Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
St000297: Binary words ⟶ ℤ
Values
[1,0,1,0] => [1] => 10 => 01 => 0
[1,0,1,0,1,0] => [2,1] => 1010 => 0101 => 0
[1,0,1,1,0,0] => [1,1] => 110 => 101 => 1
[1,1,0,0,1,0] => [2] => 100 => 001 => 0
[1,1,0,1,0,0] => [1] => 10 => 01 => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => 101010 => 010101 => 0
[1,0,1,0,1,1,0,0] => [2,2,1] => 11010 => 10101 => 1
[1,0,1,1,0,0,1,0] => [3,1,1] => 100110 => 001101 => 0
[1,0,1,1,0,1,0,0] => [2,1,1] => 10110 => 01101 => 0
[1,0,1,1,1,0,0,0] => [1,1,1] => 1110 => 1101 => 2
[1,1,0,0,1,0,1,0] => [3,2] => 10100 => 01001 => 0
[1,1,0,0,1,1,0,0] => [2,2] => 1100 => 1001 => 1
[1,1,0,1,0,0,1,0] => [3,1] => 10010 => 00101 => 0
[1,1,0,1,0,1,0,0] => [2,1] => 1010 => 0101 => 0
[1,1,0,1,1,0,0,0] => [1,1] => 110 => 101 => 1
[1,1,1,0,0,0,1,0] => [3] => 1000 => 0001 => 0
[1,1,1,0,0,1,0,0] => [2] => 100 => 001 => 0
[1,1,1,0,1,0,0,0] => [1] => 10 => 01 => 0
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 10101010 => 01010101 => 0
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 1101010 => 1010101 => 1
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 10011010 => 00110101 => 0
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 1011010 => 0110101 => 0
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 111010 => 110101 => 2
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 10100110 => 01001101 => 0
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 1100110 => 1001101 => 1
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 10010110 => 00101101 => 0
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 1010110 => 0101101 => 0
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 110110 => 101101 => 1
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 10001110 => 00011101 => 0
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1001110 => 0011101 => 0
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 101110 => 011101 => 0
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 11110 => 11101 => 3
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 1010100 => 0101001 => 0
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 110100 => 101001 => 1
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1001100 => 0011001 => 0
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 101100 => 011001 => 0
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 11100 => 11001 => 2
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 1010010 => 0100101 => 0
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 110010 => 100101 => 1
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 1001010 => 0010101 => 0
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 101010 => 010101 => 0
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 11010 => 10101 => 1
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 1000110 => 0001101 => 0
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 100110 => 001101 => 0
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 10110 => 01101 => 0
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 1110 => 1101 => 2
[1,1,1,0,0,0,1,0,1,0] => [4,3] => 101000 => 010001 => 0
[1,1,1,0,0,0,1,1,0,0] => [3,3] => 11000 => 10001 => 1
[1,1,1,0,0,1,0,0,1,0] => [4,2] => 100100 => 001001 => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 10100 => 01001 => 0
[1,1,1,0,0,1,1,0,0,0] => [2,2] => 1100 => 1001 => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 100010 => 000101 => 0
[1,1,1,0,1,0,0,1,0,0] => [3,1] => 10010 => 00101 => 0
[1,1,1,0,1,0,1,0,0,0] => [2,1] => 1010 => 0101 => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1] => 110 => 101 => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => 10000 => 00001 => 0
[1,1,1,1,0,0,0,1,0,0] => [3] => 1000 => 0001 => 0
[1,1,1,1,0,0,1,0,0,0] => [2] => 100 => 001 => 0
[1,1,1,1,0,1,0,0,0,0] => [1] => 10 => 01 => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 110101010 => 101010101 => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 1001101010 => 0011010101 => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 101101010 => 011010101 => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 11101010 => 11010101 => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 1010011010 => 0100110101 => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 110011010 => 100110101 => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 1001011010 => 0010110101 => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 101011010 => 010110101 => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 11011010 => 10110101 => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 1000111010 => 0001110101 => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 100111010 => 001110101 => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 10111010 => 01110101 => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1111010 => 1110101 => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 1010100110 => 0101001101 => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 110100110 => 101001101 => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 1001100110 => 0011001101 => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 101100110 => 011001101 => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 11100110 => 11001101 => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 1010010110 => 0100101101 => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 110010110 => 100101101 => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 1001010110 => 0010101101 => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 101010110 => 010101101 => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 11010110 => 10101101 => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 1000110110 => 0001101101 => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 100110110 => 001101101 => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 10110110 => 01101101 => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 1110110 => 1101101 => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 1010001110 => 0100011101 => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 110001110 => 100011101 => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 1001001110 => 0010011101 => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 101001110 => 010011101 => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 11001110 => 10011101 => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 1000101110 => 0001011101 => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 100101110 => 001011101 => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 10101110 => 01011101 => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1101110 => 1011101 => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 1000011110 => 0000111101 => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 100011110 => 000111101 => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 10011110 => 00111101 => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1011110 => 0111101 => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 111110 => 111101 => 4
>>> Load all 1208 entries. <<<[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 101010100 => 010101001 => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 11010100 => 10101001 => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 100110100 => 001101001 => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 10110100 => 01101001 => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1110100 => 1101001 => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 101001100 => 010011001 => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 11001100 => 10011001 => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 100101100 => 001011001 => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 10101100 => 01011001 => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 1101100 => 1011001 => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 100011100 => 000111001 => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 10011100 => 00111001 => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 1011100 => 0111001 => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 111100 => 111001 => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => 101010010 => 010100101 => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 11010010 => 10100101 => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 100110010 => 001100101 => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 10110010 => 01100101 => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 1110010 => 1100101 => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 101001010 => 010010101 => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 11001010 => 10010101 => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 100101010 => 001010101 => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 10101010 => 01010101 => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 1101010 => 1010101 => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 100011010 => 000110101 => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 10011010 => 00110101 => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 1011010 => 0110101 => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 111010 => 110101 => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 101000110 => 010001101 => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 11000110 => 10001101 => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 100100110 => 001001101 => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 10100110 => 01001101 => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 1100110 => 1001101 => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 100010110 => 000101101 => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 10010110 => 00101101 => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 1010110 => 0101101 => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 110110 => 101101 => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 100001110 => 000011101 => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 10001110 => 00011101 => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 1001110 => 0011101 => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 101110 => 011101 => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 11110 => 11101 => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 10101000 => 01010001 => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1101000 => 1010001 => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 10011000 => 00110001 => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 1011000 => 0110001 => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 111000 => 110001 => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 10100100 => 01001001 => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 1100100 => 1001001 => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 10010100 => 00101001 => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 1010100 => 0101001 => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 110100 => 101001 => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 10001100 => 00011001 => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 1001100 => 0011001 => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 101100 => 011001 => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 11100 => 11001 => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 10100010 => 01000101 => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 1100010 => 1000101 => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 10010010 => 00100101 => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 1010010 => 0100101 => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 110010 => 100101 => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 10001010 => 00010101 => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 1001010 => 0010101 => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 101010 => 010101 => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 11010 => 10101 => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 10000110 => 00001101 => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 1000110 => 0001101 => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 100110 => 001101 => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 10110 => 01101 => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1110 => 1101 => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1010000 => 0100001 => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 110000 => 100001 => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 1001000 => 0010001 => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 101000 => 010001 => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 11000 => 10001 => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 1000100 => 0001001 => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 100100 => 001001 => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 10100 => 01001 => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 1100 => 1001 => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1000010 => 0000101 => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 100010 => 000101 => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 10010 => 00101 => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1010 => 0101 => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 110 => 101 => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 100000 => 000001 => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 10000 => 00001 => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1000 => 0001 => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 100 => 001 => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 10 => 01 => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 101010101010 => 010101010101 => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 11010101010 => 10101010101 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 100110101010 => 001101010101 => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 101001101010 => 010011010101 => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2,1] => 100101101010 => 001011010101 => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 100011101010 => 000111010101 => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 111101010 => 111010101 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 101010011010 => 010100110101 => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 100110011010 => 001100110101 => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2,1] => 101001011010 => 010010110101 => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2,1] => 100101011010 => 001010110101 => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 100011011010 => 000110110101 => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 111011010 => 110110101 => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 101000111010 => 010001110101 => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 100100111010 => 001001110101 => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 100010111010 => 000101110101 => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 110111010 => 101110101 => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 100001111010 => 000011110101 => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 101111010 => 011110101 => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 11111010 => 11110101 => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 101010100110 => 010101001101 => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 100110100110 => 001101001101 => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 101001100110 => 010011001101 => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1,1] => 100101100110 => 001011001101 => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 100011100110 => 000111001101 => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 111100110 => 111001101 => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,1] => 101010010110 => 010100101101 => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1,1] => 100110010110 => 001100101101 => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,1] => 101001010110 => 010010101101 => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => 100101010110 => 001010101101 => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 100011010110 => 000110101101 => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 111010110 => 110101101 => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 101000110110 => 010001101101 => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 100100110110 => 001001101101 => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 100010110110 => 000101101101 => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 110110110 => 101101101 => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 100001110110 => 000011101101 => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 101110110 => 011101101 => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 11110110 => 11101101 => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 101010001110 => 010100011101 => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 100110001110 => 001100011101 => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => 101001001110 => 010010011101 => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => 100101001110 => 001010011101 => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 100011001110 => 000110011101 => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 111001110 => 110011101 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => 101000101110 => 010001011101 => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => 100100101110 => 001001011101 => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => 100010101110 => 000101011101 => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 110101110 => 101011101 => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 100001101110 => 000011011101 => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 101101110 => 011011101 => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 11101110 => 11011101 => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 101000011110 => 010000111101 => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => 100100011110 => 001000111101 => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => 100010011110 => 000100111101 => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 110011110 => 100111101 => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 100001011110 => 000010111101 => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 1001011110 => 0010111101 => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 101011110 => 010111101 => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 11011110 => 10111101 => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 100000111110 => 000001111101 => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 10000111110 => 00001111101 => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 1000111110 => 0001111101 => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 100111110 => 001111101 => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 10111110 => 01111101 => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1111110 => 1111101 => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 10101010100 => 01010101001 => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 1101010100 => 1010101001 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2] => 1011010100 => 0110101001 => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 111010100 => 110101001 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1100110100 => 1001101001 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 1010110100 => 0101101001 => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 110110100 => 101101001 => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 101110100 => 011101001 => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 11110100 => 11101001 => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1101001100 => 1010011001 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 1011001100 => 0110011001 => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 111001100 => 110011001 => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 1100101100 => 1001011001 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 1010101100 => 0101011001 => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 110101100 => 101011001 => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 101101100 => 011011001 => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 11101100 => 11011001 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 110011100 => 100111001 => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 101011100 => 010111001 => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 11011100 => 10111001 => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 1000111100 => 0001111001 => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 100111100 => 001111001 => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 10111100 => 01111001 => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1111100 => 1111001 => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => 10101010010 => 01010100101 => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1] => 1101010010 => 1010100101 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 1011010010 => 0110100101 => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 111010010 => 110100101 => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 1100110010 => 1001100101 => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 1010110010 => 0101100101 => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 110110010 => 101100101 => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 101110010 => 011100101 => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 11110010 => 11100101 => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1] => 10101001010 => 01010010101 => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => 1101001010 => 1010010101 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 1011001010 => 0110010101 => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 111001010 => 110010101 => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => 10100101010 => 01001010101 => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => 1100101010 => 1001010101 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 110101010 => 101010101 => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 1001101010 => 0011010101 => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 101101010 => 011010101 => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 11101010 => 11010101 => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 1010011010 => 0100110101 => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 110011010 => 100110101 => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 1001011010 => 0010110101 => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 101011010 => 010110101 => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 11011010 => 10110101 => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 1000111010 => 0001110101 => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 100111010 => 001110101 => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 10111010 => 01110101 => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1111010 => 1110101 => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 111000110 => 110001101 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 1010100110 => 0101001101 => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 110100110 => 101001101 => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 1001100110 => 0011001101 => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 101100110 => 011001101 => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 11100110 => 11001101 => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 