Identifier
-
Mp00133:
Integer compositions
—delta morphism⟶
Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
St000392: Binary words ⟶ ℤ
Values
[1] => [1] => 1 => 0 => 0
[1,1] => [2] => 10 => 01 => 1
[2] => [1] => 1 => 0 => 0
[1,1,1] => [3] => 100 => 011 => 2
[1,2] => [1,1] => 11 => 00 => 0
[2,1] => [1,1] => 11 => 00 => 0
[3] => [1] => 1 => 0 => 0
[1,1,1,1] => [4] => 1000 => 0111 => 3
[1,1,2] => [2,1] => 101 => 010 => 1
[1,2,1] => [1,1,1] => 111 => 000 => 0
[1,3] => [1,1] => 11 => 00 => 0
[2,1,1] => [1,2] => 110 => 001 => 1
[2,2] => [2] => 10 => 01 => 1
[3,1] => [1,1] => 11 => 00 => 0
[4] => [1] => 1 => 0 => 0
[1,1,1,1,1] => [5] => 10000 => 01111 => 4
[1,1,1,2] => [3,1] => 1001 => 0110 => 2
[1,1,2,1] => [2,1,1] => 1011 => 0100 => 1
[1,1,3] => [2,1] => 101 => 010 => 1
[1,2,1,1] => [1,1,2] => 1110 => 0001 => 1
[1,2,2] => [1,2] => 110 => 001 => 1
[1,3,1] => [1,1,1] => 111 => 000 => 0
[1,4] => [1,1] => 11 => 00 => 0
[2,1,1,1] => [1,3] => 1100 => 0011 => 2
[2,1,2] => [1,1,1] => 111 => 000 => 0
[2,2,1] => [2,1] => 101 => 010 => 1
[2,3] => [1,1] => 11 => 00 => 0
[3,1,1] => [1,2] => 110 => 001 => 1
[3,2] => [1,1] => 11 => 00 => 0
[4,1] => [1,1] => 11 => 00 => 0
[5] => [1] => 1 => 0 => 0
[1,1,1,1,1,1] => [6] => 100000 => 011111 => 5
[1,1,1,1,2] => [4,1] => 10001 => 01110 => 3
[1,1,1,2,1] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,3] => [3,1] => 1001 => 0110 => 2
[1,1,2,1,1] => [2,1,2] => 10110 => 01001 => 1
[1,1,2,2] => [2,2] => 1010 => 0101 => 1
[1,1,3,1] => [2,1,1] => 1011 => 0100 => 1
[1,1,4] => [2,1] => 101 => 010 => 1
[1,2,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[1,2,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,2,1] => [1,2,1] => 1101 => 0010 => 1
[1,2,3] => [1,1,1] => 111 => 000 => 0
[1,3,1,1] => [1,1,2] => 1110 => 0001 => 1
[1,3,2] => [1,1,1] => 111 => 000 => 0
[1,4,1] => [1,1,1] => 111 => 000 => 0
[1,5] => [1,1] => 11 => 00 => 0
[2,1,1,1,1] => [1,4] => 11000 => 00111 => 3
[2,1,1,2] => [1,2,1] => 1101 => 0010 => 1
[2,1,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,3] => [1,1,1] => 111 => 000 => 0
[2,2,1,1] => [2,2] => 1010 => 0101 => 1
[2,2,2] => [3] => 100 => 011 => 2
[2,3,1] => [1,1,1] => 111 => 000 => 0
[2,4] => [1,1] => 11 => 00 => 0
[3,1,1,1] => [1,3] => 1100 => 0011 => 2
[3,1,2] => [1,1,1] => 111 => 000 => 0
[3,2,1] => [1,1,1] => 111 => 000 => 0
[3,3] => [2] => 10 => 01 => 1
[4,1,1] => [1,2] => 110 => 001 => 1
[4,2] => [1,1] => 11 => 00 => 0
[5,1] => [1,1] => 11 => 00 => 0
[6] => [1] => 1 => 0 => 0
[1,1,1,1,1,1,1] => [7] => 1000000 => 0111111 => 6
[1,1,1,1,1,2] => [5,1] => 100001 => 011110 => 4
[1,1,1,1,2,1] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,3] => [4,1] => 10001 => 01110 => 3
[1,1,1,2,1,1] => [3,1,2] => 100110 => 011001 => 2
[1,1,1,2,2] => [3,2] => 10010 => 01101 => 2
[1,1,1,3,1] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,4] => [3,1] => 1001 => 0110 => 2
[1,1,2,1,1,1] => [2,1,3] => 101100 => 010011 => 2
[1,1,2,1,2] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,2,2,1] => [2,2,1] => 10101 => 01010 => 1
[1,1,2,3] => [2,1,1] => 1011 => 0100 => 1
[1,1,3,1,1] => [2,1,2] => 10110 => 01001 => 1
[1,1,3,2] => [2,1,1] => 1011 => 0100 => 1
[1,1,4,1] => [2,1,1] => 1011 => 0100 => 1
[1,1,5] => [2,1] => 101 => 010 => 1
[1,2,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[1,2,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[1,2,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,3] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,2,1,1] => [1,2,2] => 11010 => 00101 => 1
[1,2,2,2] => [1,3] => 1100 => 0011 => 2
[1,2,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,4] => [1,1,1] => 111 => 000 => 0
[1,3,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[1,3,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,3] => [1,2] => 110 => 001 => 1
[1,4,1,1] => [1,1,2] => 1110 => 0001 => 1
[1,4,2] => [1,1,1] => 111 => 000 => 0
[1,5,1] => [1,1,1] => 111 => 000 => 0
[1,6] => [1,1] => 11 => 00 => 0
[2,1,1,1,1,1] => [1,5] => 110000 => 001111 => 4
[2,1,1,1,2] => [1,3,1] => 11001 => 00110 => 2
[2,1,1,2,1] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,1,3] => [1,2,1] => 1101 => 0010 => 1
[2,1,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[2,1,2,2] => [1,1,2] => 1110 => 0001 => 1
>>> Load all 2258 entries. <<<[2,1,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,4] => [1,1,1] => 111 => 000 => 0
[2,2,1,1,1] => [2,3] => 10100 => 01011 => 2
[2,2,1,2] => [2,1,1] => 1011 => 0100 => 1
[2,2,2,1] => [3,1] => 1001 => 0110 => 2
[2,2,3] => [2,1] => 101 => 010 => 1
[2,3,1,1] => [1,1,2] => 1110 => 0001 => 1
[2,3,2] => [1,1,1] => 111 => 000 => 0
[2,4,1] => [1,1,1] => 111 => 000 => 0
[2,5] => [1,1] => 11 => 00 => 0
[3,1,1,1,1] => [1,4] => 11000 => 00111 => 3
[3,1,1,2] => [1,2,1] => 1101 => 0010 => 1
[3,1,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[3,1,3] => [1,1,1] => 111 => 000 => 0
[3,2,1,1] => [1,1,2] => 1110 => 0001 => 1
[3,2,2] => [1,2] => 110 => 001 => 1
[3,3,1] => [2,1] => 101 => 010 => 1
[3,4] => [1,1] => 11 => 00 => 0
[4,1,1,1] => [1,3] => 1100 => 0011 => 2
[4,1,2] => [1,1,1] => 111 => 000 => 0
[4,2,1] => [1,1,1] => 111 => 000 => 0
[4,3] => [1,1] => 11 => 00 => 0
[5,1,1] => [1,2] => 110 => 001 => 1
[5,2] => [1,1] => 11 => 00 => 0
[6,1] => [1,1] => 11 => 00 => 0
[7] => [1] => 1 => 0 => 0
[1,1,1,1,1,1,1,1] => [8] => 10000000 => 01111111 => 7
[1,1,1,1,1,1,2] => [6,1] => 1000001 => 0111110 => 5
[1,1,1,1,1,2,1] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,3] => [5,1] => 100001 => 011110 => 4
[1,1,1,1,2,1,1] => [4,1,2] => 1000110 => 0111001 => 3
[1,1,1,1,2,2] => [4,2] => 100010 => 011101 => 3
[1,1,1,1,3,1] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,4] => [4,1] => 10001 => 01110 => 3
[1,1,1,2,1,1,1] => [3,1,3] => 1001100 => 0110011 => 2
[1,1,1,2,1,2] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,2,2,1] => [3,2,1] => 100101 => 011010 => 2
[1,1,1,2,3] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,3,1,1] => [3,1,2] => 100110 => 011001 => 2
[1,1,1,3,2] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,4,1] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,5] => [3,1] => 1001 => 0110 => 2
[1,1,2,1,1,1,1] => [2,1,4] => 1011000 => 0100111 => 3
[1,1,2,1,1,2] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,2,1,2,1] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,1,3] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,2,2,1,1] => [2,2,2] => 101010 => 010101 => 1
[1,1,2,2,2] => [2,3] => 10100 => 01011 => 2
[1,1,2,3,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,2,4] => [2,1,1] => 1011 => 0100 => 1
[1,1,3,1,1,1] => [2,1,3] => 101100 => 010011 => 2
[1,1,3,1,2] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,3,2,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,3,3] => [2,2] => 1010 => 0101 => 1
[1,1,4,1,1] => [2,1,2] => 10110 => 01001 => 1
[1,1,4,2] => [2,1,1] => 1011 => 0100 => 1
[1,1,5,1] => [2,1,1] => 1011 => 0100 => 1
[1,1,6] => [2,1] => 101 => 010 => 1
[1,2,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[1,2,1,1,1,2] => [1,1,3,1] => 111001 => 000110 => 2
[1,2,1,1,2,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,2,1,1,3] => [1,1,2,1] => 11101 => 00010 => 1
[1,2,1,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[1,2,1,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[1,2,1,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,4] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,2,1,1,1] => [1,2,3] => 110100 => 001011 => 2
[1,2,2,1,2] => [1,2,1,1] => 11011 => 00100 => 1
[1,2,2,2,1] => [1,3,1] => 11001 => 00110 => 2
[1,2,2,3] => [1,2,1] => 1101 => 0010 => 1
[1,2,3,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,2,3,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,5] => [1,1,1] => 111 => 000 => 0
[1,3,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[1,3,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[1,3,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,1,3] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,3,2,2] => [1,1,2] => 1110 => 0001 => 1
[1,3,3,1] => [1,2,1] => 1101 => 0010 => 1
[1,3,4] => [1,1,1] => 111 => 000 => 0
[1,4,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[1,4,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,4,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,4,3] => [1,1,1] => 111 => 000 => 0
[1,5,1,1] => [1,1,2] => 1110 => 0001 => 1
[1,5,2] => [1,1,1] => 111 => 000 => 0
[1,6,1] => [1,1,1] => 111 => 000 => 0
[1,7] => [1,1] => 11 => 00 => 0
[2,1,1,1,1,1,1] => [1,6] => 1100000 => 0011111 => 5
[2,1,1,1,1,2] => [1,4,1] => 110001 => 001110 => 3
[2,1,1,1,2,1] => [1,3,1,1] => 110011 => 001100 => 2
[2,1,1,1,3] => [1,3,1] => 11001 => 00110 => 2
[2,1,1,2,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[2,1,1,2,2] => [1,2,2] => 11010 => 00101 => 1
[2,1,1,3,1] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,1,4] => [1,2,1] => 1101 => 0010 => 1
[2,1,2,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[2,1,2,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[2,1,2,3] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,3,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[2,1,3,2] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,5] => [1,1,1] => 111 => 000 => 0
[2,2,1,1,1,1] => [2,4] => 101000 => 010111 => 3
[2,2,1,1,2] => [2,2,1] => 10101 => 01010 => 1
[2,2,1,2,1] => [2,1,1,1] => 10111 => 01000 => 1
[2,2,1,3] => [2,1,1] => 1011 => 0100 => 1
[2,2,2,1,1] => [3,2] => 10010 => 01101 => 2
[2,2,2,2] => [4] => 1000 => 0111 => 3
[2,2,3,1] => [2,1,1] => 1011 => 0100 => 1
[2,2,4] => [2,1] => 101 => 010 => 1
[2,3,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[2,3,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[2,3,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,3,3] => [1,2] => 110 => 001 => 1
[2,4,1,1] => [1,1,2] => 1110 => 0001 => 1
[2,4,2] => [1,1,1] => 111 => 000 => 0
[2,5,1] => [1,1,1] => 111 => 000 => 0
[2,6] => [1,1] => 11 => 00 => 0
[3,1,1,1,1,1] => [1,5] => 110000 => 001111 => 4
[3,1,1,1,2] => [1,3,1] => 11001 => 00110 => 2
[3,1,1,2,1] => [1,2,1,1] => 11011 => 00100 => 1
[3,1,1,3] => [1,2,1] => 1101 => 0010 => 1
[3,1,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[3,1,2,2] => [1,1,2] => 1110 => 0001 => 1
[3,1,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[3,1,4] => [1,1,1] => 111 => 000 => 0
[3,2,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[3,2,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[3,2,2,1] => [1,2,1] => 1101 => 0010 => 1
[3,2,3] => [1,1,1] => 111 => 000 => 0
[3,3,1,1] => [2,2] => 1010 => 0101 => 1
[3,3,2] => [2,1] => 101 => 010 => 1
[3,4,1] => [1,1,1] => 111 => 000 => 0
[3,5] => [1,1] => 11 => 00 => 0
[4,1,1,1,1] => [1,4] => 11000 => 00111 => 3
[4,1,1,2] => [1,2,1] => 1101 => 0010 => 1
[4,1,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[4,1,3] => [1,1,1] => 111 => 000 => 0
[4,2,1,1] => [1,1,2] => 1110 => 0001 => 1
[4,2,2] => [1,2] => 110 => 001 => 1
[4,3,1] => [1,1,1] => 111 => 000 => 0
[4,4] => [2] => 10 => 01 => 1
[5,1,1,1] => [1,3] => 1100 => 0011 => 2
[5,1,2] => [1,1,1] => 111 => 000 => 0
[5,2,1] => [1,1,1] => 111 => 000 => 0
[5,3] => [1,1] => 11 => 00 => 0
[6,1,1] => [1,2] => 110 => 001 => 1
[6,2] => [1,1] => 11 => 00 => 0
[7,1] => [1,1] => 11 => 00 => 0
[8] => [1] => 1 => 0 => 0
[1,1,1,1,1,1,1,1,1] => [9] => 100000000 => 011111111 => 8
[1,1,1,1,1,1,1,2] => [7,1] => 10000001 => 01111110 => 6
[1,1,1,1,1,1,2,1] => [6,1,1] => 10000011 => 01111100 => 5
[1,1,1,1,1,1,3] => [6,1] => 1000001 => 0111110 => 5
[1,1,1,1,1,2,1,1] => [5,1,2] => 10000110 => 01111001 => 4
[1,1,1,1,1,2,2] => [5,2] => 1000010 => 0111101 => 4
[1,1,1,1,1,3,1] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,4] => [5,1] => 100001 => 011110 => 4
[1,1,1,1,2,1,1,1] => [4,1,3] => 10001100 => 01110011 => 3
[1,1,1,1,2,1,2] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,2,2,1] => [4,2,1] => 1000101 => 0111010 => 3
[1,1,1,1,2,3] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,3,1,1] => [4,1,2] => 1000110 => 0111001 => 3
[1,1,1,1,3,2] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,4,1] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,5] => [4,1] => 10001 => 01110 => 3
[1,1,1,2,1,1,1,1] => [3,1,4] => 10011000 => 01100111 => 3
[1,1,1,2,1,1,2] => [3,1,2,1] => 1001101 => 0110010 => 2
[1,1,1,2,1,2,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,1,3] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,2,2,1,1] => [3,2,2] => 1001010 => 0110101 => 2
[1,1,1,2,2,2] => [3,3] => 100100 => 011011 => 2
[1,1,1,2,3,1] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,2,4] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,3,1,1,1] => [3,1,3] => 1001100 => 0110011 => 2
[1,1,1,3,1,2] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,3,2,1] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,3,3] => [3,2] => 10010 => 01101 => 2
[1,1,1,4,1,1] => [3,1,2] => 100110 => 011001 => 2
[1,1,1,4,2] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,5,1] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,6] => [3,1] => 1001 => 0110 => 2
[1,1,2,1,1,1,1,1] => [2,1,5] => 10110000 => 01001111 => 4
[1,1,2,1,1,1,2] => [2,1,3,1] => 1011001 => 0100110 => 2
[1,1,2,1,1,2,1] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,2,1,1,3] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,2,1,2,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[1,1,2,1,2,2] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,2,1,3,1] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,1,4] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,2,2,1,1,1] => [2,2,3] => 1010100 => 0101011 => 2
[1,1,2,2,1,2] => [2,2,1,1] => 101011 => 010100 => 1
[1,1,2,2,2,1] => [2,3,1] => 101001 => 010110 => 2
[1,1,2,2,3] => [2,2,1] => 10101 => 01010 => 1
[1,1,2,3,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,2,3,2] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,2,4,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,2,5] => [2,1,1] => 1011 => 0100 => 1
[1,1,3,1,1,1,1] => [2,1,4] => 1011000 => 0100111 => 3
[1,1,3,1,1,2] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,3,1,2,1] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,3,1,3] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,3,2,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,3,2,2] => [2,1,2] => 10110 => 01001 => 1
[1,1,3,3,1] => [2,2,1] => 10101 => 01010 => 1
[1,1,3,4] => [2,1,1] => 1011 => 0100 => 1
[1,1,4,1,1,1] => [2,1,3] => 101100 => 010011 => 2
[1,1,4,1,2] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,4,2,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,4,3] => [2,1,1] => 1011 => 0100 => 1
[1,1,5,1,1] => [2,1,2] => 10110 => 01001 => 1
[1,1,5,2] => [2,1,1] => 1011 => 0100 => 1
[1,1,6,1] => [2,1,1] => 1011 => 0100 => 1
[1,1,7] => [2,1] => 101 => 010 => 1
[1,2,1,1,1,1,1,1] => [1,1,6] => 11100000 => 00011111 => 5
[1,2,1,1,1,1,2] => [1,1,4,1] => 1110001 => 0001110 => 3
[1,2,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,2,1,1,1,3] => [1,1,3,1] => 111001 => 000110 => 2
[1,2,1,1,2,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[1,2,1,1,2,2] => [1,1,2,2] => 111010 => 000101 => 1
[1,2,1,1,3,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,2,1,1,4] => [1,1,2,1] => 11101 => 00010 => 1
[1,2,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,2,1,2,1,2] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,1,2,2,1] => [1,1,1,2,1] => 111101 => 000010 => 1
