Identifier
Values
0 => 1 => [1,1] => [1,1] => 0
1 => 0 => [2] => [2] => 1
00 => 11 => [1,1,1] => [1,1,1] => 0
01 => 10 => [1,2] => [2,1] => 1
10 => 01 => [2,1] => [2,1] => 1
11 => 00 => [3] => [3] => 0
000 => 111 => [1,1,1,1] => [1,1,1,1] => 0
001 => 110 => [1,1,2] => [2,1,1] => 1
010 => 101 => [1,2,1] => [2,1,1] => 1
011 => 100 => [1,3] => [3,1] => 0
100 => 011 => [2,1,1] => [2,1,1] => 1
101 => 010 => [2,2] => [2,2] => 2
110 => 001 => [3,1] => [3,1] => 0
111 => 000 => [4] => [4] => 1
0000 => 1111 => [1,1,1,1,1] => [1,1,1,1,1] => 0
0001 => 1110 => [1,1,1,2] => [2,1,1,1] => 1
0010 => 1101 => [1,1,2,1] => [2,1,1,1] => 1
0011 => 1100 => [1,1,3] => [3,1,1] => 0
0100 => 1011 => [1,2,1,1] => [2,1,1,1] => 1
0101 => 1010 => [1,2,2] => [2,2,1] => 2
0110 => 1001 => [1,3,1] => [3,1,1] => 0
0111 => 1000 => [1,4] => [4,1] => 1
1000 => 0111 => [2,1,1,1] => [2,1,1,1] => 1
1001 => 0110 => [2,1,2] => [2,2,1] => 2
1010 => 0101 => [2,2,1] => [2,2,1] => 2
1011 => 0100 => [2,3] => [3,2] => 1
1100 => 0011 => [3,1,1] => [3,1,1] => 0
1101 => 0010 => [3,2] => [3,2] => 1
1110 => 0001 => [4,1] => [4,1] => 1
1111 => 0000 => [5] => [5] => 0
00000 => 11111 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
00001 => 11110 => [1,1,1,1,2] => [2,1,1,1,1] => 1
00010 => 11101 => [1,1,1,2,1] => [2,1,1,1,1] => 1
00011 => 11100 => [1,1,1,3] => [3,1,1,1] => 0
00100 => 11011 => [1,1,2,1,1] => [2,1,1,1,1] => 1
00101 => 11010 => [1,1,2,2] => [2,2,1,1] => 2
00110 => 11001 => [1,1,3,1] => [3,1,1,1] => 0
00111 => 11000 => [1,1,4] => [4,1,1] => 1
01000 => 10111 => [1,2,1,1,1] => [2,1,1,1,1] => 1
01001 => 10110 => [1,2,1,2] => [2,2,1,1] => 2
01010 => 10101 => [1,2,2,1] => [2,2,1,1] => 2
01011 => 10100 => [1,2,3] => [3,2,1] => 1
01100 => 10011 => [1,3,1,1] => [3,1,1,1] => 0
01101 => 10010 => [1,3,2] => [3,2,1] => 1
01110 => 10001 => [1,4,1] => [4,1,1] => 1
01111 => 10000 => [1,5] => [5,1] => 0
10000 => 01111 => [2,1,1,1,1] => [2,1,1,1,1] => 1
10001 => 01110 => [2,1,1,2] => [2,2,1,1] => 2
10010 => 01101 => [2,1,2,1] => [2,2,1,1] => 2
10011 => 01100 => [2,1,3] => [3,2,1] => 1
10100 => 01011 => [2,2,1,1] => [2,2,1,1] => 2
10101 => 01010 => [2,2,2] => [2,2,2] => 3
10110 => 01001 => [2,3,1] => [3,2,1] => 1
10111 => 01000 => [2,4] => [4,2] => 2
11000 => 00111 => [3,1,1,1] => [3,1,1,1] => 0
11001 => 00110 => [3,1,2] => [3,2,1] => 1
11010 => 00101 => [3,2,1] => [3,2,1] => 1
11011 => 00100 => [3,3] => [3,3] => 0
11100 => 00011 => [4,1,1] => [4,1,1] => 1
11101 => 00010 => [4,2] => [4,2] => 2
11110 => 00001 => [5,1] => [5,1] => 0
11111 => 00000 => [6] => [6] => 1
000000 => 111111 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
000001 => 111110 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => 1
000010 => 111101 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => 1
000011 => 111100 => [1,1,1,1,3] => [3,1,1,1,1] => 0
000100 => 111011 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => 1
000101 => 111010 => [1,1,1,2,2] => [2,2,1,1,1] => 2
000110 => 111001 => [1,1,1,3,1] => [3,1,1,1,1] => 0
000111 => 111000 => [1,1,1,4] => [4,1,1,1] => 1
001000 => 110111 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 1
001001 => 110110 => [1,1,2,1,2] => [2,2,1,1,1] => 2
001010 => 110101 => [1,1,2,2,1] => [2,2,1,1,1] => 2
001011 => 110100 => [1,1,2,3] => [3,2,1,1] => 1
001100 => 110011 => [1,1,3,1,1] => [3,1,1,1,1] => 0
001101 => 110010 => [1,1,3,2] => [3,2,1,1] => 1
001110 => 110001 => [1,1,4,1] => [4,1,1,1] => 1
001111 => 110000 => [1,1,5] => [5,1,1] => 0
010000 => 101111 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 1
010001 => 101110 => [1,2,1,1,2] => [2,2,1,1,1] => 2