1010010110 => 0100101101 => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 110010110 => 100101101 => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 1001010110 => 0010101101 => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 101010110 => 010101101 => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 11010110 => 10101101 => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1000110110 => 0001101101 => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 100110110 => 001101101 => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 10110110 => 01101101 => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 1110110 => 1101101 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 1010001110 => 0100011101 => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 110001110 => 100011101 => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 1001001110 => 0010011101 => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 101001110 => 010011101 => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 11001110 => 10011101 => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 1000101110 => 0001011101 => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 100101110 => 001011101 => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 10101110 => 01011101 => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 1101110 => 1011101 => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 10000011110 => 00000111101 => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 1000011110 => 0000111101 => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 100011110 => 000111101 => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 10011110 => 00111101 => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 1011110 => 0111101 => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 111110 => 111101 => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 110101000 => 101010001 => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 101101000 => 011010001 => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 11101000 => 11010001 => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 110011000 => 100110001 => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 1001011000 => 0010110001 => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 101011000 => 010110001 => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 11011000 => 10110001 => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1000111000 => 0001110001 => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 100111000 => 001110001 => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 10111000 => 01110001 => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1111000 => 1110001 => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => 110100100 => 101001001 => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 101100100 => 011001001 => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 11100100 => 11001001 => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => 110010100 => 100101001 => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => 1001010100 => 0010101001 => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 101010100 => 010101001 => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 11010100 => 10101001 => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => 1000110100 => 0001101001 => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 100110100 => 001101001 => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 10110100 => 01101001 => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1110100 => 1101001 => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 110001100 => 100011001 => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => 1001001100 => 0010011001 => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 101001100 => 010011001 => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 11001100 => 10011001 => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => 1000101100 => 0001011001 => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 100101100 => 001011001 => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 10101100 => 01011001 => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 1101100 => 1011001 => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 1000011100 => 0000111001 => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 100011100 => 000111001 => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 10011100 => 00111001 => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1011100 => 0111001 => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 111100 => 111001 => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => 110100010 => 101000101 => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 101100010 => 011000101 => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 11100010 => 11000101 => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => 110010010 => 100100101 => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => 1001010010 => 0010100101 => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 101010010 => 010100101 => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 11010010 => 10100101 => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => 1000110010 => 0001100101 => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 100110010 => 001100101 => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 10110010 => 01100101 => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1110010 => 1100101 => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => 110001010 => 100010101 => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => 1001001010 => 0010010101 => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 101001010 => 010010101 => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 11001010 => 10010101 => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 1000101010 => 0001010101 => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 100101010 => 001010101 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 10101010 => 01010101 => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 1101010 => 1010101 => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 100011010 => 000110101 => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 10011010 => 00110101 => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 1011010 => 0110101 => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 111010 => 110101 => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 110000110 => 100001101 => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 1001000110 => 0010001101 => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 101000110 => 010001101 => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 11000110 => 10001101 => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 100100110 => 001001101 => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 10100110 => 01001101 => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 1100110 => 1001101 => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 1000010110 => 0000101101 => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 100010110 => 000101101 => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 10010110 => 00101101 => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 1010110 => 0101101 => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 110110 => 101101 => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 1000001110 => 0000011101 => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 100001110 => 000011101 => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 10001110 => 00011101 => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1001110 => 0011101 => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 101110 => 011101 => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 11110 => 11101 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 101010000 => 010100001 => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 11010000 => 10100001 => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 100110000 => 001100001 => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 10110000 => 01100001 => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1110000 => 1100001 => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => 101001000 => 010010001 => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 11001000 => 10010001 => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => 100101000 => 001010001 => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 10101000 => 01010001 => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 1101000 => 1010001 => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 100011000 => 000110001 => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 10011000 => 00110001 => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1011000 => 0110001 => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 111000 => 110001 => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => 101000100 => 010001001 => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 11000100 => 10001001 => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 100100100 => 001001001 => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 10100100 => 01001001 => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1100100 => 1001001 => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 100010100 => 000101001 => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 10010100 => 00101001 => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 1010100 => 0101001 => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 110100 => 101001 => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 100001100 => 000011001 => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 10001100 => 00011001 => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 1001100 => 0011001 => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 101100 => 011001 => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 11100 => 11001 => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 101000010 => 010000101 => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 11000010 => 10000101 => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 100100010 => 001000101 => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 10100010 => 01000101 => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1100010 => 1000101 => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 100010010 => 000100101 => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 10010010 => 00100101 => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 1010010 => 0100101 => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 110010 => 100101 => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 100001010 => 000010101 => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 10001010 => 00010101 => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 1001010 => 0010101 => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 101010 => 010101 => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 11010 => 10101 => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 100000110 => 000001101 => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 10000110 => 00001101 => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 1000110 => 0001101 => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 100110 => 001101 => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 10110 => 01101 => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 1110 => 1101 => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 10100000 => 01000001 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1100000 => 1000001 => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 10010000 => 00100001 => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1010000 => 0100001 => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 110000 => 100001 => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 10001000 => 00010001 => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 1001000 => 0010001 => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 101000 => 010001 => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 11000 => 10001 => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 10000100 => 00001001 => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1000100 => 0001001 => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 100100 => 001001 => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 10100 => 01001 => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 1100 => 1001 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 10000010 => 00000101 => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1000010 => 0000101 => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 100010 => 000101 => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 10010 => 00101 => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1010 => 0101 => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 110 => 101 => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1000000 => 0000001 => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 100000 => 000001 => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 10000 => 00001 => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1000 => 0001 => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 100 => 001 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 10 => 01 => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 111111010 => 111110101 => 5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 111110110 => 111101101 => 4