[1,2,1,2,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,3,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[1,2,1,3,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,5] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,2,1,1,1,1] => [1,2,4] => 1101000 => 0010111 => 3
[1,2,2,1,1,2] => [1,2,2,1] => 110101 => 001010 => 1
[1,2,2,1,2,1] => [1,2,1,1,1] => 110111 => 001000 => 1
[1,2,2,1,3] => [1,2,1,1] => 11011 => 00100 => 1
[1,2,2,2,1,1] => [1,3,2] => 110010 => 001101 => 2
[1,2,2,2,2] => [1,4] => 11000 => 00111 => 3
[1,2,2,3,1] => [1,2,1,1] => 11011 => 00100 => 1
[1,2,2,4] => [1,2,1] => 1101 => 0010 => 1
[1,2,3,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[1,2,3,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,3,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,3,3] => [1,1,2] => 1110 => 0001 => 1
[1,2,4,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,2,4,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,5,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,6] => [1,1,1] => 111 => 000 => 0
[1,3,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[1,3,1,1,1,2] => [1,1,3,1] => 111001 => 000110 => 2
[1,3,1,1,2,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,3,1,1,3] => [1,1,2,1] => 11101 => 00010 => 1
[1,3,1,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[1,3,1,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[1,3,1,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,1,4] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,2,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[1,3,2,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[1,3,2,3] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,3,1,1] => [1,2,2] => 11010 => 00101 => 1
[1,3,3,2] => [1,2,1] => 1101 => 0010 => 1
[1,3,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,5] => [1,1,1] => 111 => 000 => 0
[1,4,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[1,4,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[1,4,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,1,3] => [1,1,1,1] => 1111 => 0000 => 0
[1,4,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,4,2,2] => [1,1,2] => 1110 => 0001 => 1
[1,4,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,4,4] => [1,2] => 110 => 001 => 1
[1,5,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[1,5,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,5,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,5,3] => [1,1,1] => 111 => 000 => 0
[1,6,1,1] => [1,1,2] => 1110 => 0001 => 1
[1,6,2] => [1,1,1] => 111 => 000 => 0
[1,7,1] => [1,1,1] => 111 => 000 => 0
[1,8] => [1,1] => 11 => 00 => 0
[2,1,1,1,1,1,1,1] => [1,7] => 11000000 => 00111111 => 6
[2,1,1,1,1,1,2] => [1,5,1] => 1100001 => 0011110 => 4
[2,1,1,1,1,2,1] => [1,4,1,1] => 1100011 => 0011100 => 3
[2,1,1,1,1,3] => [1,4,1] => 110001 => 001110 => 3
[2,1,1,1,2,1,1] => [1,3,1,2] => 1100110 => 0011001 => 2
[2,1,1,1,2,2] => [1,3,2] => 110010 => 001101 => 2
[2,1,1,1,3,1] => [1,3,1,1] => 110011 => 001100 => 2
[2,1,1,1,4] => [1,3,1] => 11001 => 00110 => 2
[2,1,1,2,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[2,1,1,2,1,2] => [1,2,1,1,1] => 110111 => 001000 => 1
[2,1,1,2,2,1] => [1,2,2,1] => 110101 => 001010 => 1
[2,1,1,2,3] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,1,3,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[2,1,1,3,2] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,1,4,1] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,1,5] => [1,2,1] => 1101 => 0010 => 1
[2,1,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[2,1,2,1,1,2] => [1,1,1,2,1] => 111101 => 000010 => 1
[2,1,2,1,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[2,1,2,1,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,2,2,1,1] => [1,1,2,2] => 111010 => 000101 => 1
[2,1,2,2,2] => [1,1,3] => 11100 => 00011 => 2
[2,1,2,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,2,4] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,3,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[2,1,3,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,3,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,3,3] => [1,1,2] => 1110 => 0001 => 1
[2,1,4,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[2,1,4,2] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,5,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,6] => [1,1,1] => 111 => 000 => 0
[2,2,1,1,1,1,1] => [2,5] => 1010000 => 0101111 => 4
[2,2,1,1,1,2] => [2,3,1] => 101001 => 010110 => 2
[2,2,1,1,2,1] => [2,2,1,1] => 101011 => 010100 => 1
[2,2,1,1,3] => [2,2,1] => 10101 => 01010 => 1
[2,2,1,2,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[2,2,1,2,2] => [2,1,2] => 10110 => 01001 => 1
[2,2,1,3,1] => [2,1,1,1] => 10111 => 01000 => 1
[2,2,1,4] => [2,1,1] => 1011 => 0100 => 1
[2,2,2,1,1,1] => [3,3] => 100100 => 011011 => 2
[2,2,2,1,2] => [3,1,1] => 10011 => 01100 => 2
[2,2,2,2,1] => [4,1] => 10001 => 01110 => 3
[2,2,2,3] => [3,1] => 1001 => 0110 => 2
[2,2,3,1,1] => [2,1,2] => 10110 => 01001 => 1
[2,2,3,2] => [2,1,1] => 1011 => 0100 => 1
[2,2,4,1] => [2,1,1] => 1011 => 0100 => 1
[2,2,5] => [2,1] => 101 => 010 => 1
[2,3,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[2,3,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[2,3,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,3,1,3] => [1,1,1,1] => 1111 => 0000 => 0
[2,3,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[2,3,2,2] => [1,1,2] => 1110 => 0001 => 1
[2,3,3,1] => [1,2,1] => 1101 => 0010 => 1
[2,3,4] => [1,1,1] => 111 => 000 => 0
[2,4,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[2,4,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[2,4,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,4,3] => [1,1,1] => 111 => 000 => 0
[2,5,1,1] => [1,1,2] => 1110 => 0001 => 1
[2,5,2] => [1,1,1] => 111 => 000 => 0
[2,6,1] => [1,1,1] => 111 => 000 => 0
[2,7] => [1,1] => 11 => 00 => 0
[3,1,1,1,1,1,1] => [1,6] => 1100000 => 0011111 => 5
[3,1,1,1,1,2] => [1,4,1] => 110001 => 001110 => 3
[3,1,1,1,2,1] => [1,3,1,1] => 110011 => 001100 => 2
[3,1,1,1,3] => [1,3,1] => 11001 => 00110 => 2
[3,1,1,2,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[3,1,1,2,2] => [1,2,2] => 11010 => 00101 => 1
[3,1,1,3,1] => [1,2,1,1] => 11011 => 00100 => 1
[3,1,1,4] => [1,2,1] => 1101 => 0010 => 1
[3,1,2,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[3,1,2,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[3,1,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[3,1,2,3] => [1,1,1,1] => 1111 => 0000 => 0
[3,1,3,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[3,1,3,2] => [1,1,1,1] => 1111 => 0000 => 0
[3,1,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[3,1,5] => [1,1,1] => 111 => 000 => 0
[3,2,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[3,2,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[3,2,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[3,2,1,3] => [1,1,1,1] => 1111 => 0000 => 0
[3,2,2,1,1] => [1,2,2] => 11010 => 00101 => 1
[3,2,2,2] => [1,3] => 1100 => 0011 => 2
[3,2,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[3,2,4] => [1,1,1] => 111 => 000 => 0
[3,3,1,1,1] => [2,3] => 10100 => 01011 => 2
[3,3,1,2] => [2,1,1] => 1011 => 0100 => 1
[3,3,2,1] => [2,1,1] => 1011 => 0100 => 1
[3,3,3] => [3] => 100 => 011 => 2
[3,4,1,1] => [1,1,2] => 1110 => 0001 => 1
[3,4,2] => [1,1,1] => 111 => 000 => 0
[3,5,1] => [1,1,1] => 111 => 000 => 0
[3,6] => [1,1] => 11 => 00 => 0
[4,1,1,1,1,1] => [1,5] => 110000 => 001111 => 4
[4,1,1,1,2] => [1,3,1] => 11001 => 00110 => 2
[4,1,1,2,1] => [1,2,1,1] => 11011 => 00100 => 1
[4,1,1,3] => [1,2,1] => 1101 => 0010 => 1
[4,1,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[4,1,2,2] => [1,1,2] => 1110 => 0001 => 1
[4,1,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[4,1,4] => [1,1,1] => 111 => 000 => 0
[4,2,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[4,2,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[4,2,2,1] => [1,2,1] => 1101 => 0010 => 1
[4,2,3] => [1,1,1] => 111 => 000 => 0
[4,3,1,1] => [1,1,2] => 1110 => 0001 => 1
[4,3,2] => [1,1,1] => 111 => 000 => 0
[4,4,1] => [2,1] => 101 => 010 => 1
[4,5] => [1,1] => 11 => 00 => 0
[5,1,1,1,1] => [1,4] => 11000 => 00111 => 3
[5,1,1,2] => [1,2,1] => 1101 => 0010 => 1
[5,1,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[5,1,3] => [1,1,1] => 111 => 000 => 0
[5,2,1,1] => [1,1,2] => 1110 => 0001 => 1
[5,2,2] => [1,2] => 110 => 001 => 1
[5,3,1] => [1,1,1] => 111 => 000 => 0
[5,4] => [1,1] => 11 => 00 => 0
[6,1,1,1] => [1,3] => 1100 => 0011 => 2
[6,1,2] => [1,1,1] => 111 => 000 => 0
[6,2,1] => [1,1,1] => 111 => 000 => 0
[6,3] => [1,1] => 11 => 00 => 0
[7,1,1] => [1,2] => 110 => 001 => 1
[7,2] => [1,1] => 11 => 00 => 0
[8,1] => [1,1] => 11 => 00 => 0
[9] => [1] => 1 => 0 => 0
[1,1,1,1,1,1,1,1,1,1] => [10] => 1000000000 => 0111111111 => 9
[1,1,1,1,1,1,1,1,2] => [8,1] => 100000001 => 011111110 => 7
[1,1,1,1,1,1,1,2,1] => [7,1,1] => 100000011 => 011111100 => 6
[1,1,1,1,1,1,1,3] => [7,1] => 10000001 => 01111110 => 6
[1,1,1,1,1,1,2,1,1] => [6,1,2] => 100000110 => 011111001 => 5
[1,1,1,1,1,1,2,2] => [6,2] => 10000010 => 01111101 => 5
[1,1,1,1,1,1,3,1] => [6,1,1] => 10000011 => 01111100 => 5
[1,1,1,1,1,1,4] => [6,1] => 1000001 => 0111110 => 5
[1,1,1,1,1,2,1,1,1] => [5,1,3] => 100001100 => 011110011 => 4
[1,1,1,1,1,2,1,2] => [5,1,1,1] => 10000111 => 01111000 => 4
[1,1,1,1,1,2,2,1] => [5,2,1] => 10000101 => 01111010 => 4
[1,1,1,1,1,2,3] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,3,1,1] => [5,1,2] => 10000110 => 01111001 => 4
[1,1,1,1,1,3,2] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,4,1] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,5] => [5,1] => 100001 => 011110 => 4
[1,1,1,1,2,1,1,1,1] => [4,1,4] => 100011000 => 011100111 => 3
[1,1,1,1,2,1,1,2] => [4,1,2,1] => 10001101 => 01110010 => 3
[1,1,1,1,2,1,2,1] => [4,1,1,1,1] => 10001111 => 01110000 => 3
[1,1,1,1,2,1,3] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,2,2,1,1] => [4,2,2] => 10001010 => 01110101 => 3
[1,1,1,1,2,2,2] => [4,3] => 1000100 => 0111011 => 3
[1,1,1,1,2,3,1] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,2,4] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,3,1,1,1] => [4,1,3] => 10001100 => 01110011 => 3
[1,1,1,1,3,1,2] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,3,2,1] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,3,3] => [4,2] => 100010 => 011101 => 3
[1,1,1,1,4,1,1] => [4,1,2] => 1000110 => 0111001 => 3
[1,1,1,1,4,2] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,5,1] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,6] => [4,1] => 10001 => 01110 => 3
[1,1,1,2,1,1,1,1,1] => [3,1,5] => 100110000 => 011001111 => 4
[1,1,1,2,1,1,1,2] => [3,1,3,1] => 10011001 => 01100110 => 2
[1,1,1,2,1,1,2,1] => [3,1,2,1,1] => 10011011 => 01100100 => 2
[1,1,1,2,1,1,3] => [3,1,2,1] => 1001101 => 0110010 => 2
[1,1,1,2,1,2,1,1] => [3,1,1,1,2] => 10011110 => 01100001 => 2
[1,1,1,2,1,2,2] => [3,1,1,2] => 1001110 => 0110001 => 2
[1,1,1,2,1,3,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,1,4] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,2,2,1,1,1] => [3,2,3] => 10010100 => 01101011 => 2
[1,1,1,2,2,1,2] => [3,2,1,1] => 1001011 => 0110100 => 2
[1,1,1,2,2,2,1] => [3,3,1] => 1001001 => 0110110 => 2
[1,1,1,2,2,3] => [3,2,1] => 100101 => 011010 => 2
[1,1,1,2,3,1,1] => [3,1,1,2] => 1001110 => 0110001 => 2
[1,1,1,2,3,2] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,2,4,1] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,2,5] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,3,1,1,1,1] => [3,1,4] => 10011000 => 01100111 => 3
[1,1,1,3,1,1,2] => [3,1,2,1] => 1001101 => 0110010 => 2
[1,1,1,3,1,2,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,3,1,3] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,3,2,1,1] => [3,1,1,2] => 1001110 => 0110001 => 2
[1,1,1,3,2,2] => [3,1,2] => 100110 => 011001 => 2
[1,1,1,3,3,1] => [3,2,1] => 100101 => 011010 => 2
[1,1,1,3,4] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,4,1,1,1] => [3,1,3] => 1001100 => 0110011 => 2
[1,1,1,4,1,2] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,4,2,1] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,4,3] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,5,1,1] => [3,1,2] => 100110 => 011001 => 2
[1,1,1,5,2] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,6,1] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,7] => [3,1] => 1001 => 0110 => 2
[1,1,2,1,1,1,1,1,1] => [2,1,6] => 101100000 => 010011111 => 5
[1,1,2,1,1,1,1,2] => [2,1,4,1] => 10110001 => 01001110 => 3
[1,1,2,1,1,1,2,1] => [2,1,3,1,1] => 10110011 => 01001100 => 2
[1,1,2,1,1,1,3] => [2,1,3,1] => 1011001 => 0100110 => 2
[1,1,2,1,1,2,1,1] => [2,1,2,1,2] => 10110110 => 01001001 => 1
[1,1,2,1,1,2,2] => [2,1,2,2] => 1011010 => 0100101 => 1
[1,1,2,1,1,3,1] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,2,1,1,4] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,2,1,2,1,1,1] => [2,1,1,1,3] => 10111100 => 01000011 => 2
[1,1,2,1,2,1,2] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,2,1,2,2,1] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[1,1,2,1,2,3] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,1,3,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[1,1,2,1,3,2] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,1,4,1] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,1,5] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,2,2,1,1,1,1] => [2,2,4] => 10101000 => 01010111 => 3
[1,1,2,2,1,1,2] => [2,2,2,1] => 1010101 => 0101010 => 1
[1,1,2,2,1,2,1] => [2,2,1,1,1] => 1010111 => 0101000 => 1
[1,1,2,2,1,3] => [2,2,1,1] => 101011 => 010100 => 1
[1,1,2,2,2,1,1] => [2,3,2] => 1010010 => 0101101 => 2
[1,1,2,2,2,2] => [2,4] => 101000 => 010111 => 3
[1,1,2,2,3,1] => [2,2,1,1] => 101011 => 010100 => 1
[1,1,2,2,4] => [2,2,1] => 10101 => 01010 => 1
[1,1,2,3,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[1,1,2,3,1,2] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,3,2,1] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,3,3] => [2,1,2] => 10110 => 01001 => 1
[1,1,2,4,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,2,4,2] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,2,5,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,2,6] => [2,1,1] => 1011 => 0100 => 1
[1,1,3,1,1,1,1,1] => [2,1,5] => 10110000 => 01001111 => 4
[1,1,3,1,1,1,2] => [2,1,3,1] => 1011001 => 0100110 => 2
[1,1,3,1,1,2,1] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,3,1,1,3] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,3,1,2,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[1,1,3,1,2,2] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,3,1,3,1] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,3,1,4] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,3,2,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[1,1,3,2,1,2] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,3,2,2,1] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,3,2,3] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,3,3,1,1] => [2,2,2] => 101010 => 010101 => 1
[1,1,3,3,2] => [2,2,1] => 10101 => 01010 => 1
[1,1,3,4,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,3,5] => [2,1,1] => 1011 => 0100 => 1
[1,1,4,1,1,1,1] => [2,1,4] => 1011000 => 0100111 => 3
[1,1,4,1,1,2] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,4,1,2,1] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,4,1,3] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,4,2,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,4,2,2] => [2,1,2] => 10110 => 01001 => 1
