000
[3,2,2,2,1,1,1] => 100101010111 => 111010101001 => 111101010100
[3,2,3,1,1,1,1] => 100101001111 => 111100101001 => 111110010100
[3,3,2,1,1,1,1] => 100100101111 => 111101001001 => 111110100100
[3,4,1,1,1,1,1] => 100100011111 => 111110001001 => 111111000100
[4,1,2,2,1,1,1] => 100011010111 => 111010110001 => 111101011000
[4,1,3,1,1,1,1] => 100011001111 => 111100110001 => 111110011000
[4,2,1,2,1,1,1] => 100010110111 => 111011010001 => 111101101000
[4,2,2,1,1,1,1] => 100010101111 => 111101010001 => 111110101000
[4,3,1,1,1,1,1] => 100010011111 => 111110010001 => 111111001000
[5,1,2,1,1,1,1] => 100001101111 => 111101100001 => 111110110000
[5,2,1,1,1,1,1] => 100001011111 => 111110100001 => 111111010000
[6,1,1,1,1,1,1] => 100000111111 => 111111000001 => 111111100000
[11] => 10000000000 => 00000000001 => 10000000000
[1,1,2,3,2,3] => 111010010100 => 001010010111 => 100101001011
[1,2,2,2,2,3] => 110101010100 => 001010101011 => 100101010101
[2,3,2,5] => 101001010000 => 000010100101 => 100001010010
[5,1,1,1,1,2] => 10000111110 => 01111100001 => 10111110000
[1,1,1,1,1,1,1,1,2,1] => 11111111101 => 10111111111 => 11011111111
[1,1,1,1,1,1,1,1,1,1,1] => 11111111111 => 11111111111 => 11111111111
[1,1,1,2,1,2,1,1,1] => 11110110111 => 11101101111 => 11110110111
[1,1,1,2,1,1,1,2,1] => 11110111101 => 10111101111 => 11011110111
[1,2,1,1,1,2,1,1,1] => 11011110111 => 11101111011 => 11110111101
[1,2,2,1,2,2,1] => 11010110101 => 10101101011 => 11010110101
[1,1,9] => 11100000000 => 00000000111 => 10000000011
[1,1,1,1,1,1,1,1,3] => 11111111100 => 00111111111 => 10011111111
[2,2,2,2,1,1,2] => 101010101110 => 011101010101 => 101110101010
[1,1,2,2,1,2,3] => 111010110100 => 001011010111 => 100101101011
[2,2,2,6] => 101010100000 => 000001010101 => 100000101010
[2,2,6,2] => 101010000010 => 010000010101 => 101000001010
[1,6,4] => 11000001000 => 00010000011 => 10001000001
[1,4,6] => 11000100000 => 00000100011 => 10000010001
[1,2,1,2,1,1,1,1,1,1] => 110110111111 => 111111011011 => 111111101101
[1,2,1,1,1,1,1,2,1,1] => 110111111011 => 110111111011 => 111011111101
[1,1,2,1,1,1,1,1,2,1] => 111011111101 => 101111110111 => 110111111011
[1,1,1,1,1,2,1,2,1,1] => 111111011011 => 110110111111 => 111011011111
[1,1,1,1,1,1,2,1,2,1] => 111111101101 => 101101111111 => 110110111111
[1,2,2,2,4,1] => 110101010001 => 100010101011 => 110001010101
[1,1,2,1,1,1,2,1,1] => 11101111011 => 11011110111 => 11101111011
[1,1,2,2,2,2,1] => 11101010101 => 10101010111 => 11010101011
[1,1,2,2,2,1,1,1] => 11101010111 => 11101010111 => 11110101011
[1,1,2,2,1,2,1,1] => 11101011011 => 11011010111 => 11101101011
[1,1,2,1,2,2,1,1] => 11101101011 => 11010110111 => 11101011011
[1,2,2,2,2,1,1] => 11010101011 => 11010101011 => 11101010101
[1,1,2,2,2,4] => 111010101000 => 000101010111 => 100010101011
Map
to binary word
Description
Return the composition as a binary word, treating ones as separators.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Map
reverse
Description
Return the reversal of a binary word.
Map
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.
This is the word obtained by moving the last letter to the beginnig.
searching the database
Sorry, this map was not found in the database.