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 111101110 => 111011101 => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 111011110 => 110111101 => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1010111110 => 0101111101 => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 110111110 => 101111101 => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 10001111110 => 00011111101 => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1001111110 => 0011111101 => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 101111110 => 011111101 => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 11111110 => 11111101 => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2] => 110101010100 => 101010101001 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2] => 101101010100 => 011010101001 => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2] => 101011010100 => 010110101001 => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2] => 101010110100 => 010101101001 => 0
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,2] => 1011110100 => 0111101001 => 0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 111110100 => 111101001 => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2] => 101010101100 => 010101011001 => 0
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 111101100 => 111011001 => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 111011100 => 110111001 => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 110111100 => 101111001 => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 101111100 => 011111001 => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 11111100 => 11111001 => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1] => 110101010010 => 101010100101 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1] => 101101010010 => 011010100101 => 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 111110010 => 111100101 => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,6,5,3,2,1] => 110100101010 => 101001010101 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,6,4,3,2,1] => 110010101010 => 100101010101 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => 101010101010 => 010101010101 => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 11010101010 => 10101010101 => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => 100110101010 => 001101010101 => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => 101001101010 => 010011010101 => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,1] => 100101101010 => 001011010101 => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 100011101010 => 000111010101 => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 111101010 => 111010101 => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => 101010011010 => 010100110101 => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 100110011010 => 001100110101 => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,1] => 101001011010 => 010010110101 => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,1] => 100101011010 => 001010110101 => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 100011011010 => 000110110101 => 0
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 111011010 => 110110101 => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 101000111010 => 010001110101 => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => 100100111010 => 001001110101 => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => 100010111010 => 000101110101 => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 110111010 => 101110101 => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 100001111010 => 000011110101 => 0
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 101111010 => 011110101 => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 11111010 => 11110101 => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => 101010100110 => 010101001101 => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 100110100110 => 001101001101 => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 101001100110 => 010011001101 => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1,1] => 100101100110 => 001011001101 => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 100011100110 => 000111001101 => 0
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 111100110 => 111001101 => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1] => 101010010110 => 010100101101 => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1,1] => 100110010110 => 001100101101 => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1] => 101001010110 => 010010101101 => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => 100101010110 => 001010101101 => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 100011010110 => 000110101101 => 0
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 111010110 => 110101101 => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => 101000110110 => 010001101101 => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 100100110110 => 001001101101 => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 100010110110 => 000101101101 => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 110110110 => 101101101 => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 100001110110 => 000011101101 => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 101110110 => 011101101 => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 11110110 => 11101101 => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => 101010001110 => 010100011101 => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 100110001110 => 001100011101 => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => 101001001110 => 010010011101 => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => 100101001110 => 001010011101 => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 100011001110 => 000110011101 => 0
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 111001110 => 110011101 => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => 101000101110 => 010001011101 => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => 100100101110 => 001001011101 => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => 100010101110 => 000101011101 => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 110101110 => 101011101 => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => 100001101110 => 000011011101 => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 101101110 => 011011101 => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 11101110 => 11011101 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => 101000011110 => 010000111101 => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => 100100011110 => 001000111101 => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => 100010011110 => 000100111101 => 0
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 110011110 => 100111101 => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 100001011110 => 000010111101 => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 1001011110 => 0010111101 => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 101011110 => 010111101 => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 11011110 => 10111101 => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 100000111110 => 000001111101 => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 10000111110 => 00001111101 => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 1000111110 => 0001111101 => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 100111110 => 001111101 => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 10111110 => 01111101 => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1111110 => 1111101 => 5
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3] => 1011101000 => 0111010001 => 0
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3] => 1010111000 => 0101110001 => 0
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 110111000 => 101110001 => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 101111000 => 011110001 => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 11111000 => 11110001 => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 111100100 => 111001001 => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => 10101010100 => 01010101001 => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 1101010100 => 1010101001 => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2] => 1011010100 => 0110101001 => 0
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 111010100 => 110101001 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 1100110100 => 1001101001 => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 1010110100 => 0101101001 => 0
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 110110100 => 101101001 => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 101110100 => 011101001 => 0
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 11110100 => 11101001 => 3
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 1101001100 => 1010011001 => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 1011001100 => 0110011001 => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 111001100 => 110011001 => 2
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 1100101100 => 1001011001 => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 1010101100 => 0101011001 => 0
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 110101100 => 101011001 => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 101101100 => 011011001 => 0
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 11101100 => 11011001 => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 110011100 => 100111001 => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 101011100 => 010111001 => 0
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 11011100 => 10111001 => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 1000111100 => 0001111001 => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 100111100 => 001111001 => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 10111100 => 01111001 => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 1111100 => 1111001 => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 111100010 => 111000101 => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => 10101010010 => 01010100101 => 0
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1] => 1101010010 => 1010100101 => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 1011010010 => 0110100101 => 0