[1,1,4,3,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,4,4] => [2,2] => 1010 => 0101 => 1
[1,1,5,1,1,1] => [2,1,3] => 101100 => 010011 => 2
[1,1,5,1,2] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,5,2,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,5,3] => [2,1,1] => 1011 => 0100 => 1
[1,1,6,1,1] => [2,1,2] => 10110 => 01001 => 1
[1,1,6,2] => [2,1,1] => 1011 => 0100 => 1
[1,1,7,1] => [2,1,1] => 1011 => 0100 => 1
[1,1,8] => [2,1] => 101 => 010 => 1
[1,2,1,1,1,1,1,1,1] => [1,1,7] => 111000000 => 000111111 => 6
[1,2,1,1,1,1,1,2] => [1,1,5,1] => 11100001 => 00011110 => 4
[1,2,1,1,1,1,2,1] => [1,1,4,1,1] => 11100011 => 00011100 => 3
[1,2,1,1,1,1,3] => [1,1,4,1] => 1110001 => 0001110 => 3
[1,2,1,1,1,2,1,1] => [1,1,3,1,2] => 11100110 => 00011001 => 2
[1,2,1,1,1,2,2] => [1,1,3,2] => 1110010 => 0001101 => 2
[1,2,1,1,1,3,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,2,1,1,1,4] => [1,1,3,1] => 111001 => 000110 => 2
[1,2,1,1,2,1,1,1] => [1,1,2,1,3] => 11101100 => 00010011 => 2
[1,2,1,1,2,1,2] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,1,1,2,2,1] => [1,1,2,2,1] => 1110101 => 0001010 => 1
[1,2,1,1,2,3] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,2,1,1,3,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[1,2,1,1,3,2] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,2,1,1,4,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,2,1,1,5] => [1,1,2,1] => 11101 => 00010 => 1
[1,2,1,2,1,1,1,1] => [1,1,1,1,4] => 11111000 => 00000111 => 3
[1,2,1,2,1,1,2] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[1,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,2,1,3] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,1,2,2,1,1] => [1,1,1,2,2] => 1111010 => 0000101 => 1
[1,2,1,2,2,2] => [1,1,1,3] => 111100 => 000011 => 2
[1,2,1,2,3,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,1,2,4] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,2,1,3,1,2] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,1,3,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,1,3,3] => [1,1,1,2] => 11110 => 00001 => 1
[1,2,1,4,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[1,2,1,4,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,5,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,6] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,2,1,1,1,1,1] => [1,2,5] => 11010000 => 00101111 => 4
[1,2,2,1,1,1,2] => [1,2,3,1] => 1101001 => 0010110 => 2
[1,2,2,1,1,2,1] => [1,2,2,1,1] => 1101011 => 0010100 => 1
[1,2,2,1,1,3] => [1,2,2,1] => 110101 => 001010 => 1
[1,2,2,1,2,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[1,2,2,1,2,2] => [1,2,1,2] => 110110 => 001001 => 1
[1,2,2,1,3,1] => [1,2,1,1,1] => 110111 => 001000 => 1
[1,2,2,1,4] => [1,2,1,1] => 11011 => 00100 => 1
[1,2,2,2,1,1,1] => [1,3,3] => 1100100 => 0011011 => 2
[1,2,2,2,1,2] => [1,3,1,1] => 110011 => 001100 => 2
[1,2,2,2,2,1] => [1,4,1] => 110001 => 001110 => 3
[1,2,2,2,3] => [1,3,1] => 11001 => 00110 => 2
[1,2,2,3,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[1,2,2,3,2] => [1,2,1,1] => 11011 => 00100 => 1
[1,2,2,4,1] => [1,2,1,1] => 11011 => 00100 => 1
[1,2,2,5] => [1,2,1] => 1101 => 0010 => 1
[1,2,3,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[1,2,3,1,1,2] => [1,1,1,2,1] => 111101 => 000010 => 1
[1,2,3,1,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,3,1,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,3,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[1,2,3,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[1,2,3,3,1] => [1,1,2,1] => 11101 => 00010 => 1
[1,2,3,4] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,4,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[1,2,4,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,4,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,4,3] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,5,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,2,5,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,6,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,7] => [1,1,1] => 111 => 000 => 0
[1,3,1,1,1,1,1,1] => [1,1,6] => 11100000 => 00011111 => 5
[1,3,1,1,1,1,2] => [1,1,4,1] => 1110001 => 0001110 => 3
[1,3,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,3,1,1,1,3] => [1,1,3,1] => 111001 => 000110 => 2
[1,3,1,1,2,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[1,3,1,1,2,2] => [1,1,2,2] => 111010 => 000101 => 1
[1,3,1,1,3,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,3,1,1,4] => [1,1,2,1] => 11101 => 00010 => 1
[1,3,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,3,1,2,1,2] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,3,1,2,2,1] => [1,1,1,2,1] => 111101 => 000010 => 1
[1,3,1,2,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,1,3,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[1,3,1,3,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,1,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,1,5] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[1,3,2,1,1,2] => [1,1,1,2,1] => 111101 => 000010 => 1
[1,3,2,1,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,3,2,1,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,2,2,1,1] => [1,1,2,2] => 111010 => 000101 => 1
[1,3,2,2,2] => [1,1,3] => 11100 => 00011 => 2
[1,3,2,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,2,4] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,3,1,1,1] => [1,2,3] => 110100 => 001011 => 2
[1,3,3,1,2] => [1,2,1,1] => 11011 => 00100 => 1
[1,3,3,2,1] => [1,2,1,1] => 11011 => 00100 => 1
[1,3,3,3] => [1,3] => 1100 => 0011 => 2
[1,3,4,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,3,4,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,5,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,6] => [1,1,1] => 111 => 000 => 0
[1,4,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[1,4,1,1,1,2] => [1,1,3,1] => 111001 => 000110 => 2
[1,4,1,1,2,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,4,1,1,3] => [1,1,2,1] => 11101 => 00010 => 1
[1,4,1,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[1,4,1,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[1,4,1,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,1,4] => [1,1,1,1] => 1111 => 0000 => 0
[1,4,2,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[1,4,2,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[1,4,2,3] => [1,1,1,1] => 1111 => 0000 => 0
[1,4,3,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,4,3,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,4,4,1] => [1,2,1] => 1101 => 0010 => 1
[1,4,5] => [1,1,1] => 111 => 000 => 0
[1,5,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[1,5,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[1,5,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,5,1,3] => [1,1,1,1] => 1111 => 0000 => 0
[1,5,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,5,2,2] => [1,1,2] => 1110 => 0001 => 1
[1,5,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,5,4] => [1,1,1] => 111 => 000 => 0
[1,6,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[1,6,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,6,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,6,3] => [1,1,1] => 111 => 000 => 0
[1,7,1,1] => [1,1,2] => 1110 => 0001 => 1
[1,7,2] => [1,1,1] => 111 => 000 => 0
[1,8,1] => [1,1,1] => 111 => 000 => 0
[1,9] => [1,1] => 11 => 00 => 0
[2,1,1,1,1,1,1,1,1] => [1,8] => 110000000 => 001111111 => 7
[2,1,1,1,1,1,1,2] => [1,6,1] => 11000001 => 00111110 => 5
[2,1,1,1,1,1,2,1] => [1,5,1,1] => 11000011 => 00111100 => 4
[2,1,1,1,1,1,3] => [1,5,1] => 1100001 => 0011110 => 4
[2,1,1,1,1,2,1,1] => [1,4,1,2] => 11000110 => 00111001 => 3
[2,1,1,1,1,2,2] => [1,4,2] => 1100010 => 0011101 => 3
[2,1,1,1,1,3,1] => [1,4,1,1] => 1100011 => 0011100 => 3
[2,1,1,1,1,4] => [1,4,1] => 110001 => 001110 => 3
[2,1,1,1,2,1,1,1] => [1,3,1,3] => 11001100 => 00110011 => 2
[2,1,1,1,2,1,2] => [1,3,1,1,1] => 1100111 => 0011000 => 2
[2,1,1,1,2,2,1] => [1,3,2,1] => 1100101 => 0011010 => 2
[2,1,1,1,2,3] => [1,3,1,1] => 110011 => 001100 => 2
[2,1,1,1,3,1,1] => [1,3,1,2] => 1100110 => 0011001 => 2
[2,1,1,1,3,2] => [1,3,1,1] => 110011 => 001100 => 2
[2,1,1,1,4,1] => [1,3,1,1] => 110011 => 001100 => 2
[2,1,1,1,5] => [1,3,1] => 11001 => 00110 => 2
[2,1,1,2,1,1,1,1] => [1,2,1,4] => 11011000 => 00100111 => 3
[2,1,1,2,1,1,2] => [1,2,1,2,1] => 1101101 => 0010010 => 1
[2,1,1,2,1,2,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[2,1,1,2,1,3] => [1,2,1,1,1] => 110111 => 001000 => 1
[2,1,1,2,2,1,1] => [1,2,2,2] => 1101010 => 0010101 => 1
[2,1,1,2,2,2] => [1,2,3] => 110100 => 001011 => 2
[2,1,1,2,3,1] => [1,2,1,1,1] => 110111 => 001000 => 1
[2,1,1,2,4] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,1,3,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[2,1,1,3,1,2] => [1,2,1,1,1] => 110111 => 001000 => 1
[2,1,1,3,2,1] => [1,2,1,1,1] => 110111 => 001000 => 1
[2,1,1,3,3] => [1,2,2] => 11010 => 00101 => 1
[2,1,1,4,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[2,1,1,4,2] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,1,5,1] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,1,6] => [1,2,1] => 1101 => 0010 => 1
[2,1,2,1,1,1,1,1] => [1,1,1,5] => 11110000 => 00001111 => 4
[2,1,2,1,1,1,2] => [1,1,1,3,1] => 1111001 => 0000110 => 2
[2,1,2,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[2,1,2,1,1,3] => [1,1,1,2,1] => 111101 => 000010 => 1
[2,1,2,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,1,2,1,2,2] => [1,1,1,1,2] => 111110 => 000001 => 1
[2,1,2,1,3,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[2,1,2,1,4] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,2,2,1,1,1] => [1,1,2,3] => 1110100 => 0001011 => 2
[2,1,2,2,1,2] => [1,1,2,1,1] => 111011 => 000100 => 1
[2,1,2,2,2,1] => [1,1,3,1] => 111001 => 000110 => 2
[2,1,2,2,3] => [1,1,2,1] => 11101 => 00010 => 1
[2,1,2,3,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[2,1,2,3,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,2,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,2,5] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,3,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[2,1,3,1,1,2] => [1,1,1,2,1] => 111101 => 000010 => 1
[2,1,3,1,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[2,1,3,1,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,3,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[2,1,3,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[2,1,3,3,1] => [1,1,2,1] => 11101 => 00010 => 1
[2,1,3,4] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,4,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[2,1,4,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,4,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,4,3] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,5,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[2,1,5,2] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,6,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,7] => [1,1,1] => 111 => 000 => 0
[2,2,1,1,1,1,1,1] => [2,6] => 10100000 => 01011111 => 5
[2,2,1,1,1,1,2] => [2,4,1] => 1010001 => 0101110 => 3
[2,2,1,1,1,2,1] => [2,3,1,1] => 1010011 => 0101100 => 2
[2,2,1,1,1,3] => [2,3,1] => 101001 => 010110 => 2
[2,2,1,1,2,1,1] => [2,2,1,2] => 1010110 => 0101001 => 1
[2,2,1,1,2,2] => [2,2,2] => 101010 => 010101 => 1
[2,2,1,1,3,1] => [2,2,1,1] => 101011 => 010100 => 1
[2,2,1,1,4] => [2,2,1] => 10101 => 01010 => 1
[2,2,1,2,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[2,2,1,2,1,2] => [2,1,1,1,1] => 101111 => 010000 => 1
[2,2,1,2,2,1] => [2,1,2,1] => 101101 => 010010 => 1
[2,2,1,2,3] => [2,1,1,1] => 10111 => 01000 => 1
[2,2,1,3,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[2,2,1,3,2] => [2,1,1,1] => 10111 => 01000 => 1
[2,2,1,4,1] => [2,1,1,1] => 10111 => 01000 => 1
[2,2,1,5] => [2,1,1] => 1011 => 0100 => 1
[2,2,2,1,1,1,1] => [3,4] => 1001000 => 0110111 => 3
[2,2,2,1,1,2] => [3,2,1] => 100101 => 011010 => 2
[2,2,2,1,2,1] => [3,1,1,1] => 100111 => 011000 => 2
[2,2,2,1,3] => [3,1,1] => 10011 => 01100 => 2
[2,2,2,2,1,1] => [4,2] => 100010 => 011101 => 3
[2,2,2,2,2] => [5] => 10000 => 01111 => 4
[2,2,2,3,1] => [3,1,1] => 10011 => 01100 => 2
[2,2,2,4] => [3,1] => 1001 => 0110 => 2
[2,2,3,1,1,1] => [2,1,3] => 101100 => 010011 => 2
[2,2,3,1,2] => [2,1,1,1] => 10111 => 01000 => 1
[2,2,3,2,1] => [2,1,1,1] => 10111 => 01000 => 1
[2,2,3,3] => [2,2] => 1010 => 0101 => 1
[2,2,4,1,1] => [2,1,2] => 10110 => 01001 => 1
[2,2,4,2] => [2,1,1] => 1011 => 0100 => 1
[2,2,5,1] => [2,1,1] => 1011 => 0100 => 1
[2,2,6] => [2,1] => 101 => 010 => 1
[2,3,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[2,3,1,1,1,2] => [1,1,3,1] => 111001 => 000110 => 2
[2,3,1,1,2,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[2,3,1,1,3] => [1,1,2,1] => 11101 => 00010 => 1
[2,3,1,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[2,3,1,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[2,3,1,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,3,1,4] => [1,1,1,1] => 1111 => 0000 => 0
[2,3,2,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[2,3,2,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,3,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[2,3,2,3] => [1,1,1,1] => 1111 => 0000 => 0
[2,3,3,1,1] => [1,2,2] => 11010 => 00101 => 1
[2,3,3,2] => [1,2,1] => 1101 => 0010 => 1
[2,3,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,3,5] => [1,1,1] => 111 => 000 => 0
[2,4,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[2,4,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[2,4,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,4,1,3] => [1,1,1,1] => 1111 => 0000 => 0
[2,4,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[2,4,2,2] => [1,1,2] => 1110 => 0001 => 1
[2,4,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,4,4] => [1,2] => 110 => 001 => 1
[2,5,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[2,5,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[2,5,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,5,3] => [1,1,1] => 111 => 000 => 0
[2,6,1,1] => [1,1,2] => 1110 => 0001 => 1
[2,6,2] => [1,1,1] => 111 => 000 => 0
[2,7,1] => [1,1,1] => 111 => 000 => 0
[2,8] => [1,1] => 11 => 00 => 0
[3,1,1,1,1,1,1,1] => [1,7] => 11000000 => 00111111 => 6
[3,1,1,1,1,1,2] => [1,5,1] => 1100001 => 0011110 => 4
[3,1,1,1,1,2,1] => [1,4,1,1] => 1100011 => 0011100 => 3
[3,1,1,1,1,3] => [1,4,1] => 110001 => 001110 => 3
[3,1,1,1,2,1,1] => [1,3,1,2] => 1100110 => 0011001 => 2
[3,1,1,1,2,2] => [1,3,2] => 110010 => 001101 => 2
[3,1,1,1,3,1] => [1,3,1,1] => 110011 => 001100 => 2
[3,1,1,1,4] => [1,3,1] => 11001 => 00110 => 2
[3,1,1,2,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[3,1,1,2,1,2] => [1,2,1,1,1] => 110111 => 001000 => 1
[3,1,1,2,2,1] => [1,2,2,1] => 110101 => 001010 => 1
[3,1,1,2,3] => [1,2,1,1] => 11011 => 00100 => 1
[3,1,1,3,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[3,1,1,3,2] => [1,2,1,1] => 11011 => 00100 => 1
[3,1,1,4,1] => [1,2,1,1] => 11011 => 00100 => 1
[3,1,1,5] => [1,2,1] => 1101 => 0010 => 1
[3,1,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[3,1,2,1,1,2] => [1,1,1,2,1] => 111101 => 000010 => 1
[3,1,2,1,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[3,1,2,1,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[3,1,2,2,1,1] => [1,1,2,2] => 111010 => 000101 => 1
[3,1,2,2,2] => [1,1,3] => 11100 => 00011 => 2
[3,1,2,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[3,1,2,4] => [1,1,1,1] => 1111 => 0000 => 0
[3,1,3,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[3,1,3,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[3,1,3,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[3,1,3,3] => [1,1,2] => 1110 => 0001 => 1
[3,1,4,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[3,1,4,2] => [1,1,1,1] => 1111 => 0000 => 0
[3,1,5,1] => [1,1,1,1] => 1111 => 0000 => 0
[3,1,6] => [1,1,1] => 111 => 000 => 0
[3,2,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[3,2,1,1,1,2] => [1,1,3,1] => 111001 => 000110 => 2
[3,2,1,1,2,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[3,2,1,1,3] => [1,1,2,1] => 11101 => 00010 => 1
[3,2,1,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[3,2,1,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[3,2,1,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[3,2,1,4] => [1,1,1,1] => 1111 => 0000 => 0
[3,2,2,1,1,1] => [1,2,3] => 110100 => 001011 => 2
[3,2,2,1,2] => [1,2,1,1] => 11011 => 00100 => 1
[3,2,2,2,1] => [1,3,1] => 11001 => 00110 => 2
[3,2,2,3] => [1,2,1] => 1101 => 0010 => 1
[3,2,3,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[3,2,3,2] => [1,1,1,1] => 1111 => 0000 => 0
[3,2,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[3,2,5] => [1,1,1] => 111 => 000 => 0
[3,3,1,1,1,1] => [2,4] => 101000 => 010111 => 3
[3,3,1,1,2] => [2,2,1] => 10101 => 01010 => 1
[3,3,1,2,1] => [2,1,1,1] => 10111 => 01000 => 1
[3,3,1,3] => [2,1,1] => 1011 => 0100 => 1
[3,3,2,1,1] => [2,1,2] => 10110 => 01001 => 1
[3,3,2,2] => [2,2] => 1010 => 0101 => 1
[3,3,3,1] => [3,1] => 1001 => 0110 => 2
[3,3,4] => [2,1] => 101 => 010 => 1
[3,4,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[3,4,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[3,4,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[3,4,3] => [1,1,1] => 111 => 000 => 0
[3,5,1,1] => [1,1,2] => 1110 => 0001 => 1
[3,5,2] => [1,1,1] => 111 => 000 => 0
[3,6,1] => [1,1,1] => 111 => 000 => 0
[3,7] => [1,1] => 11 => 00 => 0
[4,1,1,1,1,1,1] => [1,6] => 1100000 => 0011111 => 5
[4,1,1,1,1,2] => [1,4,1] => 110001 => 001110 => 3
[4,1,1,1,2,1] => [1,3,1,1] => 110011 => 001100 => 2
[4,1,1,1,3] => [1,3,1] => 11001 => 00110 => 2
[4,1,1,2,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[4,1,1,2,2] => [1,2,2] => 11010 => 00101 => 1
[4,1,1,3,1] => [1,2,1,1] => 11011 => 00100 => 1
[4,1,1,4] => [1,2,1] => 1101 => 0010 => 1
[4,1,2,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[4,1,2,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[4,1,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[4,1,2,3] => [1,1,1,1] => 1111 => 0000 => 0
[4,1,3,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[4,1,3,2] => [1,1,1,1] => 1111 => 0000 => 0
[4,1,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[4,1,5] => [1,1,1] => 111 => 000 => 0
[4,2,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[4,2,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[4,2,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[4,2,1,3] => [1,1,1,1] => 1111 => 0000 => 0
[4,2,2,1,1] => [1,2,2] => 11010 => 00101 => 1
[4,2,2,2] => [1,3] => 1100 => 0011 => 2
[4,2,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[4,2,4] => [1,1,1] => 111 => 000 => 0
[4,3,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[4,3,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[4,3,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[4,3,3] => [1,2] => 110 => 001 => 1
[4,4,1,1] => [2,2] => 1010 => 0101 => 1
[4,4,2] => [2,1] => 101 => 010 => 1
[4,5,1] => [1,1,1] => 111 => 000 => 0
[4,6] => [1,1] => 11 => 00 => 0
[5,1,1,1,1,1] => [1,5] => 110000 => 001111 => 4
[5,1,1,1,2] => [1,3,1] => 11001 => 00110 => 2
[5,1,1,2,1] => [1,2,1,1] => 11011 => 00100 => 1
[5,1,1,3] => [1,2,1] => 1101 => 0010 => 1
[5,1,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[5,1,2,2] => [1,1,2] => 1110 => 0001 => 1
[5,1,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[5,1,4] => [1,1,1] => 111 => 000 => 0
[5,2,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[5,2,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[5,2,2,1] => [1,2,1] => 1101 => 0010 => 1
[5,2,3] => [1,1,1] => 111 => 000 => 0
[5,3,1,1] => [1,1,2] => 1110 => 0001 => 1
[5,3,2] => [1,1,1] => 111 => 000 => 0
[5,4,1] => [1,1,1] => 111 => 000 => 0
[5,5] => [2] => 10 => 01 => 1
[6,1,1,1,1] => [1,4] => 11000 => 00111 => 3
[6,1,1,2] => [1,2,1] => 1101 => 0010 => 1
[6,1,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[6,1,3] => [1,1,1] => 111 => 000 => 0
[6,2,1,1] => [1,1,2] => 1110 => 0001 => 1
[6,2,2] => [1,2] => 110 => 001 => 1
[6,3,1] => [1,1,1] => 111 => 000 => 0
[6,4] => [1,1] => 11 => 00 => 0
[7,1,1,1] => [1,3] => 1100 => 0011 => 2
[7,1,2] => [1,1,1] => 111 => 000 => 0
[7,2,1] => [1,1,1] => 111 => 000 => 0
[7,3] => [1,1] => 11 => 00 => 0
[8,1,1] => [1,2] => 110 => 001 => 1
[8,2] => [1,1] => 11 => 00 => 0
[9,1] => [1,1] => 11 => 00 => 0
[10] => [1] => 1 => 0 => 0
[1,10] => [1,1] => 11 => 00 => 0
[1,8,1,1] => [1,1,2] => 1110 => 0001 => 1
[1,7,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,6,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,5,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,4,5,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,6,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,2,7,1] => [1,1,1,1] => 1111 => 0000 => 0
[1,1,8,1] => [2,1,1] => 1011 => 0100 => 1
[10,1] => [1,1] => 11 => 00 => 0
[1,1,1,1,1,1,1,1,2,2] => [8,2] => 1000000010 => 0111111101 => 7
[1,1,1,1,1,1,2,2,1,1] => [6,2,2] => 1000001010 => 0111110101 => 5
[1,1,1,1,1,1,3,3] => [6,2] => 10000010 => 01111101 => 5
[1,1,1,1,2,2,2,2] => [4,4] => 10001000 => 01110111 => 3
[1,1,1,1,2,1,1,2,1,1] => [4,1,2,1,2] => 1000110110 => 0111001001 => 3
[1,1,1,1,2,1,2,3] => [4,1,1,1,1] => 10001111 => 01110000 => 3
[1,1,1,1,3,3,1,1] => [4,2,2] => 10001010 => 01110101 => 3
[1,1,1,1,3,2,1,2] => [4,1,1,1,1] => 10001111 => 01110000 => 3
[1,1,1,1,3,1,1,3] => [4,1,2,1] => 10001101 => 01110010 => 3
[1,1,1,1,4,4] => [4,2] => 100010 => 011101 => 3
[1,1,2,2,1,1,1,1,1,1] => [2,2,6] => 1010100000 => 0101011111 => 5
[1,1,2,2,1,1,2,2] => [2,2,2,2] => 10101010 => 01010101 => 1
[1,1,2,2,2,2,1,1] => [2,4,2] => 10100010 => 01011101 => 3
[1,1,2,2,2,1,1,2] => [2,3,2,1] => 10100101 => 01011010 => 2
[1,1,2,2,3,3] => [2,2,2] => 101010 => 010101 => 1
[1,1,2,1,1,2,1,1,1,1] => [2,1,2,1,4] => 1011011000 => 0100100111 => 3
[1,1,2,1,1,2,2,2] => [2,1,2,3] => 10110100 => 01001011 => 2
[1,1,2,1,1,1,2,3] => [2,1,3,1,1] => 10110011 => 01001100 => 2
[1,1,2,1,2,3,1,1] => [2,1,1,1,1,2] => 10111110 => 01000001 => 1
[1,1,2,1,2,2,1,2] => [2,1,1,2,1,1] => 10111011 => 01000100 => 1
[1,1,2,1,2,1,1,3] => [2,1,1,1,2,1] => 10111101 => 01000010 => 1
[1,1,2,1,3,4] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,3,3,1,1,1,1] => [2,2,4] => 10101000 => 01010111 => 3
[1,1,3,3,2,2] => [2,2,2] => 101010 => 010101 => 1
[1,1,3,2,1,2,1,1] => [2,1,1,1,1,2] => 10111110 => 01000001 => 1
[1,1,3,2,1,1,1,2] => [2,1,1,3,1] => 10111001 => 01000110 => 2
[1,1,3,2,2,3] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,3,1,1,3,1,1] => [2,1,2,1,2] => 10110110 => 01001001 => 1
[1,1,3,1,1,2,1,2] => [2,1,2,1,1,1] => 10110111 => 01001000 => 1
[1,1,3,1,1,1,1,3] => [2,1,4,1] => 10110001 => 01001110 => 3
[1,1,3,1,2,4] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,4,4,1,1] => [2,2,2] => 101010 => 010101 => 1
[1,1,4,3,1,2] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,4,2,1,3] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,4,1,1,4] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,5,5] => [2,2] => 1010 => 0101 => 1
[2,2,1,1,1,1,1,1,1,1] => [2,8] => 1010000000 => 0101111111 => 7
[2,2,1,1,1,1,2,2] => [2,4,2] => 10100010 => 01011101 => 3
[2,2,1,1,2,2,1,1] => [2,2,2,2] => 10101010 => 01010101 => 1
[2,2,1,1,2,1,1,2] => [2,2,1,2,1] => 10101101 => 01010010 => 1
[2,2,1,1,3,3] => [2,2,2] => 101010 => 010101 => 1
[2,2,2,2,1,1,1,1] => [4,4] => 10001000 => 01110111 => 3
[2,2,2,2,2,2] => [6] => 100000 => 011111 => 5
[2,2,2,1,1,2,1,1] => [3,2,1,2] => 10010110 => 01101001 => 2
[2,2,2,1,1,1,1,2] => [3,4,1] => 10010001 => 01101110 => 3
[2,2,2,1,2,3] => [3,1,1,1] => 100111 => 011000 => 2
[2,2,3,3,1,1] => [2,2,2] => 101010 => 010101 => 1
[2,2,3,2,1,2] => [2,1,1,1,1] => 101111 => 010000 => 1
[2,2,3,1,1,3] => [2,1,2,1] => 101101 => 010010 => 1
[2,2,4,4] => [2,2] => 1010 => 0101 => 1
[2,1,1,2,1,1,1,1,1,1] => [1,2,1,6] => 1101100000 => 0010011111 => 5
[2,1,1,2,1,1,2,2] => [1,2,1,2,2] => 11011010 => 00100101 => 1
[2,1,1,2,2,2,1,1] => [1,2,3,2] => 11010010 => 00101101 => 2
[2,1,1,2,2,1,1,2] => [1,2,2,2,1] => 11010101 => 00101010 => 1
[2,1,1,2,3,3] => [1,2,1,2] => 110110 => 001001 => 1
[2,1,1,1,1,2,2,2] => [1,4,3] => 11000100 => 00111011 => 3
[2,1,1,1,1,1,2,3] => [1,5,1,1] => 11000011 => 00111100 => 4
[2,1,1,1,2,3,1,1] => [1,3,1,1,2] => 11001110 => 00110001 => 2
[2,1,1,1,2,2,1,2] => [1,3,2,1,1] => 11001011 => 00110100 => 2
[2,1,1,1,2,1,1,3] => [1,3,1,2,1] => 11001101 => 00110010 => 2
[2,1,1,1,3,4] => [1,3,1,1] => 110011 => 001100 => 2
[2,1,2,3,1,1,1,1] => [1,1,1,1,4] => 11111000 => 00000111 => 3
[2,1,2,3,2,2] => [1,1,1,1,2] => 111110 => 000001 => 1
[2,1,2,2,1,2,1,1] => [1,1,2,1,1,2] => 11101110 => 00010001 => 1
[2,1,2,2,1,1,1,2] => [1,1,2,3,1] => 11101001 => 00010110 => 2
[2,1,2,2,2,3] => [1,1,3,1] => 111001 => 000110 => 2
[2,1,2,1,1,3,1,1] => [1,1,1,2,1,2] => 11110110 => 00001001 => 1
[2,1,2,1,1,2,1,2] => [1,1,1,2,1,1,1] => 11110111 => 00001000 => 1
[2,1,2,1,1,1,1,3] => [1,1,1,4,1] => 11110001 => 00001110 => 3
[2,1,2,1,2,4] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[2,1,3,4,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[2,1,3,3,1,2] => [1,1,2,1,1] => 111011 => 000100 => 1
[2,1,3,2,1,3] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[2,1,3,1,1,4] => [1,1,1,2,1] => 111101 => 000010 => 1
[2,1,4,5] => [1,1,1,1] => 1111 => 0000 => 0
[3,3,1,1,1,1,1,1] => [2,6] => 10100000 => 01011111 => 5
[3,3,1,1,2,2] => [2,2,2] => 101010 => 010101 => 1
[3,3,2,2,1,1] => [2,2,2] => 101010 => 010101 => 1
[3,3,2,1,1,2] => [2,1,2,1] => 101101 => 010010 => 1
[3,3,3,3] => [4] => 1000 => 0111 => 3
[3,2,1,2,1,1,1,1] => [1,1,1,1,4] => 11111000 => 00000111 => 3
[3,2,1,2,2,2] => [1,1,1,3] => 111100 => 000011 => 2
[3,2,1,1,1,2,1,1] => [1,1,3,1,2] => 11100110 => 00011001 => 2
[3,2,1,1,1,1,1,2] => [1,1,5,1] => 11100001 => 00011110 => 4
[3,2,1,1,2,3] => [1,1,2,1,1] => 111011 => 000100 => 1
[3,2,2,3,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[3,2,2,2,1,2] => [1,3,1,1] => 110011 => 001100 => 2
[3,2,2,1,1,3] => [1,2,2,1] => 110101 => 001010 => 1
[3,2,3,4] => [1,1,1,1] => 1111 => 0000 => 0
[3,1,1,3,1,1,1,1] => [1,2,1,4] => 11011000 => 00100111 => 3
[3,1,1,3,2,2] => [1,2,1,2] => 110110 => 001001 => 1
[3,1,1,2,1,2,1,1] => [1,2,1,1,1,2] => 11011110 => 00100001 => 1
[3,1,1,2,1,1,1,2] => [1,2,1,3,1] => 11011001 => 00100110 => 2
[3,1,1,2,2,3] => [1,2,2,1] => 110101 => 001010 => 1
[3,1,1,1,1,3,1,1] => [1,4,1,2] => 11000110 => 00111001 => 3
[3,1,1,1,1,2,1,2] => [1,4,1,1,1] => 11000111 => 00111000 => 3
[3,1,1,1,1,1,1,3] => [1,6,1] => 11000001 => 00111110 => 5
[3,1,1,1,2,4] => [1,3,1,1] => 110011 => 001100 => 2
[3,1,2,4,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[3,1,2,3,1,2] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[3,1,2,2,1,3] => [1,1,2,1,1] => 111011 => 000100 => 1
[3,1,2,1,1,4] => [1,1,1,2,1] => 111101 => 000010 => 1
[3,1,3,5] => [1,1,1,1] => 1111 => 0000 => 0
[4,4,1,1,1,1] => [2,4] => 101000 => 010111 => 3
[4,4,2,2] => [2,2] => 1010 => 0101 => 1
[4,3,1,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[4,3,1,1,1,2] => [1,1,3,1] => 111001 => 000110 => 2
[4,3,2,3] => [1,1,1,1] => 1111 => 0000 => 0
[4,2,1,3,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[4,2,1,2,1,2] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[4,2,1,1,1,3] => [1,1,3,1] => 111001 => 000110 => 2
[4,2,2,4] => [1,2,1] => 1101 => 0010 => 1
[4,1,1,4,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[4,1,1,3,1,2] => [1,2,1,1,1] => 110111 => 001000 => 1
[4,1,1,2,1,3] => [1,2,1,1,1] => 110111 => 001000 => 1
[4,1,1,1,1,4] => [1,4,1] => 110001 => 001110 => 3
[4,1,2,5] => [1,1,1,1] => 1111 => 0000 => 0
[5,5,1,1] => [2,2] => 1010 => 0101 => 1
[5,4,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[5,3,1,3] => [1,1,1,1] => 1111 => 0000 => 0
[5,2,1,4] => [1,1,1,1] => 1111 => 0000 => 0
[5,1,1,5] => [1,2,1] => 1101 => 0010 => 1
[6,6] => [2] => 10 => 01 => 1
[1,2,2,2,2,2,1] => [1,5,1] => 1100001 => 0011110 => 4
[1,2,2,2,3,2] => [1,3,1,1] => 110011 => 001100 => 2
[1,2,2,3,3,1] => [1,2,2,1] => 110101 => 001010 => 1
[1,2,2,3,2,2] => [1,2,1,2] => 110110 => 001001 => 1
[1,2,2,4,3] => [1,2,1,1] => 11011 => 00100 => 1
[1,2,3,3,2,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,2,3,4,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,3,2,3,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,3,2,2,2] => [1,1,1,3] => 111100 => 000011 => 2
[1,2,3,3,3] => [1,1,3] => 11100 => 00011 => 2
[1,2,4,4,1] => [1,1,2,1] => 11101 => 00010 => 1
[1,2,4,3,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,4,2,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,5,4] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,3,2,2,1] => [1,2,2,1] => 110101 => 001010 => 1
[1,3,3,3,2] => [1,3,1] => 11001 => 00110 => 2
[1,3,4,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,4,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[1,3,5,3] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,2,3,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,3,2,4,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,2,2,3,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,3,2,2,2,2] => [1,1,4] => 111000 => 000111 => 3
[1,3,2,3,3] => [1,1,1,2] => 11110 => 00001 => 1
[1,3,3,4,1] => [1,2,1,1] => 11011 => 00100 => 1
[1,3,3,2,3] => [1,2,1,1] => 11011 => 00100 => 1
[1,3,4,4] => [1,1,2] => 1110 => 0001 => 1
[1,4,4,2,1] => [1,2,1,1] => 11011 => 00100 => 1
[1,4,5,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,4,3,3,1] => [1,1,2,1] => 11101 => 00010 => 1
[1,4,3,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[1,4,4,3] => [1,2,1] => 1101 => 0010 => 1
[1,4,2,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,2,3,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,2,2,3] => [1,1,2,1] => 11101 => 00010 => 1
[1,4,3,4] => [1,1,1,1] => 1111 => 0000 => 0
[1,5,5,1] => [1,2,1] => 1101 => 0010 => 1
[1,5,4,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,5,3,3] => [1,1,2] => 1110 => 0001 => 1
[1,5,2,4] => [1,1,1,1] => 1111 => 0000 => 0
[1,6,5] => [1,1,1] => 111 => 000 => 0
[2,3,2,2,2,1] => [1,1,3,1] => 111001 => 000110 => 2
[2,3,2,3,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,3,3,3,1] => [1,3,1] => 11001 => 00110 => 2
[2,3,3,2,2] => [1,2,2] => 11010 => 00101 => 1
[2,3,4,3] => [1,1,1,1] => 1111 => 0000 => 0
[2,4,3,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,4,4,2] => [1,2,1] => 1101 => 0010 => 1
[2,4,2,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,4,2,2,2] => [1,1,3] => 11100 => 00011 => 2
[2,4,3,3] => [1,1,2] => 1110 => 0001 => 1
[2,5,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,5,3,2] => [1,1,1,1] => 1111 => 0000 => 0
[2,5,2,3] => [1,1,1,1] => 1111 => 0000 => 0
[2,6,4] => [1,1,1] => 111 => 000 => 0
[2,2,3,2,2,1] => [2,1,2,1] => 101101 => 010010 => 1
[2,2,3,3,2] => [2,2,1] => 10101 => 01010 => 1
[2,2,4,3,1] => [2,1,1,1] => 10111 => 01000 => 1
[2,2,4,2,2] => [2,1,2] => 10110 => 01001 => 1
[2,2,5,3] => [2,1,1] => 1011 => 0100 => 1
[2,2,2,3,2,1] => [3,1,1,1] => 100111 => 011000 => 2