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 111010010 => 110100101 => 2
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 1100110010 => 1001100101 => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 1010110010 => 0101100101 => 0
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 110110010 => 101100101 => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 101110010 => 011100101 => 0
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 11110010 => 11100101 => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1] => 10101001010 => 01010010101 => 0
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => 1101001010 => 1010010101 => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 1011001010 => 0110010101 => 0
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => 111001010 => 110010101 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => 10100101010 => 01001010101 => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => 1100101010 => 1001010101 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 110101010 => 101010101 => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 1001101010 => 0011010101 => 0
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 101101010 => 011010101 => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 11101010 => 11010101 => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 1010011010 => 0100110101 => 0
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 110011010 => 100110101 => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 1001011010 => 0010110101 => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 101011010 => 010110101 => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 11011010 => 10110101 => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 1000111010 => 0001110101 => 0
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 100111010 => 001110101 => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 10111010 => 01110101 => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1111010 => 1110101 => 3
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 111000110 => 110001101 => 2
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => 1010100110 => 0101001101 => 0
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 110100110 => 101001101 => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 1001100110 => 0011001101 => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 101100110 => 011001101 => 0
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 11100110 => 11001101 => 2
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 1010010110 => 0100101101 => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 110010110 => 100101101 => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 1001010110 => 0010101101 => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 101010110 => 010101101 => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 11010110 => 10101101 => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 1000110110 => 0001101101 => 0
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 100110110 => 001101101 => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 10110110 => 01101101 => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 1110110 => 1101101 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 1010001110 => 0100011101 => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 110001110 => 100011101 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 1001001110 => 0010011101 => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 101001110 => 010011101 => 0
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 11001110 => 10011101 => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 1000101110 => 0001011101 => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 100101110 => 001011101 => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 10101110 => 01011101 => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 1101110 => 1011101 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 10000011110 => 00000111101 => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 1000011110 => 0000111101 => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 100011110 => 000111101 => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 10011110 => 00111101 => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 1011110 => 0111101 => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 111110 => 111101 => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4] => 1011010000 => 0110100001 => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 101110000 => 011100001 => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 11110000 => 11100001 => 3
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => 110101000 => 101010001 => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 101101000 => 011010001 => 0
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 11101000 => 11010001 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 110011000 => 100110001 => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 1001011000 => 0010110001 => 0
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 101011000 => 010110001 => 0
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 11011000 => 10110001 => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 1000111000 => 0001110001 => 0
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 100111000 => 001110001 => 0
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 10111000 => 01110001 => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 1111000 => 1110001 => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2] => 10101000100 => 01010001001 => 0
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 111000100 => 110001001 => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => 110100100 => 101001001 => 1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 101100100 => 011001001 => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 11100100 => 11001001 => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => 10010010100 => 00100101001 => 0
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => 110010100 => 100101001 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => 1001010100 => 0010101001 => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 101010100 => 010101001 => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 11010100 => 10101001 => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => 1000110100 => 0001101001 => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 100110100 => 001101001 => 0
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 10110100 => 01101001 => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1110100 => 1101001 => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 110001100 => 100011001 => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => 1001001100 => 0010011001 => 0
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 101001100 => 010011001 => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 11001100 => 10011001 => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => 1000101100 => 0001011001 => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 100101100 => 001011001 => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 10101100 => 01011001 => 0
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 1101100 => 1011001 => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 1000011100 => 0000111001 => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 100011100 => 000111001 => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 10011100 => 00111001 => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1011100 => 0111001 => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 111100 => 111001 => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 111000010 => 110000101 => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1] => 10010100010 => 00101000101 => 0
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => 110100010 => 101000101 => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 101100010 => 011000101 => 0
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 11100010 => 11000101 => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1] => 10100010010 => 01000100101 => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => 10010010010 => 00100100101 => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => 110010010 => 100100101 => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => 1001010010 => 0010100101 => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 101010010 => 010100101 => 0
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 11010010 => 10100101 => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => 1000110010 => 0001100101 => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 100110010 => 001100101 => 0
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 10110010 => 01100101 => 0
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1110010 => 1100101 => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => 10010001010 => 00100010101 => 0
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => 110001010 => 100010101 => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => 1001001010 => 0010010101 => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 101001010 => 010010101 => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 11001010 => 10010101 => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 1000101010 => 0001010101 => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 100101010 => 001010101 => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 10101010 => 01010101 => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 1101010 => 1010101 => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 100011010 => 000110101 => 0
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 10011010 => 00110101 => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 1011010 => 0110101 => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 111010 => 110101 => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 110000110 => 100001101 => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 1001000110 => 0010001101 => 0
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 101000110 => 010001101 => 0
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 11000110 => 10001101 => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 100100110 => 001001101 => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 10100110 => 01001101 => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 1100110 => 1001101 => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 1000010110 => 0000101101 => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 100010110 => 000101101 => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 10010110 => 00101101 => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 1010110 => 0101101 => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 110110 => 101101 => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 10000001110 => 00000011101 => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 1000001110 => 0000011101 => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 100001110 => 000011101 => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 10001110 => 00011101 => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 1001110 => 0011101 => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 101110 => 011101 => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 11110 => 11101 => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => 110100000 => 101000001 => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 101100000 => 011000001 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 11100000 => 11000001 => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 110010000 => 100100001 => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => 101010000 => 010100001 => 0