[2,2,2,4,2] => [3,1,1] => 10011 => 01100 => 2
[2,2,2,2,3,1] => [4,1,1] => 100011 => 011100 => 3
[2,2,2,3,3] => [3,2] => 10010 => 01101 => 2
[2,2,3,4,1] => [2,1,1,1] => 10111 => 01000 => 1
[2,2,3,2,3] => [2,1,1,1] => 10111 => 01000 => 1
[2,3,4,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,3,5,2] => [1,1,1,1] => 1111 => 0000 => 0
[2,3,2,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,3,2,2,3] => [1,1,2,1] => 11101 => 00010 => 1
[2,3,3,4] => [1,2,1] => 1101 => 0010 => 1
[2,4,5,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,4,2,4] => [1,1,1,1] => 1111 => 0000 => 0
[2,5,5] => [1,2] => 110 => 001 => 1
[3,4,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[3,4,3,2] => [1,1,1,1] => 1111 => 0000 => 0
[3,5,3,1] => [1,1,1,1] => 1111 => 0000 => 0
[3,5,2,2] => [1,1,2] => 1110 => 0001 => 1
[3,6,3] => [1,1,1] => 111 => 000 => 0
[3,3,3,2,1] => [3,1,1] => 10011 => 01100 => 2
[3,3,4,2] => [2,1,1] => 1011 => 0100 => 1
[3,3,2,3,1] => [2,1,1,1] => 10111 => 01000 => 1
[3,3,2,2,2] => [2,3] => 10100 => 01011 => 2
[3,4,4,1] => [1,2,1] => 1101 => 0010 => 1
[3,4,2,3] => [1,1,1,1] => 1111 => 0000 => 0
[3,5,4] => [1,1,1] => 111 => 000 => 0
[3,2,4,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[3,2,5,2] => [1,1,1,1] => 1111 => 0000 => 0
[3,2,3,3,1] => [1,1,2,1] => 11101 => 00010 => 1
[3,2,3,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[3,2,4,3] => [1,1,1,1] => 1111 => 0000 => 0
[3,2,2,4,1] => [1,2,1,1] => 11011 => 00100 => 1
[3,2,2,3,2] => [1,2,1,1] => 11011 => 00100 => 1
[3,2,2,2,3] => [1,3,1] => 11001 => 00110 => 2
[3,3,5,1] => [2,1,1] => 1011 => 0100 => 1
[3,3,2,4] => [2,1,1] => 1011 => 0100 => 1
[3,4,5] => [1,1,1] => 111 => 000 => 0
[4,5,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[4,6,2] => [1,1,1] => 111 => 000 => 0
[4,4,3,1] => [2,1,1] => 1011 => 0100 => 1
[4,5,3] => [1,1,1] => 111 => 000 => 0
[4,3,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[4,3,3,2] => [1,2,1] => 1101 => 0010 => 1
[4,4,4] => [3] => 100 => 011 => 2
[4,2,5,1] => [1,1,1,1] => 1111 => 0000 => 0
[4,2,4,2] => [1,1,1,1] => 1111 => 0000 => 0
[4,2,3,3] => [1,1,2] => 1110 => 0001 => 1
[4,3,5] => [1,1,1] => 111 => 000 => 0
[5,6,1] => [1,1,1] => 111 => 000 => 0
[5,5,2] => [2,1] => 101 => 010 => 1
[5,4,3] => [1,1,1] => 111 => 000 => 0
[5,3,4] => [1,1,1] => 111 => 000 => 0
[5,2,5] => [1,1,1] => 111 => 000 => 0
[1,8,2] => [1,1,1] => 111 => 000 => 0
[1,7,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,6,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[1,5,1,1,1,2] => [1,1,3,1] => 111001 => 000110 => 2
[1,4,1,1,1,1,2] => [1,1,4,1] => 1110001 => 0001110 => 3
[1,3,1,1,1,1,1,2] => [1,1,5,1] => 11100001 => 00011110 => 4
[1,2,1,1,1,1,1,1,2] => [1,1,6,1] => 111000001 => 000111110 => 5
[1,11] => [1,1] => 11 => 00 => 0
[1,9,2] => [1,1,1] => 111 => 000 => 0
[1,7,3] => [1,1,1] => 111 => 000 => 0
[1,8,1,2] => [1,1,1,1] => 1111 => 0000 => 0
[1,6,2,2] => [1,1,2] => 1110 => 0001 => 1
[1,7,1,1,2] => [1,1,2,1] => 11101 => 00010 => 1
[1,5,2,1,2] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,6,1,1,1,2] => [1,1,3,1] => 111001 => 000110 => 2
[1,4,2,1,1,2] => [1,1,1,2,1] => 111101 => 000010 => 1
[1,5,1,1,1,1,2] => [1,1,4,1] => 1110001 => 0001110 => 3
[1,3,2,1,1,1,2] => [1,1,1,3,1] => 1111001 => 0000110 => 2
[1,4,1,1,1,1,1,2] => [1,1,5,1] => 11100001 => 00011110 => 4
[1,2,2,1,1,1,1,2] => [1,2,4,1] => 11010001 => 00101110 => 3
[1,3,1,1,1,1,1,1,2] => [1,1,6,1] => 111000001 => 000111110 => 5
[1,1,2,1,1,1,1,1,2] => [2,1,5,1] => 101100001 => 010011110 => 4
[1,2,1,1,1,1,1,1,1,2] => [1,1,7,1] => 1110000001 => 0001111110 => 6
[1,2,2,2,2,2] => [1,5] => 110000 => 001111 => 4
[1,2,2,2,1,3] => [1,3,1,1] => 110011 => 001100 => 2
[1,2,2,1,3,2] => [1,2,1,1,1] => 110111 => 001000 => 1
[1,2,2,1,2,3] => [1,2,1,1,1] => 110111 => 001000 => 1
[1,2,2,1,1,4] => [1,2,2,1] => 110101 => 001010 => 1
[1,2,1,3,2,2] => [1,1,1,1,2] => 111110 => 000001 => 1
[1,2,1,3,1,3] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,1,2,3,2] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,1,2,2,3] => [1,1,1,2,1] => 111101 => 000010 => 1
[1,2,1,2,1,4] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[1,2,1,1,4,2] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,2,1,1,3,3] => [1,1,2,2] => 111010 => 000101 => 1
[1,2,1,1,2,4] => [1,1,2,1,1] => 111011 => 000100 => 1
[1,2,1,1,1,5] => [1,1,3,1] => 111001 => 000110 => 2
[1,1,3,2,2,2] => [2,1,3] => 101100 => 010011 => 2
[1,1,3,2,1,3] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,3,1,3,2] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,3,1,2,3] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,3,1,1,4] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,2,3,2,2] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,2,3,1,3] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,2,3,2] => [2,2,1,1] => 101011 => 010100 => 1
[1,1,2,2,2,3] => [2,3,1] => 101001 => 010110 => 2
[1,1,2,2,1,4] => [2,2,1,1] => 101011 => 010100 => 1
[1,1,2,1,4,2] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,1,3,3] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,2,1,2,4] => [2,1,1,1,1] => 101111 => 010000 => 1
[1,1,2,1,1,5] => [2,1,2,1] => 101101 => 010010 => 1
[1,1,1,4,2,2] => [3,1,2] => 100110 => 011001 => 2
[1,1,1,4,1,3] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,3,3,2] => [3,2,1] => 100101 => 011010 => 2
[1,1,1,3,2,3] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,3,1,4] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,2,4,2] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,2,3,3] => [3,1,2] => 100110 => 011001 => 2
[1,1,1,2,2,4] => [3,2,1] => 100101 => 011010 => 2
[1,1,1,2,1,5] => [3,1,1,1] => 100111 => 011000 => 2
[1,1,1,1,5,2] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,4,3] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,3,4] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,2,5] => [4,1,1] => 100011 => 011100 => 3
[1,1,1,1,1,6] => [5,1] => 100001 => 011110 => 4
[1,2,2,2,2,2,2] => [1,6] => 1100000 => 0011111 => 5
[1,2,2,2,2,1,3] => [1,4,1,1] => 1100011 => 0011100 => 3
[1,2,2,2,1,3,2] => [1,3,1,1,1] => 1100111 => 0011000 => 2
[1,2,2,2,1,2,3] => [1,3,1,1,1] => 1100111 => 0011000 => 2
[1,2,2,2,1,1,4] => [1,3,2,1] => 1100101 => 0011010 => 2
[1,2,2,1,3,2,2] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[1,2,2,1,3,1,3] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[1,2,2,1,2,3,2] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[1,2,2,1,2,2,3] => [1,2,1,2,1] => 1101101 => 0010010 => 1
[1,2,2,1,2,1,4] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[1,2,2,1,1,4,2] => [1,2,2,1,1] => 1101011 => 0010100 => 1
[1,2,2,1,1,3,3] => [1,2,2,2] => 1101010 => 0010101 => 1
[1,2,2,1,1,2,4] => [1,2,2,1,1] => 1101011 => 0010100 => 1
[1,2,2,1,1,1,5] => [1,2,3,1] => 1101001 => 0010110 => 2
[1,2,1,3,2,2,2] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,2,1,3,2,1,3] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,3,1,3,2] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,3,1,2,3] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,3,1,1,4] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[1,2,1,2,3,2,2] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[1,2,1,2,3,1,3] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,2,2,3,2] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[1,2,1,2,2,2,3] => [1,1,1,3,1] => 1111001 => 0000110 => 2
[1,2,1,2,2,1,4] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[1,2,1,2,1,4,2] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,2,1,3,3] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[1,2,1,2,1,2,4] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,2,1,1,5] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[1,2,1,1,4,2,2] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[1,2,1,1,4,1,3] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,1,1,3,3,2] => [1,1,2,2,1] => 1110101 => 0001010 => 1
[1,2,1,1,3,2,3] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,1,1,3,1,4] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,1,1,2,4,2] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,1,1,2,3,3] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[1,2,1,1,2,2,4] => [1,1,2,2,1] => 1110101 => 0001010 => 1
[1,2,1,1,2,1,5] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,1,1,1,5,2] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,2,1,1,1,4,3] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,2,1,1,1,3,4] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,2,1,1,1,2,5] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,2,1,1,1,1,6] => [1,1,4,1] => 1110001 => 0001110 => 3
[1,1,3,2,2,2,2] => [2,1,4] => 1011000 => 0100111 => 3
[1,1,3,2,2,1,3] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,3,2,1,3,2] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,3,2,1,2,3] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,3,2,1,1,4] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[1,1,3,1,3,2,2] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[1,1,3,1,3,1,3] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,3,1,2,3,2] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,3,1,2,2,3] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[1,1,3,1,2,1,4] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,3,1,1,4,2] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,3,1,1,3,3] => [2,1,2,2] => 1011010 => 0100101 => 1
[1,1,3,1,1,2,4] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,3,1,1,1,5] => [2,1,3,1] => 1011001 => 0100110 => 2
[1,1,2,3,2,2,2] => [2,1,1,3] => 1011100 => 0100011 => 2
[1,1,2,3,2,1,3] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,2,3,1,3,2] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,2,3,1,2,3] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,2,3,1,1,4] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[1,1,2,2,3,2,2] => [2,2,1,2] => 1010110 => 0101001 => 1
[1,1,2,2,3,1,3] => [2,2,1,1,1] => 1010111 => 0101000 => 1
[1,1,2,2,2,3,2] => [2,3,1,1] => 1010011 => 0101100 => 2
[1,1,2,2,2,2,3] => [2,4,1] => 1010001 => 0101110 => 3
[1,1,2,2,2,1,4] => [2,3,1,1] => 1010011 => 0101100 => 2
[1,1,2,2,1,4,2] => [2,2,1,1,1] => 1010111 => 0101000 => 1
[1,1,2,2,1,3,3] => [2,2,1,2] => 1010110 => 0101001 => 1
[1,1,2,2,1,2,4] => [2,2,1,1,1] => 1010111 => 0101000 => 1
[1,1,2,2,1,1,5] => [2,2,2,1] => 1010101 => 0101010 => 1
[1,1,2,1,4,2,2] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[1,1,2,1,4,1,3] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,2,1,3,3,2] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[1,1,2,1,3,2,3] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,2,1,3,1,4] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,2,1,2,4,2] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,2,1,2,3,3] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[1,1,2,1,2,2,4] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[1,1,2,1,2,1,5] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,2,1,1,5,2] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,2,1,1,4,3] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,2,1,1,3,4] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,2,1,1,2,5] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[1,1,2,1,1,1,6] => [2,1,3,1] => 1011001 => 0100110 => 2
[1,1,1,4,2,2,2] => [3,1,3] => 1001100 => 0110011 => 2
[1,1,1,4,2,1,3] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,4,1,3,2] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,4,1,2,3] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,4,1,1,4] => [3,1,2,1] => 1001101 => 0110010 => 2
[1,1,1,3,3,2,2] => [3,2,2] => 1001010 => 0110101 => 2
[1,1,1,3,3,1,3] => [3,2,1,1] => 1001011 => 0110100 => 2
[1,1,1,3,2,3,2] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,3,2,2,3] => [3,1,2,1] => 1001101 => 0110010 => 2
[1,1,1,3,2,1,4] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,3,1,4,2] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,3,1,3,3] => [3,1,1,2] => 1001110 => 0110001 => 2
[1,1,1,3,1,2,4] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,3,1,1,5] => [3,1,2,1] => 1001101 => 0110010 => 2
[1,1,1,2,4,2,2] => [3,1,1,2] => 1001110 => 0110001 => 2
[1,1,1,2,4,1,3] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,3,3,2] => [3,1,2,1] => 1001101 => 0110010 => 2
[1,1,1,2,3,2,3] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,3,1,4] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,2,4,2] => [3,2,1,1] => 1001011 => 0110100 => 2
[1,1,1,2,2,3,3] => [3,2,2] => 1001010 => 0110101 => 2
[1,1,1,2,2,2,4] => [3,3,1] => 1001001 => 0110110 => 2
[1,1,1,2,2,1,5] => [3,2,1,1] => 1001011 => 0110100 => 2
[1,1,1,2,1,5,2] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,1,4,3] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,1,3,4] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,1,2,5] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,1,1,6] => [3,1,2,1] => 1001101 => 0110010 => 2
[1,1,1,1,5,2,2] => [4,1,2] => 1000110 => 0111001 => 3
[1,1,1,1,5,1,3] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,4,3,2] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,4,2,3] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,4,1,4] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,3,4,2] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,3,3,3] => [4,3] => 1000100 => 0111011 => 3
[1,1,1,1,3,2,4] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,3,1,5] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,2,5,2] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,2,4,3] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,2,3,4] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,2,2,5] => [4,2,1] => 1000101 => 0111010 => 3
[1,1,1,1,2,1,6] => [4,1,1,1] => 1000111 => 0111000 => 3
[1,1,1,1,1,6,2] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,5,3] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,4,4] => [5,2] => 1000010 => 0111101 => 4
[1,1,1,1,1,3,5] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,2,6] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,1,7] => [6,1] => 1000001 => 0111110 => 5
[12] => [1] => 1 => 0 => 0
[1,2,9] => [1,1,1] => 111 => 000 => 0
[3,2,7] => [1,1,1] => 111 => 000 => 0
[1,4,7] => [1,1,1] => 111 => 000 => 0
[1,1,2,1,7] => [2,1,1,1] => 10111 => 01000 => 1
[1,2,2,2,5] => [1,3,1] => 11001 => 00110 => 2
[1,1,2,3,5] => [2,1,1,1] => 10111 => 01000 => 1
[3,1,2,1,5] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,2,1,5] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,1,4,1,5] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,1,2,1,1,5] => [3,1,2,1] => 1001101 => 0110010 => 2
[7,2,3] => [1,1,1] => 111 => 000 => 0
[1,1,2,1,2,2,3] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[1,8,3] => [1,1,1] => 111 => 000 => 0
[1,1,2,5,3] => [2,1,1,1] => 10111 => 01000 => 1
[3,1,2,3,3] => [1,1,1,2] => 11110 => 00001 => 1
[1,1,4,3,3] => [2,1,2] => 10110 => 01001 => 1
[1,1,1,2,1,3,3] => [3,1,1,2] => 1001110 => 0110001 => 2
[5,1,2,1,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,2,1,2,1,3] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[3,3,2,1,3] => [2,1,1,1] => 10111 => 01000 => 1
[1,5,2,1,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,1,2,2,2,1,3] => [2,3,1,1] => 1010011 => 0101100 => 2
[3,1,4,1,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,4,1,3] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,1,6,1,3] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,1,2,3,1,3] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[3,1,1,2,1,1,3] => [1,2,1,2,1] => 1101101 => 0010010 => 1
[1,3,1,2,1,1,3] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[1,1,3,2,1,1,3] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[1,1,1,4,1,1,3] => [3,1,2,1] => 1001101 => 0110010 => 2
[1,1,1,1,2,1,1,1,3] => [4,1,3,1] => 100011001 => 011100110 => 3
[9,2,1] => [1,1,1] => 111 => 000 => 0
[1,2,6,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,1,2,1,4,2,1] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[5,2,2,2,1] => [1,3,1] => 11001 => 00110 => 2
[1,6,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[1,1,2,3,2,2,1] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[3,1,2,1,2,2,1] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[1,3,2,1,2,2,1] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[1,1,4,1,2,2,1] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[1,1,1,2,1,1,2,2,1] => [3,1,2,2,1] => 100110101 => 011001010 => 2
[7,4,1] => [1,1,1] => 111 => 000 => 0
[1,1,2,1,2,4,1] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,2,2,6,1] => [1,2,1,1] => 11011 => 00100 => 1
[3,8,1] => [1,1,1] => 111 => 000 => 0
[1,10,1] => [1,1,1] => 111 => 000 => 0
[1,1,2,7,1] => [2,1,1,1] => 10111 => 01000 => 1
[3,1,2,5,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,2,5,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,1,4,5,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,1,2,1,5,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[5,1,2,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,2,1,2,3,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[1,5,2,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,1,2,2,2,3,1] => [2,3,1,1] => 1010011 => 0101100 => 2
[3,1,4,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,1,6,3,1] => [2,1,1,1] => 10111 => 01000 => 1
[1,1,1,2,3,3,1] => [3,1,2,1] => 1001101 => 0110010 => 2
[3,1,1,2,1,3,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[1,3,1,2,1,3,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,1,3,2,1,3,1] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[1,1,1,4,1,3,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,1,2,1,1,3,1] => [4,1,2,1,1] => 100011011 => 011100100 => 3
[7,1,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,2,4,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[3,2,2,1,2,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[1,4,2,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[1,1,2,1,2,1,2,1,1] => [2,1,1,1,1,1,2] => 101111110 => 010000001 => 1
[5,3,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,2,2,3,2,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[3,5,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,7,2,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,1,2,4,2,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[3,1,2,2,2,1,1] => [1,1,3,2] => 1110010 => 0001101 => 2
[1,3,2,2,2,1,1] => [1,1,3,2] => 1110010 => 0001101 => 2
[1,1,4,2,2,1,1] => [2,1,2,2] => 1011010 => 0100101 => 1
[1,1,1,2,1,2,2,1,1] => [3,1,1,2,2] => 100111010 => 011000101 => 2
[5,1,4,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,2,2,1,4,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[3,3,4,1,1] => [2,1,2] => 10110 => 01001 => 1
[1,5,4,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,1,2,2,4,1,1] => [2,2,1,2] => 1010110 => 0101001 => 1
[3,1,6,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,3,6,1,1] => [1,1,1,2] => 11110 => 00001 => 1
[1,1,8,1,1] => [2,1,2] => 10110 => 01001 => 1
[1,1,1,2,5,1,1] => [3,1,1,2] => 1001110 => 0110001 => 2
[3,1,1,2,3,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[1,3,1,2,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[1,1,3,2,3,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[1,1,1,4,3,1,1] => [3,1,1,2] => 1001110 => 0110001 => 2
[1,1,1,1,2,1,3,1,1] => [4,1,1,1,2] => 100011110 => 011100001 => 3
[5,1,1,2,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[1,2,2,1,1,2,1,1,1] => [1,2,2,1,3] => 110101100 => 001010011 => 2
[3,3,1,2,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[1,5,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,1,2,2,1,2,1,1,1] => [2,2,1,1,3] => 101011100 => 010100011 => 2
[3,1,3,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,3,3,2,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[1,1,5,2,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[1,1,1,2,2,2,1,1,1] => [3,3,3] => 100100100 => 011011011 => 2
[3,1,1,4,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[1,3,1,4,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,1,3,4,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[1,1,1,6,1,1,1] => [3,1,3] => 1001100 => 0110011 => 2
[1,1,1,1,2,3,1,1,1] => [4,1,1,3] => 100011100 => 011100011 => 3
[3,1,1,1,2,1,1,1,1] => [1,3,1,4] => 110011000 => 001100111 => 3
[1,3,1,1,2,1,1,1,1] => [1,1,2,1,4] => 111011000 => 000100111 => 3
[1,1,3,1,2,1,1,1,1] => [2,1,1,1,4] => 101111000 => 010000111 => 3
[1,1,1,3,2,1,1,1,1] => [3,1,1,4] => 100111000 => 011000111 => 3
[1,1,1,1,4,1,1,1,1] => [4,1,4] => 100011000 => 011100111 => 3
[2,2,2,2,1,2,1] => [4,1,1,1] => 1000111 => 0111000 => 3
[2,2,2,1,2,1,2] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[2,2,2,1,2,2,1] => [3,1,2,1] => 1001101 => 0110010 => 2
[2,2,2,1,1,2,2] => [3,2,2] => 1001010 => 0110101 => 2
[2,2,1,2,1,2,2] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[2,2,1,2,1,1,2,1] => [2,1,1,2,1,1] => 10111011 => 01000100 => 1
[2,2,1,2,2,1,2] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[2,2,1,2,2,2,1] => [2,1,3,1] => 1011001 => 0100110 => 2
[2,2,1,1,2,2,2] => [2,2,3] => 1010100 => 0101011 => 2
[2,2,1,1,2,1,2,1] => [2,2,1,1,1,1] => 10101111 => 01010000 => 1
[2,2,1,1,1,2,2,1] => [2,3,2,1] => 10100101 => 01011010 => 2
[2,1,2,1,2,2,2] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[2,1,2,1,2,1,2,1] => [1,1,1,1,1,1,1,1] => 11111111 => 00000000 => 0
[2,1,2,1,1,2,2,1] => [1,1,1,2,2,1] => 11110101 => 00001010 => 1
[2,1,2,1,1,1,2,2] => [1,1,1,3,2] => 11110010 => 00001101 => 2
[2,1,2,2,1,2,2] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[2,1,2,2,1,1,2,1] => [1,1,2,2,1,1] => 11101011 => 00010100 => 1
[2,1,2,2,2,1,2] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[2,1,2,2,2,2,1] => [1,1,4,1] => 1110001 => 0001110 => 3
[2,1,1,2,2,2,2] => [1,2,4] => 1101000 => 0010111 => 3
[2,1,1,2,2,1,2,1] => [1,2,2,1,1,1] => 11010111 => 00101000 => 1
[2,1,1,2,1,2,1,2] => [1,2,1,1,1,1,1] => 11011111 => 00100000 => 1
[2,1,1,2,1,2,2,1] => [1,2,1,1,2,1] => 11011101 => 00100010 => 1
[2,1,1,1,2,2,2,1] => [1,3,3,1] => 11001001 => 00110110 => 2
[2,1,1,1,2,1,2,2] => [1,3,1,1,2] => 11001110 => 00110001 => 2
[1,2,1,2,2,2,2] => [1,1,1,4] => 1111000 => 0000111 => 3
[1,2,1,2,2,1,2,1] => [1,1,1,2,1,1,1] => 11110111 => 00001000 => 1
[1,2,1,2,1,2,1,2] => [1,1,1,1,1,1,1,1] => 11111111 => 00000000 => 0
[1,2,1,2,1,2,2,1] => [1,1,1,1,1,2,1] => 11111101 => 00000010 => 1
[1,2,1,2,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 00000101 => 1
[1,2,1,1,2,1,2,2] => [1,1,2,1,1,2] => 11101110 => 00010001 => 1
[1,2,1,1,2,1,1,2,1] => [1,1,2,1,2,1,1] => 111011011 => 000100100 => 1
[1,2,1,1,2,2,1,2] => [1,1,2,2,1,1] => 11101011 => 00010100 => 1
[1,2,1,1,2,2,2,1] => [1,1,2,3,1] => 11101001 => 00010110 => 2
[1,2,1,1,1,2,2,2] => [1,1,3,3] => 11100100 => 00011011 => 2
[1,2,1,1,1,2,1,2,1] => [1,1,3,1,1,1,1] => 111001111 => 000110000 => 2
[1,2,1,1,1,1,2,2,1] => [1,1,4,2,1] => 111000101 => 000111010 => 3
[1,2,2,1,2,2,2] => [1,2,1,3] => 1101100 => 0010011 => 2
[1,2,2,1,2,1,2,1] => [1,2,1,1,1,1,1] => 11011111 => 00100000 => 1
[1,2,2,1,1,2,1,2] => [1,2,2,1,1,1] => 11010111 => 00101000 => 1
[1,2,2,1,1,2,2,1] => [1,2,2,2,1] => 11010101 => 00101010 => 1
[1,2,2,1,1,1,2,2] => [1,2,3,2] => 11010010 => 00101101 => 2
[1,2,2,2,1,2,2] => [1,3,1,2] => 1100110 => 0011001 => 2
[1,2,2,2,1,1,2,1] => [1,3,2,1,1] => 11001011 => 00110100 => 2
[1,2,2,2,2,1,2] => [1,4,1,1] => 1100011 => 0011100 => 3
[1,1,2,2,2,2,2] => [2,5] => 1010000 => 0101111 => 4
[1,1,2,2,2,1,2,1] => [2,3,1,1,1] => 10100111 => 01011000 => 2
[1,1,2,2,1,2,1,2] => [2,2,1,1,1,1] => 10101111 => 01010000 => 1
[1,1,2,2,1,2,2,1] => [2,2,1,2,1] => 10101101 => 01010010 => 1
[1,1,2,1,2,1,2,2] => [2,1,1,1,1,2] => 10111110 => 01000001 => 1
[1,1,2,1,2,1,1,2,1] => [2,1,1,1,2,1,1] => 101111011 => 010000100 => 1
[1,1,2,1,2,2,2,1] => [2,1,1,3,1] => 10111001 => 01000110 => 2
[1,1,2,1,1,2,1,2,1] => [2,1,2,1,1,1,1] => 101101111 => 010010000 => 1
[1,1,2,1,1,1,2,2,1] => [2,1,3,2,1] => 101100101 => 010011010 => 2
[1,1,1,2,2,1,2,2] => [3,2,1,2] => 10010110 => 01101001 => 2
[1,1,1,2,2,1,1,2,1] => [3,2,2,1,1] => 100101011 => 011010100 => 2
[1,1,1,2,2,2,1,2] => [3,3,1,1] => 10010011 => 01101100 => 2
[1,1,1,2,2,2,2,1] => [3,4,1] => 10010001 => 01101110 => 3
[1,1,1,2,1,2,2,2] => [3,1,1,3] => 10011100 => 01100011 => 2
[1,1,1,2,1,2,1,2,1] => [3,1,1,1,1,1,1] => 100111111 => 011000000 => 2
[1,1,1,1,2,2,1,2,1] => [4,2,1,1,1] => 100010111 => 011101000 => 3
[1,1,1,1,2,1,2,2,1] => [4,1,1,2,1] => 100011101 => 011100010 => 3
[1,1,1,1,1,2,2,2,1] => [5,3,1] => 100001001 => 011110110 => 4
[3,3,3,2] => [3,1] => 1001 => 0110 => 2
[3,4,4] => [1,2] => 110 => 001 => 1
[2,3,3,3] => [1,3] => 1100 => 0011 => 2
[4,4,3] => [2,1] => 101 => 010 => 1
[3,2,2,2,2,1] => [1,4,1] => 110001 => 001110 => 3
[4,3,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[4,2,3,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[4,2,2,3,1] => [1,2,1,1] => 11011 => 00100 => 1
[4,2,2,2,2] => [1,4] => 11000 => 00111 => 3
[5,4,2,1] => [1,1,1,1] => 1111 => 0000 => 0
[5,3,3,1] => [1,2,1] => 1101 => 0010 => 1
[5,3,2,2] => [1,1,2] => 1110 => 0001 => 1
[5,2,4,1] => [1,1,1,1] => 1111 => 0000 => 0
[5,2,3,2] => [1,1,1,1] => 1111 => 0000 => 0
[5,2,2,3] => [1,2,1] => 1101 => 0010 => 1
[6,5,1] => [1,1,1] => 111 => 000 => 0
[6,4,2] => [1,1,1] => 111 => 000 => 0
[6,3,3] => [1,2] => 110 => 001 => 1
[6,2,4] => [1,1,1] => 111 => 000 => 0
[7,5] => [1,1] => 11 => 00 => 0
[2,8,1] => [1,1,1] => 111 => 000 => 0
[2,1,7,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,1,1,6,1] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,1,1,5,1] => [1,3,1,1] => 110011 => 001100 => 2
[2,1,1,1,1,4,1] => [1,4,1,1] => 1100011 => 0011100 => 3
[2,1,1,1,1,1,3,1] => [1,5,1,1] => 11000011 => 00111100 => 4
[2,1,1,1,1,1,1,2,1] => [1,6,1,1] => 110000011 => 001111100 => 5
[11,1] => [1,1] => 11 => 00 => 0
[2,9,1] => [1,1,1] => 111 => 000 => 0
[3,7,1] => [1,1,1] => 111 => 000 => 0
[2,1,8,1] => [1,1,1,1] => 1111 => 0000 => 0
[2,2,6,1] => [2,1,1] => 1011 => 0100 => 1
[2,1,1,7,1] => [1,2,1,1] => 11011 => 00100 => 1
[2,1,2,5,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,1,1,1,6,1] => [1,3,1,1] => 110011 => 001100 => 2
[2,1,1,2,4,1] => [1,2,1,1,1] => 110111 => 001000 => 1
[2,1,1,1,1,5,1] => [1,4,1,1] => 1100011 => 0011100 => 3
[2,1,1,1,2,3,1] => [1,3,1,1,1] => 1100111 => 0011000 => 2
[2,1,1,1,1,1,4,1] => [1,5,1,1] => 11000011 => 00111100 => 4
[2,1,1,1,1,2,2,1] => [1,4,2,1] => 11000101 => 00111010 => 3
[2,1,1,1,1,1,1,3,1] => [1,6,1,1] => 110000011 => 001111100 => 5
[2,1,1,1,1,1,2,1,1] => [1,5,1,2] => 110000110 => 001111001 => 4
[2,2,2,2,2,1] => [5,1] => 100001 => 011110 => 4
[3,1,2,2,2,1] => [1,1,3,1] => 111001 => 000110 => 2
[2,3,1,2,2,1] => [1,1,1,2,1] => 111101 => 000010 => 1
[3,2,1,2,2,1] => [1,1,1,2,1] => 111101 => 000010 => 1
[4,1,1,2,2,1] => [1,2,2,1] => 110101 => 001010 => 1
[2,2,3,1,2,1] => [2,1,1,1,1] => 101111 => 010000 => 1
[3,1,3,1,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[2,3,2,1,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[3,2,2,1,2,1] => [1,2,1,1,1] => 110111 => 001000 => 1
[4,1,2,1,2,1] => [1,1,1,1,1,1] => 111111 => 000000 => 0
[2,4,1,1,2,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[3,3,1,1,2,1] => [2,2,1,1] => 101011 => 010100 => 1
[4,2,1,1,2,1] => [1,1,2,1,1] => 111011 => 000100 => 1
[5,1,1,1,2,1] => [1,3,1,1] => 110011 => 001100 => 2
[2,2,2,3,1,1] => [3,1,2] => 100110 => 011001 => 2
[3,1,2,3,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[2,3,1,3,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[3,2,1,3,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[4,1,1,3,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[2,2,3,2,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[3,1,3,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[2,3,2,2,1,1] => [1,1,2,2] => 111010 => 000101 => 1
[3,2,2,2,1,1] => [1,3,2] => 110010 => 001101 => 2
[4,1,2,2,1,1] => [1,1,2,2] => 111010 => 000101 => 1
[2,4,1,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[3,3,1,2,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[4,2,1,2,1,1] => [1,1,1,1,2] => 111110 => 000001 => 1
[5,1,1,2,1,1] => [1,2,1,2] => 110110 => 001001 => 1
[2,2,4,1,1,1] => [2,1,3] => 101100 => 010011 => 2
[3,1,4,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[2,3,3,1,1,1] => [1,2,3] => 110100 => 001011 => 2
[3,2,3,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[4,1,3,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[2,4,2,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[3,3,2,1,1,1] => [2,1,3] => 101100 => 010011 => 2
[4,2,2,1,1,1] => [1,2,3] => 110100 => 001011 => 2
[5,1,2,1,1,1] => [1,1,1,3] => 111100 => 000011 => 2
[2,5,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[3,4,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[4,3,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[5,2,1,1,1,1] => [1,1,4] => 111000 => 000111 => 3
[6,1,1,1,1,1] => [1,5] => 110000 => 001111 => 4
[2,2,2,2,2,2,1] => [6,1] => 1000001 => 0111110 => 5
[3,1,2,2,2,2,1] => [1,1,4,1] => 1110001 => 0001110 => 3
[2,3,1,2,2,2,1] => [1,1,1,3,1] => 1111001 => 0000110 => 2
[3,2,1,2,2,2,1] => [1,1,1,3,1] => 1111001 => 0000110 => 2
[4,1,1,2,2,2,1] => [1,2,3,1] => 1101001 => 0010110 => 2
[2,2,3,1,2,2,1] => [2,1,1,2,1] => 1011101 => 0100010 => 1
[3,1,3,1,2,2,1] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[2,3,2,1,2,2,1] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[3,2,2,1,2,2,1] => [1,2,1,2,1] => 1101101 => 0010010 => 1
[4,1,2,1,2,2,1] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[2,4,1,1,2,2,1] => [1,1,2,2,1] => 1110101 => 0001010 => 1
[3,3,1,1,2,2,1] => [2,2,2,1] => 1010101 => 0101010 => 1
[4,2,1,1,2,2,1] => [1,1,2,2,1] => 1110101 => 0001010 => 1
[5,1,1,1,2,2,1] => [1,3,2,1] => 1100101 => 0011010 => 2
[2,2,2,3,1,2,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[3,1,2,3,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[2,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[3,2,1,3,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[4,1,1,3,1,2,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[2,2,3,2,1,2,1] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[3,1,3,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[2,3,2,2,1,2,1] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[3,2,2,2,1,2,1] => [1,3,1,1,1] => 1100111 => 0011000 => 2
[4,1,2,2,1,2,1] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[2,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[3,3,1,2,1,2,1] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[4,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[5,1,1,2,1,2,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[2,2,4,1,1,2,1] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[3,1,4,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[2,3,3,1,1,2,1] => [1,2,2,1,1] => 1101011 => 0010100 => 1
[3,2,3,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[4,1,3,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[2,4,2,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[3,3,2,1,1,2,1] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[4,2,2,1,1,2,1] => [1,2,2,1,1] => 1101011 => 0010100 => 1