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 11010000 => 10100001 => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 100110000 => 001100001 => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 10110000 => 01100001 => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 1110000 => 1100001 => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 110001000 => 100010001 => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => 101001000 => 010010001 => 0
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 11001000 => 10010001 => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => 100101000 => 001010001 => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 10101000 => 01010001 => 0
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 1101000 => 1010001 => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 100011000 => 000110001 => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 10011000 => 00110001 => 0
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1011000 => 0110001 => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 111000 => 110001 => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 110000100 => 100001001 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => 101000100 => 010001001 => 0
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 11000100 => 10001001 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 100100100 => 001001001 => 0
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 10100100 => 01001001 => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1100100 => 1001001 => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 100010100 => 000101001 => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 10010100 => 00101001 => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 1010100 => 0101001 => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 110100 => 101001 => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 100001100 => 000011001 => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 10001100 => 00011001 => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 1001100 => 0011001 => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 101100 => 011001 => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 11100 => 11001 => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => 1010000010 => 0100000101 => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 110000010 => 100000101 => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 101000010 => 010000101 => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 11000010 => 10000101 => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 100100010 => 001000101 => 0
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 10100010 => 01000101 => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 1100010 => 1000101 => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 100010010 => 000100101 => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 10010010 => 00100101 => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 1010010 => 0100101 => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 110010 => 100101 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1000001010 => 0000010101 => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 100001010 => 000010101 => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 10001010 => 00010101 => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 1001010 => 0010101 => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 101010 => 010101 => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 11010 => 10101 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 1000000110 => 0000001101 => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 100000110 => 000001101 => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 10000110 => 00001101 => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 1000110 => 0001101 => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 100110 => 001101 => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 10110 => 01101 => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 1110 => 1101 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => 101000000 => 010000001 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 11000000 => 10000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 100100000 => 001000001 => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 10100000 => 01000001 => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 1100000 => 1000001 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 100010000 => 000100001 => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 10010000 => 00100001 => 0
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1010000 => 0100001 => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 110000 => 100001 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 100001000 => 000010001 => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 10001000 => 00010001 => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 1001000 => 0010001 => 0
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 101000 => 010001 => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 11000 => 10001 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 100000100 => 000001001 => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 10000100 => 00001001 => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 1000100 => 0001001 => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 100100 => 001001 => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 10100 => 01001 => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 1100 => 1001 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 100000010 => 000000101 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 10000010 => 00000101 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 1000010 => 0000101 => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 100010 => 000101 => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 10010 => 00101 => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1010 => 0101 => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 110 => 101 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 10000000 => 00000001 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1000000 => 0000001 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 100000 => 000001 => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 10000 => 00001 => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1000 => 0001 => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 100 => 001 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 10 => 01 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 100000000 => 000000001 => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 111111110 => 111111101 => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1000000000 => 0000000001 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1000000010 => 0000000101 => 0
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 1011111110 => 0111111101 => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 1111111101 => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 10000000000 => 00000000001 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 10000000010 => 00000000101 => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 1000000100 => 0000001001 => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 10000000110 => 00000001101 => 0
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => 10011111110 => 00111111101 => 0
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => 1101111110 => 1011111101 => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => 10111111110 => 01111111101 => 0
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 11111111101 => 9
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => 1000010000 => 0000100001 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => 1001000000 => 0010000001 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 110000000 => 100000001 => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 111111100 => 111111001 => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => 10001001000 => 00010010001 => 0
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 111111010 => 111110101 => 5
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 111110110 => 111101101 => 4
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 111011110 => 110111101 => 2
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1010111110 => 0101111101 => 0
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 110111110 => 101111101 => 1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => 10001111110 => 00011111101 => 0
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1001111110 => 0011111101 => 0
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 101111110 => 011111101 => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 11111110 => 11111101 => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2] => 110101010100 => 101010101001 => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4,3,2] => 101101010100 => 011010101001 => 0
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,4,3,2] => 101011010100 => 010110101001 => 0
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,2] => 1011110100 => 0111101001 => 0
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2] => 111110100 => 111101001 => 4
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,2] => 101010101100 => 010101011001 => 0
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => 110111100 => 101111001 => 1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => 101111100 => 011111001 => 0
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 11111100 => 11111001 => 5
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4,3,1] => 101101010010 => 011010100101 => 0
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1] => 111110010 => 111100101 => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,6,4,3,2,1] => 110010101010 => 100101010101 => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1] => 101010101010 => 010101010101 => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2,1] => 11010101010 => 10101010101 => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,2,1] => 100110101010 => 001101010101 => 0
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => 111101010 => 111010101 => 3
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,2,1] => 100101011010 => 001010110101 => 0
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,1] => 101000111010 => 010001110101 => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,2,2,1] => 100010111010 => 000101110101 => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1] => 100001111010 => 000011110101 => 0
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 11111010 => 11110101 => 4
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1] => 101010100110 => 010101001101 => 0
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,1,1] => 100110100110 => 001101001101 => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,1] => 101001010110 => 010010101101 => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,1] => 100101010110 => 001010101101 => 0
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => 11110110 => 11101101 => 3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1] => 101010001110 => 010100011101 => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1,1,1] => 101000101110 => 010001011101 => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,1,1] => 100100101110 => 001001011101 => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1] => 100010101110 => 000101011101 => 0
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => 110101110 => 101011101 => 1
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 11101110 => 11011101 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1] => 101000011110 => 010000111101 => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => 100001011110 => 000010111101 => 0
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 101011110 => 010111101 => 0
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 11011110 => 10111101 => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => 100000111110 => 000001111101 => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => 10000111110 => 00001111101 => 0