[5,1,2,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[2,5,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[3,4,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[4,3,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[5,2,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[6,1,1,1,1,2,1] => [1,4,1,1] => 1100011 => 0011100 => 3
[2,2,2,2,3,1,1] => [4,1,2] => 1000110 => 0111001 => 3
[3,1,2,2,3,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[2,3,1,2,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[3,2,1,2,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[4,1,1,2,3,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[2,2,3,1,3,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[3,1,3,1,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,3,2,1,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[3,2,2,1,3,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[4,1,2,1,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,4,1,1,3,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[3,3,1,1,3,1,1] => [2,2,1,2] => 1010110 => 0101001 => 1
[4,2,1,1,3,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[5,1,1,1,3,1,1] => [1,3,1,2] => 1100110 => 0011001 => 2
[2,2,2,3,2,1,1] => [3,1,1,2] => 1001110 => 0110001 => 2
[3,1,2,3,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,3,1,3,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[3,2,1,3,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[4,1,1,3,2,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[2,2,3,2,2,1,1] => [2,1,2,2] => 1011010 => 0100101 => 1
[3,1,3,2,2,1,1] => [1,1,1,2,2] => 1111010 => 0000101 => 1
[2,3,2,2,2,1,1] => [1,1,3,2] => 1110010 => 0001101 => 2
[3,2,2,2,2,1,1] => [1,4,2] => 1100010 => 0011101 => 3
[4,1,2,2,2,1,1] => [1,1,3,2] => 1110010 => 0001101 => 2
[2,4,1,2,2,1,1] => [1,1,1,2,2] => 1111010 => 0000101 => 1
[3,3,1,2,2,1,1] => [2,1,2,2] => 1011010 => 0100101 => 1
[4,2,1,2,2,1,1] => [1,1,1,2,2] => 1111010 => 0000101 => 1
[5,1,1,2,2,1,1] => [1,2,2,2] => 1101010 => 0010101 => 1
[2,2,4,1,2,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[3,1,4,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,3,3,1,2,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[3,2,3,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[4,1,3,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,4,2,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[3,3,2,1,2,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[4,2,2,1,2,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[5,1,2,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,5,1,1,2,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[3,4,1,1,2,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[4,3,1,1,2,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[5,2,1,1,2,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[6,1,1,1,2,1,1] => [1,3,1,2] => 1100110 => 0011001 => 2
[2,2,2,4,1,1,1] => [3,1,3] => 1001100 => 0110011 => 2
[3,1,2,4,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[2,3,1,4,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[3,2,1,4,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[4,1,1,4,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[2,2,3,3,1,1,1] => [2,2,3] => 1010100 => 0101011 => 2
[3,1,3,3,1,1,1] => [1,1,2,3] => 1110100 => 0001011 => 2
[2,3,2,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[3,2,2,3,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[4,1,2,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[2,4,1,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[3,3,1,3,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[4,2,1,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[5,1,1,3,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[2,2,4,2,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[3,1,4,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[2,3,3,2,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[3,2,3,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[4,1,3,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[2,4,2,2,1,1,1] => [1,1,2,3] => 1110100 => 0001011 => 2
[3,3,2,2,1,1,1] => [2,2,3] => 1010100 => 0101011 => 2
[4,2,2,2,1,1,1] => [1,3,3] => 1100100 => 0011011 => 2
[5,1,2,2,1,1,1] => [1,1,2,3] => 1110100 => 0001011 => 2
[2,5,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[3,4,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[4,3,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[5,2,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[6,1,1,2,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[2,2,5,1,1,1,1] => [2,1,4] => 1011000 => 0100111 => 3
[3,1,5,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[2,3,4,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[3,2,4,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[4,1,4,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[2,4,3,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[3,3,3,1,1,1,1] => [3,4] => 1001000 => 0110111 => 3
[4,2,3,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[5,1,3,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[2,5,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[3,4,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[4,3,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[5,2,2,1,1,1,1] => [1,2,4] => 1101000 => 0010111 => 3
[6,1,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[2,6,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[3,5,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[4,4,1,1,1,1,1] => [2,5] => 1010000 => 0101111 => 4
[5,3,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[6,2,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[7,1,1,1,1,1,1] => [1,6] => 1100000 => 0011111 => 5
[2,2,1,2,1,2,1,1] => [2,1,1,1,1,2] => 10111110 => 01000001 => 1
[2,2,1,1,1,2,1,1,1] => [2,3,1,3] => 101001100 => 010110011 => 2
[2,1,2,1,1,1,2,1,1] => [1,1,1,3,1,2] => 111100110 => 000011001 => 2
[2,1,2,1,2,1,1,2] => [1,1,1,1,1,2,1] => 11111101 => 00000010 => 1
[2,1,2,1,2,2,1,1] => [1,1,1,1,2,2] => 11111010 => 00000101 => 1
[2,1,2,1,1,2,1,1,1] => [1,1,1,2,1,3] => 111101100 => 000010011 => 2
[2,1,1,2,1,1,1,2,1] => [1,2,1,3,1,1] => 110110011 => 001001100 => 2
[2,1,1,2,1,1,2,1,1] => [1,2,1,2,1,2] => 110110110 => 001001001 => 1
[2,1,1,2,1,2,1,1,1] => [1,2,1,1,1,3] => 110111100 => 001000011 => 2
[2,1,1,1,2,1,1,1,2] => [1,3,1,3,1] => 110011001 => 001100110 => 2
[2,1,1,1,2,1,1,2,1] => [1,3,1,2,1,1] => 110011011 => 001100100 => 2
[2,1,1,1,2,1,2,1,1] => [1,3,1,1,1,2] => 110011110 => 001100001 => 2
[2,1,1,1,2,2,1,1,1] => [1,3,2,3] => 110010100 => 001101011 => 2
[1,2,1,2,1,1,2,1,1] => [1,1,1,1,2,1,2] => 111110110 => 000001001 => 1
[1,2,1,1,2,1,2,1,1] => [1,1,2,1,1,1,2] => 111011110 => 000100001 => 1
[1,2,1,1,1,2,1,1,2] => [1,1,3,1,2,1] => 111001101 => 000110010 => 2
[1,2,1,1,1,2,2,1,1] => [1,1,3,2,2] => 111001010 => 000110101 => 2
[1,2,1,1,1,1,2,1,1,1] => [1,1,4,1,3] => 1110001100 => 0001110011 => 3
[1,2,2,1,1,1,2,1,1] => [1,2,3,1,2] => 110100110 => 001011001 => 2
[1,2,2,2,1,2,1,1] => [1,3,1,1,2] => 11001110 => 00110001 => 2
[1,2,2,1,2,1,1,2] => [1,2,1,1,2,1] => 11011101 => 00100010 => 1
[1,2,2,1,2,2,1,1] => [1,2,1,2,2] => 11011010 => 00100101 => 1
[1,2,1,2,1,1,1,2,1] => [1,1,1,1,3,1,1] => 111110011 => 000001100 => 2
[1,2,1,2,2,1,1,2] => [1,1,1,2,2,1] => 11110101 => 00001010 => 1
[1,2,1,2,2,2,1,1] => [1,1,1,3,2] => 11110010 => 00001101 => 2
[1,2,1,2,1,2,1,1,1] => [1,1,1,1,1,1,3] => 111111100 => 000000011 => 2
[1,2,1,1,2,1,1,1,2] => [1,1,2,1,3,1] => 111011001 => 000100110 => 2
[1,2,1,1,2,2,1,1,1] => [1,1,2,2,3] => 111010100 => 000101011 => 2
[1,2,1,1,1,2,1,1,1,1] => [1,1,3,1,4] => 1110011000 => 0001100111 => 3
[1,1,2,1,1,1,2,1,2] => [2,1,3,1,1,1] => 101100111 => 010011000 => 2
[1,1,2,1,1,2,1,1,2] => [2,1,2,1,2,1] => 101101101 => 010010010 => 1
[1,1,2,1,1,2,2,1,1] => [2,1,2,2,2] => 101101010 => 010010101 => 1
[1,1,2,1,1,1,2,1,1,1] => [2,1,3,1,3] => 1011001100 => 0100110011 => 2
[1,1,2,2,1,1,1,2,1] => [2,2,3,1,1] => 101010011 => 010101100 => 2
[1,1,2,2,1,1,2,1,1] => [2,2,2,1,2] => 101010110 => 010101001 => 1
[1,1,2,1,2,1,1,1,2] => [2,1,1,1,3,1] => 101111001 => 010000110 => 2
[1,1,2,1,2,2,1,1,1] => [2,1,1,2,3] => 101110100 => 010001011 => 2
[1,1,1,2,1,1,1,2,2] => [3,1,3,2] => 100110010 => 011001101 => 2
[1,1,1,2,1,1,1,1,2,1] => [3,1,4,1,1] => 1001100011 => 0110011100 => 3
[1,1,1,2,1,1,2,1,2] => [3,1,2,1,1,1] => 100110111 => 011001000 => 2
[1,1,1,2,1,1,1,2,1,1] => [3,1,3,1,2] => 1001100110 => 0110011001 => 2
[1,1,1,2,1,2,1,1,2] => [3,1,1,1,2,1] => 100111101 => 011000010 => 2
[1,1,1,2,2,1,1,1,2] => [3,2,3,1] => 100101001 => 011010110 => 2
[1,1,1,2,2,1,2,1,1] => [3,2,1,1,2] => 100101110 => 011010001 => 2
[1,1,1,1,2,1,1,1,2,1] => [4,1,3,1,1] => 1000110011 => 0111001100 => 3
[2,1,1,1,1,1,1,3] => [1,6,1] => 11000001 => 00111110 => 5
[2,1,1,1,1,1,2,2] => [1,5,2] => 11000010 => 00111101 => 4
[2,1,1,1,1,2,1,2] => [1,4,1,1,1] => 11000111 => 00111000 => 3
[2,1,1,1,2,1,1,2] => [1,3,1,2,1] => 11001101 => 00110010 => 2
[2,1,1,2,1,1,1,2] => [1,2,1,3,1] => 11011001 => 00100110 => 2
[2,1,2,1,1,1,1,2] => [1,1,1,4,1] => 11110001 => 00001110 => 3
[2,2,1,1,1,1,1,2] => [2,5,1] => 10100001 => 01011110 => 4
[3,1,1,1,1,1,1,2] => [1,6,1] => 11000001 => 00111110 => 5
[1,2,2,4,2,1] => [1,2,1,1,1] => 110111 => 001000 => 1
[1,2,4,2,2,1] => [1,1,1,2,1] => 111101 => 000010 => 1
[1,2,5,2,2] => [1,1,1,2] => 11110 => 00001 => 1
[1,3,5,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,2,2,2,1] => [1,1,3,1] => 111001 => 000110 => 2
[1,5,2,2,2] => [1,1,3] => 11100 => 00011 => 2
[1,5,3,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,5,2,2,1] => [1,1,2,1] => 11101 => 00010 => 1
[2,6,2,2] => [1,1,2] => 1110 => 0001 => 1
[2,2,5,2,1] => [2,1,1,1] => 10111 => 01000 => 1
[6,2,2,2] => [1,3] => 1100 => 0011 => 2
[2,2,2,2,2,1,1] => [5,2] => 1000010 => 0111101 => 4
[2,2,2,1,2,1,1,1] => [3,1,1,3] => 10011100 => 01100011 => 2
[2,2,1,2,2,1,1,1] => [2,1,2,3] => 10110100 => 01001011 => 2
[2,1,2,2,2,1,1,1] => [1,1,3,3] => 11100100 => 00011011 => 2
[1,2,2,2,2,1,1,1] => [1,4,3] => 11000100 => 00111011 => 3
[1,2,2,1,2,1,1,1,1] => [1,2,1,1,4] => 110111000 => 001000111 => 3
[1,2,1,2,2,1,1,1,1] => [1,1,1,2,4] => 111101000 => 000010111 => 3
[1,1,2,2,2,1,1,1,1] => [2,3,4] => 101001000 => 010110111 => 3
[1,2,1,1,2,1,1,1,1,1] => [1,1,2,1,5] => 1110110000 => 0001001111 => 4
[1,1,2,1,2,1,1,1,1,1] => [2,1,1,1,5] => 1011110000 => 0100001111 => 4
[9,2] => [1,1] => 11 => 00 => 0
[1,9,1] => [1,1,1] => 111 => 000 => 0
[10,2] => [1,1] => 11 => 00 => 0
[1,1,1,1,1,2,1,1,2,1] => [5,1,2,1,1] => 1000011011 => 0111100100 => 4
[1,2,1,1,1,1,1,1,2,1] => [1,1,6,1,1] => 1110000011 => 0001111100 => 5
[1,2,2,2,3,1,1] => [1,3,1,2] => 1100110 => 0011001 => 2
[1,2,2,3,1,2,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[1,2,2,4,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[1,2,3,1,2,2,1] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[1,2,3,1,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[1,2,3,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,4,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[1,2,3,2,2,1,1] => [1,1,1,2,2] => 1111010 => 0000101 => 1
[1,2,3,3,1,1,1] => [1,1,2,3] => 1110100 => 0001011 => 2
[1,2,4,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,2,5,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[1,3,1,2,2,2,1] => [1,1,1,3,1] => 1111001 => 0000110 => 2
[1,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,3,1,3,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[1,3,2,1,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[1,4,1,1,2,2,1] => [1,1,2,2,1] => 1110101 => 0001010 => 1
[1,4,1,1,3,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[1,3,2,2,1,2,1] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,3,3,1,1,2,1] => [1,2,2,1,1] => 1101011 => 0010100 => 1
[1,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,4,2,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[1,5,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,3,2,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,3,3,1,2,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[1,3,4,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[1,4,1,2,2,1,1] => [1,1,1,2,2] => 1111010 => 0000101 => 1
[1,4,1,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,5,1,1,2,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[1,4,2,2,1,1,1] => [1,1,2,3] => 1110100 => 0001011 => 2
[1,4,3,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[1,5,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[1,6,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[2,1,2,2,3,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[2,1,2,3,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[2,1,2,3,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,1,2,4,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[2,1,3,1,2,2,1] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[2,1,3,1,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,1,3,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[2,1,4,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[2,1,3,2,2,1,1] => [1,1,1,2,2] => 1111010 => 0000101 => 1
[2,1,3,3,1,1,1] => [1,1,2,3] => 1110100 => 0001011 => 2
[2,1,4,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,1,4,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[2,1,5,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[2,2,1,2,3,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[2,2,1,3,1,2,1] => [2,1,1,1,1,1] => 1011111 => 0100000 => 1
[2,2,1,3,2,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[2,2,1,4,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[3,1,1,2,2,2,1] => [1,2,3,1] => 1101001 => 0010110 => 2
[3,1,1,3,1,2,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[3,1,1,3,2,1,1] => [1,2,1,1,2] => 1101110 => 0010001 => 1
[2,2,2,1,3,1,1] => [3,1,1,2] => 1001110 => 0110001 => 2
[2,3,1,1,2,2,1] => [1,1,2,2,1] => 1110101 => 0001010 => 1
[2,3,1,1,3,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[3,1,2,1,3,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[3,2,1,1,2,2,1] => [1,1,2,2,1] => 1110101 => 0001010 => 1
[3,2,1,1,3,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[4,1,1,1,2,2,1] => [1,3,2,1] => 1100101 => 0011010 => 2
[4,1,1,1,3,1,1] => [1,3,1,2] => 1100110 => 0011001 => 2
[2,2,3,1,1,2,1] => [2,1,2,1,1] => 1011011 => 0100100 => 1
[2,3,1,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[2,3,2,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[2,4,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[3,1,2,2,1,2,1] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[3,1,3,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[3,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[4,1,1,2,1,2,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[3,2,2,1,1,2,1] => [1,2,2,1,1] => 1101011 => 0010100 => 1
[3,3,1,1,1,2,1] => [2,3,1,1] => 1010011 => 0101100 => 2
[4,1,2,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[4,2,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[5,1,1,1,1,2,1] => [1,4,1,1] => 1100011 => 0011100 => 3
[2,2,2,3,1,1,1] => [3,1,3] => 1001100 => 0110011 => 2
[2,2,3,1,2,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[2,2,3,2,1,1,1] => [2,1,1,3] => 1011100 => 0100011 => 2
[2,2,4,1,1,1,1] => [2,1,4] => 1011000 => 0100111 => 3
[2,3,1,2,2,1,1] => [1,1,1,2,2] => 1111010 => 0000101 => 1