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => 1000111110 => 0001111101 => 0
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => 100111110 => 001111101 => 0
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 10111110 => 01111101 => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1111110 => 1111101 => 5
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => 101111000 => 011110001 => 0
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => 11111000 => 11110001 => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2] => 10101010100 => 01010101001 => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2] => 1101010100 => 1010101001 => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2] => 1011010100 => 0110101001 => 0
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => 111010100 => 110101001 => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,2] => 1100110100 => 1001101001 => 1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => 110110100 => 101101001 => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2] => 1010101100 => 0101011001 => 0
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2] => 101011100 => 010111001 => 0
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => 100111100 => 001111001 => 0
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => 10111100 => 01111001 => 0
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => 1111100 => 1111001 => 4
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,1] => 111100010 => 111000101 => 3
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1] => 10101010010 => 01010100101 => 0
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,1] => 1011010010 => 0110100101 => 0
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => 11110010 => 11100101 => 3
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1] => 10101001010 => 01010010101 => 0
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,4,4,2,1] => 111001010 => 110010101 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1] => 10100101010 => 01001010101 => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1] => 1100101010 => 1001010101 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => 110101010 => 101010101 => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => 1001101010 => 0011010101 => 0
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => 101101010 => 011010101 => 0
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => 11101010 => 11010101 => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => 1010011010 => 0100110101 => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => 1001011010 => 0010110101 => 0
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => 101011010 => 010110101 => 0
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => 10111010 => 01110101 => 0
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 1111010 => 1110101 => 3
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => 110100110 => 101001101 => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => 1010010110 => 0100101101 => 0
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => 101010110 => 010101101 => 0
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 10110110 => 01101101 => 0
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 1110110 => 1101101 => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => 1010001110 => 0100011101 => 0
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => 110001110 => 100011101 => 1
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => 101001110 => 010011101 => 0
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 11001110 => 10011101 => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => 1000101110 => 0001011101 => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 10101110 => 01011101 => 0
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 1101110 => 1011101 => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => 10000011110 => 00000111101 => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 1000011110 => 0000111101 => 0
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => 1011110 => 0111101 => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 111110 => 111101 => 4
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4] => 1011010000 => 0110100001 => 0
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => 11110000 => 11100001 => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => 110101000 => 101010001 => 1
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => 11101000 => 11010001 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => 110011000 => 100110001 => 1
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => 10111000 => 01110001 => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2] => 1001010100 => 0010101001 => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => 101010100 => 010101001 => 0
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => 11010100 => 10101001 => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,3,2] => 1000110100 => 0001101001 => 0
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => 11001100 => 10011001 => 1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => 1101100 => 1011001 => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => 100011100 => 000111001 => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5,1] => 111000010 => 110000101 => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1] => 10010010010 => 00100100101 => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => 101010010 => 010100101 => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => 1000110010 => 0001100101 => 0
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => 10110010 => 01100101 => 0
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => 1110010 => 1100101 => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1] => 10010001010 => 00100010101 => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => 101001010 => 010010101 => 0
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => 11001010 => 10010101 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => 1000101010 => 0001010101 => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => 100101010 => 001010101 => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 10101010 => 01010101 => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 1101010 => 1010101 => 1
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 10011010 => 00110101 => 0
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 1011010 => 0110101 => 0
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 111010 => 110101 => 2
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 10100110 => 01001101 => 0
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 1100110 => 1001101 => 1
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 10010110 => 00101101 => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 1010110 => 0101101 => 0
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 110110 => 101101 => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => 10000001110 => 00000011101 => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => 1000001110 => 0000011101 => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => 100001110 => 000011101 => 0
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 10001110 => 00011101 => 0
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => 1001110 => 0011101 => 0
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => 101110 => 011101 => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 11110 => 11101 => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,6,5] => 110100000 => 101000001 => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => 101100000 => 011000001 => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => 11100000 => 11000001 => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => 10110000 => 01100001 => 0
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => 1110000 => 1100001 => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => 10101000 => 01010001 => 0
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => 1101000 => 1010001 => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => 100011000 => 000110001 => 0
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => 1011000 => 0110001 => 0
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 111000 => 110001 => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => 100100100 => 001001001 => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => 10100100 => 01001001 => 0
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => 1100100 => 1001001 => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => 10010100 => 00101001 => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 1010100 => 0101001 => 0
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 110100 => 101001 => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 1001100 => 0011001 => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 101100 => 011001 => 0
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 11100 => 11001 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1] => 1010000010 => 0100000101 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => 110000010 => 100000101 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => 101000010 => 010000101 => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => 10100010 => 01000101 => 0
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 1100010 => 1000101 => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => 100010010 => 000100101 => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 10010010 => 00100101 => 0
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 1010010 => 0100101 => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 110010 => 100101 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => 1000001010 => 0000010101 => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 100001010 => 000010101 => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 10001010 => 00010101 => 0
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 1001010 => 0010101 => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 101010 => 010101 => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 11010 => 10101 => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 1000000110 => 0000001101 => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => 100000110 => 000001101 => 0
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 1000110 => 0001101 => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 100110 => 001101 => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 10110 => 01101 => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 1110 => 1101 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => 101000000 => 010000001 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 11000000 => 10000001 => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => 100100000 => 001000001 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => 1100000 => 1000001 => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => 110000 => 100001 => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => 100001000 => 000010001 => 0
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 101000 => 010001 => 0
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 11000 => 10001 => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 100000100 => 000001001 => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 100100 => 001001 => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 10100 => 01001 => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 1100 => 1001 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 100000010 => 000000101 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => 10000010 => 00000101 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => 1000010 => 0000101 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => 100010 => 000101 => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 10010 => 00101 => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1010 => 0101 => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 110 => 101 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 10000000 => 00000001 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1000000 => 0000001 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 100000 => 000001 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 10000 => 00001 => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1000 => 0001 => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 100 => 001 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 10 => 01 => 0
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 111111000 => 111110001 => 5
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 111110000 => 111100001 => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 111100000 => 111000001 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 111000000 => 110000001 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5,5,5,5] => 1111100000 => 1111000001 => 4
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => 110101010 => 101010101 => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => 101010100 => 010101001 => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,5,4,3,2,1] => 11010101010 => 10101010101 => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2,1] => 11010101010 => 10101010101 => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2] => 10101010100 => 01010101001 => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2] => 10101010100 => 01010101001 => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => 110 => 101 => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 100 => 001 => 0
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => 110 => 101 => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => 11010 => 10101 => 1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 10100 => 01001 => 0
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 100 => 001 => 0
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 111111110 => 111111101 => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 100000000 => 000000001 => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 1000000000 => 0000000001 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 1000000010 => 0000000101 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 10 => 01 => 0
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => 1110 => 1101 => 2
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => 11110 => 11101 => 3
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 111110 => 111101 => 4
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1111110 => 1111101 => 5
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 11111110 => 11111101 => 6
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 10 => 01 => 0
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5,1] => 1111000010 => 1110000101 => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1] => 101010101010 => 010101010101 => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,4,4,4] => 1011110000 => 0111100001 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 10000000 => 00000001 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,5,5] => 1011100000 => 0111000001 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 1000000 => 0000001 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 100000 => 000001 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 10000 => 00001 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 1000 => 0001 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => 10000000010 => 00000000101 => 0
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => 10111111110 => 01111111101 => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => 1100 => 1001 => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 11000 => 10001 => 1
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 111000 => 110001 => 2
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => 1110000 => 1100001 => 2
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => 11110000 => 11100001 => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,5,5,5] => 111100000 => 111000001 => 3
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => 10110 => 01101 => 0
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 1011111110 => 0111111101 => 0
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 1111111101 => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => 10000000110 => 00000001101 => 0
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => 10011111110 => 00111111101 => 0
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => 1101111110 => 1011111101 => 1
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 11111111101 => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 1010100 => 0101001 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 10010 => 00101 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [6,6,6] => 111000000 => 110000001 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => 11000000 => 10000001 => 1
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 10111110 => 01111101 => 0
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => 100111110 => 001111101 => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => 1000111110 => 0001111101 => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => 10000111110 => 00001111101 => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1010 => 0101 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 1010 => 0101 => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 10101010 => 01010101 => 0
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 101010 => 010101 => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 1000 => 0001 => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => 1000001010 => 0000010101 => 0
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1010111110 => 0101111101 => 0
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => 111101010 => 111010101 => 3
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 111111010 => 111110101 => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => 110000000 => 100000001 => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4] => 111110000 => 111100001 => 4
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3] => 111111000 => 111110001 => 5
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 111111100 => 111111001 => 6
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => 100000111110 => 000001111101 => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => 100101010 => 001010101 => 0
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => 101001010 => 010010101 => 0
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => 101010010 => 010100101 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => 10010 => 00101 => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => 100100 => 001001 => 0
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 11111010 => 11110101 => 4
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => 1000101010 => 0001010101 => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => 101101010 => 011010101 => 0
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => 101011010 => 010110101 => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => 101010110 => 010101101 => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2] => 1101010100 => 1010101001 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1] => 101010101010 => 010101010101 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [7,6,1] => 1010000010 => 0100000101 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => 101000010 => 010000101 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => 10100010 => 01000101 => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 1010010 => 0100101 => 0
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 11100 => 11001 => 2
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,2] => 1010101100 => 0101011001 => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1] => 10101010010 => 01010100101 => 0
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 11111100 => 11111001 => 5
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => 100000010 => 000000101 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => 10000010 => 00000101 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => 1000010 => 0000101 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 100010 => 000101 => 0
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => 101110 => 011101 => 0
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => 1011110 => 0111101 => 0
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 101111110 => 011111101 => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,1] => 101010100110 => 010101001101 => 0
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => 10110 => 01101 => 0
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => 1011010 => 0110101 => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1] => 10010010010 => 00100100101 => 0
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => 1110 => 1101 => 2
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1,1] => 100101010110 => 001010101101 => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1,1,1] => 100010101110 => 000101011101 => 0
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => 100110 => 001101 => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,6,5,4,3,2] => 110101010100 => 101010101001 => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,6,5,4,3,2] => 110101010100 => 101010101001 => 1
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 110110 => 101101 => 1
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 1010110 => 0101101 => 0
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => 1100 => 1001 => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => 1010101010 => 0101010101 => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => 11000 => 10001 => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => 1000 => 0001 => 0
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => 110 => 101 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,5,3,2,1] => 1100101010 => 1001010101 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [6,5,3,2,1] => 10100101010 => 01001010101 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => 1000000010 => 0000000101 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => 100000010 => 000000101 => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1,1,1,1] => 101000011110 => 010000111101 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => 10000010 => 00000101 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => 1000010 => 0000101 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => 100010 => 000101 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => 1100000 => 1000001 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 110000 => 100001 => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 10010010 => 00100101 => 0
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 111010 => 110101 => 2
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => 110100 => 101001 => 1
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Description
The number of leading ones in a binary word.
Map
rotate front-to-back
Description
The rotation of a binary word, first letter last.
This is the word obtained by moving the first letter to the end.
This is the word obtained by moving the first letter to the end.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi is the number of down-steps before the (n+1−i)-th up-step of D.
This map is a bijection between Dyck paths of size n and partitions inside the staircase partition (n−1,…,2,1).
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi is the number of down-steps before the (n+1−i)-th up-step of D.
This map is a bijection between Dyck paths of size n and partitions inside the staircase partition (n−1,…,2,1).
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.
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