[2,3,1,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[2,3,2,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[2,4,1,1,2,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[2,3,2,2,1,1,1] => [1,1,2,3] => 1110100 => 0001011 => 2
[2,3,3,1,1,1,1] => [1,2,4] => 1101000 => 0010111 => 3
[2,4,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[2,4,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[2,5,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[3,1,2,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[3,1,3,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[3,1,4,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[3,2,1,2,2,1,1] => [1,1,1,2,2] => 1111010 => 0000101 => 1
[3,2,1,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[4,1,1,2,2,1,1] => [1,2,2,2] => 1101010 => 0010101 => 1
[4,1,1,3,1,1,1] => [1,2,1,3] => 1101100 => 0010011 => 2
[3,3,1,1,2,1,1] => [2,2,1,2] => 1010110 => 0101001 => 1
[4,1,2,1,2,1,1] => [1,1,1,1,1,2] => 1111110 => 0000001 => 1
[4,2,1,1,2,1,1] => [1,1,2,1,2] => 1110110 => 0001001 => 1
[5,1,1,1,2,1,1] => [1,3,1,2] => 1100110 => 0011001 => 2
[3,2,2,2,1,1,1] => [1,3,3] => 1100100 => 0011011 => 2
[3,2,3,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[3,3,2,1,1,1,1] => [2,1,4] => 1011000 => 0100111 => 3
[3,4,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[4,1,2,2,1,1,1] => [1,1,2,3] => 1110100 => 0001011 => 2
[4,1,3,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[4,2,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[4,2,2,1,1,1,1] => [1,2,4] => 1101000 => 0010111 => 3
[4,3,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[5,1,2,1,1,1,1] => [1,1,1,4] => 1111000 => 0000111 => 3
[5,2,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[6,1,1,1,1,1,1] => [1,6] => 1100000 => 0011111 => 5
[11] => [1] => 1 => 0 => 0
[2,9] => [1,1] => 11 => 00 => 0
[1,1,2,2,4,1] => [2,2,1,1] => 101011 => 010100 => 1
[1,3,1,3,1,3,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,3,1,2,3,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,3,1,2,1,4,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,3,1,1,1,5,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,2,3,2,1,3,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,3,1,3,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,3,1,1,4,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[1,2,2,3,2,2,1] => [1,2,1,2,1] => 1101101 => 0010010 => 1
[1,2,2,1,4,2,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[1,2,2,1,2,4,1] => [1,2,1,1,1,1] => 1101111 => 0010000 => 1
[1,2,1,4,1,3,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,3,3,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[1,2,1,3,1,4,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,2,1,5,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,1,5,2,1] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,1,1,3,4,1] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,1,1,1,6,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,1,1,5,1,3,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,4,3,2,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,4,1,4,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,3,1,5,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,5,2,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,3,4,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,1,6,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,1,1,7,1] => [5,1,1] => 1000011 => 0111100 => 4
[1,2,2,2,1,1,1,1,1] => [1,3,5] => 110010000 => 001101111 => 4
[1,2,2,1,1,1,1,2,1] => [1,2,4,1,1] => 110100011 => 001011100 => 3
[1,1,2,3,2,3] => [2,1,1,1,1] => 101111 => 010000 => 1
[2,2,2,2,4] => [4,1] => 10001 => 01110 => 3
[1,2,2,2,2,3] => [1,4,1] => 110001 => 001110 => 3
[1,2,2,3,4] => [1,2,1,1] => 11011 => 00100 => 1
[2,2,3,5] => [2,1,1] => 1011 => 0100 => 1
[1,2,3,2,4] => [1,1,1,1,1] => 11111 => 00000 => 0
[2,3,2,5] => [1,1,1,1] => 1111 => 0000 => 0
[1,3,2,2,4] => [1,1,2,1] => 11101 => 00010 => 1
[5,1,1,1,1,2] => [1,4,1] => 110001 => 001110 => 3
[1,2,1,1,1,1,1,2,1] => [1,1,5,1,1] => 111000011 => 000111100 => 4
[1,1,1,1,1,1,1,1,1,1,1] => [11] => 10000000000 => 01111111111 => 10
[1,1,1,1,1,1,1,3,1] => [7,1,1] => 100000011 => 011111100 => 6
[1,1,1,1,1,3,1,1,1] => [5,1,3] => 100001100 => 011110011 => 4
[1,1,1,1,1,5,1] => [5,1,1] => 1000011 => 0111100 => 4
[1,1,1,1,1,2,1,2,1] => [5,1,1,1,1] => 100001111 => 011110000 => 4
[1,1,1,3,1,1,1,1,1] => [3,1,5] => 100110000 => 011001111 => 4
[1,1,1,3,1,3,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,5,1,1,1] => [3,1,3] => 1001100 => 0110011 => 2
[1,1,1,7,1] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,4,1,2,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,1,2,1,1,1] => [3,1,1,1,3] => 100111100 => 011000011 => 2
[1,1,1,2,1,4,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,2,1,1,1,2,1] => [3,1,3,1,1] => 100110011 => 011001100 => 2
[1,1,1,2,3,2,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,3,1,1,1,1,1,1,1] => [1,1,7] => 111000000 => 000111111 => 6
[1,3,1,1,1,3,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,3,1,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,3,1,5,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,1,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,5,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[1,5,1,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,7,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[1,6,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,4,1,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,4,3,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,2,1,1,1,1,1] => [1,1,1,1,5] => 111110000 => 000001111 => 4
[1,2,1,2,1,3,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,4,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,2,1,6,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,3,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,1,1,2,1,1,1] => [1,1,3,1,3] => 111001100 => 000110011 => 2
[1,2,1,1,1,4,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,2,1,1,3,2,1] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,3,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,2,3,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,3,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[1,2,5,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,2,1,2,2,1] => [1,2,1,2,1] => 1101101 => 0010010 => 1
[1,1,1,1,1,1,1,5,1] => [7,1,1] => 100000011 => 011111100 => 6
[1,1,1,1,1,3,1,3,1] => [5,1,1,1,1] => 100001111 => 011110000 => 4
[1,1,1,1,1,5,1,1,1] => [5,1,3] => 100001100 => 011110011 => 4
[1,1,1,1,1,4,1,2,1] => [5,1,1,1,1] => 100001111 => 011110000 => 4
[1,1,1,1,1,2,1,4,1] => [5,1,1,1,1] => 100001111 => 011110000 => 4
[1,1,1,1,1,2,3,2,1] => [5,1,1,1,1] => 100001111 => 011110000 => 4
[1,1,1,3,1,1,1,3,1] => [3,1,3,1,1] => 100110011 => 011001100 => 2
[1,1,1,3,1,3,1,1,1] => [3,1,1,1,3] => 100111100 => 011000011 => 2
[1,1,1,3,1,2,1,2,1] => [3,1,1,1,1,1,1] => 100111111 => 011000000 => 2
[1,1,1,5,1,1,1,1,1] => [3,1,5] => 100110000 => 011001111 => 4
[1,1,1,7,1,1,1] => [3,1,3] => 1001100 => 0110011 => 2
[1,1,1,9,1] => [3,1,1] => 10011 => 01100 => 2
[1,1,1,6,1,2,1] => [3,1,1,1,1] => 1001111 => 0110000 => 2
[1,1,1,4,1,2,1,1,1] => [3,1,1,1,3] => 100111100 => 011000011 => 2
[1,1,1,4,1,1,1,2,1] => [3,1,3,1,1] => 100110011 => 011001100 => 2
[1,1,1,2,1,2,1,3,1] => [3,1,1,1,1,1,1] => 100111111 => 011000000 => 2
[1,1,1,2,1,4,1,1,1] => [3,1,1,1,3] => 100111100 => 011000011 => 2
[1,1,1,2,1,3,1,2,1] => [3,1,1,1,1,1,1] => 100111111 => 011000000 => 2
[1,1,1,2,1,1,1,4,1] => [3,1,3,1,1] => 100110011 => 011001100 => 2
[1,1,1,2,1,1,3,2,1] => [3,1,2,1,1,1] => 100110111 => 011001000 => 2
[1,1,1,2,3,2,1,1,1] => [3,1,1,1,3] => 100111100 => 011000011 => 2
[1,1,1,2,3,1,1,2,1] => [3,1,1,2,1,1] => 100111011 => 011000100 => 2
[1,1,1,2,2,1,2,2,1] => [3,2,1,2,1] => 100101101 => 011010010 => 2
[1,3,1,1,1,1,1,3,1] => [1,1,5,1,1] => 111000011 => 000111100 => 4
[1,3,1,1,1,3,1,1,1] => [1,1,3,1,3] => 111001100 => 000110011 => 2
[1,3,1,1,1,2,1,2,1] => [1,1,3,1,1,1,1] => 111001111 => 000110000 => 2
[1,3,1,3,1,1,1,1,1] => [1,1,1,1,5] => 111110000 => 000001111 => 4
[1,3,1,5,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,3,1,7,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,3,1,4,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,3,1,2,1,2,1,1,1] => [1,1,1,1,1,1,3] => 111111100 => 000000011 => 2
[1,3,1,2,1,1,1,2,1] => [1,1,1,1,3,1,1] => 111110011 => 000001100 => 2
[1,5,1,1,1,1,1,1,1] => [1,1,7] => 111000000 => 000111111 => 6
[1,5,1,1,1,3,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,5,1,3,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,5,1,5,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,5,1,2,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,7,1,1,1,1,1] => [1,1,5] => 1110000 => 0001111 => 4
[1,7,1,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,9,1,1,1] => [1,1,3] => 11100 => 00011 => 2
[1,11,1] => [1,1,1] => 111 => 000 => 0
[1,8,1,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,6,1,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,6,1,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,6,1,1,1,2,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,6,3,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,1,2,1,1,1,1,1] => [1,1,1,1,5] => 111110000 => 000001111 => 4
[1,4,1,2,1,3,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,4,1,4,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,4,1,6,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,1,3,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,4,1,1,1,2,1,1,1] => [1,1,3,1,3] => 111001100 => 000110011 => 2
[1,4,1,1,1,4,1] => [1,1,3,1,1] => 1110011 => 0001100 => 2
[1,4,1,1,1,1,1,2,1] => [1,1,5,1,1] => 111000011 => 000111100 => 4
[1,4,1,1,3,2,1] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,4,3,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,4,3,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,3,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[1,4,5,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,4,2,1,2,2,1] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[1,2,1,2,1,1,1,3,1] => [1,1,1,1,3,1,1] => 111110011 => 000001100 => 2
[1,2,1,2,1,3,1,1,1] => [1,1,1,1,1,1,3] => 111111100 => 000000011 => 2
[1,2,1,2,1,2,1,2,1] => [1,1,1,1,1,1,1,1,1] => 111111111 => 000000000 => 0
[1,2,1,4,1,1,1,1,1] => [1,1,1,1,5] => 111110000 => 000001111 => 4
[1,2,1,6,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,2,1,8,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,1,5,1,2,1] => [1,1,1,1,1,1,1] => 1111111 => 0000000 => 0
[1,2,1,3,1,2,1,1,1] => [1,1,1,1,1,1,3] => 111111100 => 000000011 => 2
[1,2,1,3,1,1,1,2,1] => [1,1,1,1,3,1,1] => 111110011 => 000001100 => 2
[1,2,1,1,1,2,1,3,1] => [1,1,3,1,1,1,1] => 111001111 => 000110000 => 2
[1,2,1,1,1,4,1,1,1] => [1,1,3,1,3] => 111001100 => 000110011 => 2
[1,2,1,1,1,3,1,2,1] => [1,1,3,1,1,1,1] => 111001111 => 000110000 => 2
[1,2,1,1,1,1,1,4,1] => [1,1,5,1,1] => 111000011 => 000111100 => 4
[1,2,1,1,1,1,3,2,1] => [1,1,4,1,1,1] => 111000111 => 000111000 => 3
[1,2,1,1,3,2,1,1,1] => [1,1,2,1,1,3] => 111011100 => 000100011 => 2
[1,2,1,1,3,1,1,2,1] => [1,1,2,1,2,1,1] => 111011011 => 000100100 => 1
[1,2,1,1,2,1,2,2,1] => [1,1,2,1,1,2,1] => 111011101 => 000100010 => 1
[1,2,3,2,1,1,1,1,1] => [1,1,1,1,5] => 111110000 => 000001111 => 4
[1,2,3,4,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,2,3,6,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,3,3,1,2,1] => [1,1,2,1,1,1] => 1110111 => 0001000 => 1
[1,2,3,1,1,2,1,1,1] => [1,1,1,2,1,3] => 111101100 => 000010011 => 2
[1,2,3,1,1,1,1,2,1] => [1,1,1,4,1,1] => 111100011 => 000011100 => 3
[1,2,5,2,1,1,1] => [1,1,1,1,3] => 1111100 => 0000011 => 2
[1,2,5,4,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,5,1,1,2,1] => [1,1,1,2,1,1] => 1111011 => 0000100 => 1
[1,2,7,2,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,4,1,2,2,1] => [1,1,1,1,2,1] => 1111101 => 0000010 => 1
[1,2,2,1,2,2,1,1,1] => [1,2,1,2,3] => 110110100 => 001001011 => 2
[1,2,2,1,2,1,1,2,1] => [1,2,1,1,2,1,1] => 110111011 => 001000100 => 1
[1,2,2,1,1,1,2,2,1] => [1,2,3,2,1] => 110100101 => 001011010 => 2
[1,1,9] => [2,1] => 101 => 010 => 1
[1,1,1,1,1,1,1,1,3] => [8,1] => 100000001 => 011111110 => 7
[2,2,2,2,1,1,2] => [4,2,1] => 1000101 => 0111010 => 3
[1,1,2,2,1,2,3] => [2,2,1,1,1] => 1010111 => 0101000 => 1
[1,1,1,1,2,2,2,1,1] => [4,3,2] => 100010010 => 011101101 => 3
[1,1,1,2,2,2,3] => [3,3,1] => 1001001 => 0110110 => 2
[2,2,2,6] => [3,1] => 1001 => 0110 => 2
[2,2,6,2] => [2,1,1] => 1011 => 0100 => 1
[1,6,4] => [1,1,1] => 111 => 000 => 0
[1,5,5] => [1,2] => 110 => 001 => 1
[1,4,6] => [1,1,1] => 111 => 000 => 0
[1,3,7] => [1,1,1] => 111 => 000 => 0
[1,2,8] => [1,1,1] => 111 => 000 => 0
[1,2,1,2,1,1,1,1,1,1] => [1,1,1,1,6] => 1111100000 => 0000011111 => 5
[1,2,1,1,1,1,1,2,1,1] => [1,1,5,1,2] => 1110000110 => 0001111001 => 4
[1,1,2,1,1,1,1,1,2,1] => [2,1,5,1,1] => 1011000011 => 0100111100 => 4
[1,1,1,1,1,2,1,2,1,1] => [5,1,1,1,2] => 1000011110 => 0111100001 => 4
[1,1,1,1,1,1,2,1,2,1] => [6,1,1,1,1] => 1000001111 => 0111110000 => 5
[1,2,5,3,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,2,2,4,1] => [1,3,1,1] => 110011 => 001100 => 2
[2,2,2,5,1] => [3,1,1] => 10011 => 01100 => 2
[1,2,3,5,1] => [1,1,1,1,1] => 11111 => 00000 => 0
[1,2,2,5,2] => [1,2,1,1] => 11011 => 00100 => 1
[1,1,2,1,1,1,2,1,1] => [2,1,3,1,2] => 101100110 => 010011001 => 2
[1,1,2,2,2,2,1] => [2,4,1] => 1010001 => 0101110 => 3
[1,1,2,2,2,1,1,1] => [2,3,3] => 10100100 => 01011011 => 2
[1,1,2,2,3,1,1] => [2,2,1,2] => 1010110 => 0101001 => 1
[1,1,2,2,1,2,1,1] => [2,2,1,1,2] => 10101110 => 01010001 => 1
[1,1,2,3,2,1,1] => [2,1,1,1,2] => 1011110 => 0100001 => 1
[1,1,2,1,2,2,1,1] => [2,1,1,2,2] => 10111010 => 01000101 => 1
[1,1,3,2,2,1,1] => [2,1,2,2] => 1011010 => 0100101 => 1
[1,1,1,2,2,2,1,1] => [3,3,2] => 10010010 => 01101101 => 2
[1,2,2,2,2,1,1] => [1,4,2] => 1100010 => 0011101 => 3
[1,1,2,2,2,4] => [2,3,1] => 101001 => 010110 => 2
[1,1,2,2,1,1,1,1,1] => [2,2,5] => 101010000 => 010101111 => 4
[1,1,2,5,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,5,2,1,1] => [2,1,1,2] => 101110 => 010001 => 1
[1,1,1,1,1,2,2,1,1] => [5,2,2] => 100001010 => 011110101 => 4
[1,4,2,2,1,1] => [1,1,2,2] => 111010 => 000101 => 1
[2,2,1,1,1,2,1,2] => [2,3,1,1,1] => 10100111 => 01011000 => 2
[1,2,2,2,1,1,1,2] => [1,3,3,1] => 11001001 => 00110110 => 2
[2,2,1,2,1,1,1,2] => [2,1,1,3,1] => 10111001 => 01000110 => 2
[2,2,2,1,1,1,2,1] => [3,3,1,1] => 10010011 => 01101100 => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,0,1 4,3,0,1 7,6,2,0,1 14,10,5,2,0,1 23,23,11,4,2,0,1 39,50,22,10,4,2,0,1 71,99,48,22,9,4,2,0,1 124,200,105,46,21,9,4,2,0,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 3 + q^{2}$
$F_{4} = 4 + 3\ q + q^{3}$
$F_{5} = 7 + 6\ q + 2\ q^{2} + q^{4}$
$F_{6} = 14 + 10\ q + 5\ q^{2} + 2\ q^{3} + q^{5}$
$F_{7} = 23 + 23\ q + 11\ q^{2} + 4\ q^{3} + 2\ q^{4} + q^{6}$
$F_{8} = 39 + 50\ q + 22\ q^{2} + 10\ q^{3} + 4\ q^{4} + 2\ q^{5} + q^{7}$
$F_{9} = 71 + 99\ q + 48\ q^{2} + 22\ q^{3} + 9\ q^{4} + 4\ q^{5} + 2\ q^{6} + q^{8}$
$F_{10} = 124 + 200\ q + 105\ q^{2} + 46\ q^{3} + 21\ q^{4} + 9\ q^{5} + 4\ q^{6} + 2\ q^{7} + q^{9}$
Description
The length of the longest run of ones in a binary word.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
Map
to binary word
Description
Return the composition as a binary word, treating ones as separators.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
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