010010 => 101101 => [1,2,1,2,1] => [2,2,1,1,1] => 2
010011 => 101100 => [1,2,1,3] => [3,2,1,1] => 1
010100 => 101011 => [1,2,2,1,1] => [2,2,1,1,1] => 2
010101 => 101010 => [1,2,2,2] => [2,2,2,1] => 3
010110 => 101001 => [1,2,3,1] => [3,2,1,1] => 1
010111 => 101000 => [1,2,4] => [4,2,1] => 2
011000 => 100111 => [1,3,1,1,1] => [3,1,1,1,1] => 0
011001 => 100110 => [1,3,1,2] => [3,2,1,1] => 1
011010 => 100101 => [1,3,2,1] => [3,2,1,1] => 1
011011 => 100100 => [1,3,3] => [3,3,1] => 0
011100 => 100011 => [1,4,1,1] => [4,1,1,1] => 1
011101 => 100010 => [1,4,2] => [4,2,1] => 2
011110 => 100001 => [1,5,1] => [5,1,1] => 0
011111 => 100000 => [1,6] => [6,1] => 1
100000 => 011111 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
100001 => 011110 => [2,1,1,1,2] => [2,2,1,1,1] => 2
100010 => 011101 => [2,1,1,2,1] => [2,2,1,1,1] => 2
100011 => 011100 => [2,1,1,3] => [3,2,1,1] => 1
100100 => 011011 => [2,1,2,1,1] => [2,2,1,1,1] => 2
100101 => 011010 => [2,1,2,2] => [2,2,2,1] => 3
100110 => 011001 => [2,1,3,1] => [3,2,1,1] => 1
>>> Load all 1160 entries. <<<
100111 => 011000 => [2,1,4] => [4,2,1] => 2
101000 => 010111 => [2,2,1,1,1] => [2,2,1,1,1] => 2
101001 => 010110 => [2,2,1,2] => [2,2,2,1] => 3
101010 => 010101 => [2,2,2,1] => [2,2,2,1] => 3
101011 => 010100 => [2,2,3] => [3,2,2] => 2
101100 => 010011 => [2,3,1,1] => [3,2,1,1] => 1
101101 => 010010 => [2,3,2] => [3,2,2] => 2
101110 => 010001 => [2,4,1] => [4,2,1] => 2
101111 => 010000 => [2,5] => [5,2] => 1
110000 => 001111 => [3,1,1,1,1] => [3,1,1,1,1] => 0
110001 => 001110 => [3,1,1,2] => [3,2,1,1] => 1
110010 => 001101 => [3,1,2,1] => [3,2,1,1] => 1
110011 => 001100 => [3,1,3] => [3,3,1] => 0
110100 => 001011 => [3,2,1,1] => [3,2,1,1] => 1
110101 => 001010 => [3,2,2] => [3,2,2] => 2
110110 => 001001 => [3,3,1] => [3,3,1] => 0
110111 => 001000 => [3,4] => [4,3] => 1
111000 => 000111 => [4,1,1,1] => [4,1,1,1] => 1
111001 => 000110 => [4,1,2] => [4,2,1] => 2
111010 => 000101 => [4,2,1] => [4,2,1] => 2
111011 => 000100 => [4,3] => [4,3] => 1
111100 => 000011 => [5,1,1] => [5,1,1] => 0
111101 => 000010 => [5,2] => [5,2] => 1
111110 => 000001 => [6,1] => [6,1] => 1
111111 => 000000 => [7] => [7] => 0
0000000 => 1111111 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0000001 => 1111110 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => 1
0000010 => 1111101 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 1
0000011 => 1111100 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => 0
0000100 => 1111011 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 1
0000101 => 1111010 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => 2
0000110 => 1111001 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 0
0000111 => 1111000 => [1,1,1,1,4] => [4,1,1,1,1] => 1
0001000 => 1110111 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => 1
0001001 => 1110110 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => 2
0001010 => 1110101 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => 2
0001011 => 1110100 => [1,1,1,2,3] => [3,2,1,1,1] => 1
0001100 => 1110011 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 0
0001101 => 1110010 => [1,1,1,3,2] => [3,2,1,1,1] => 1
0001110 => 1110001 => [1,1,1,4,1] => [4,1,1,1,1] => 1
0001111 => 1110000 => [1,1,1,5] => [5,1,1,1] => 0
0010000 => 1101111 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => 1
0010001 => 1101110 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => 2
0010010 => 1101101 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => 2
0010011 => 1101100 => [1,1,2,1,3] => [3,2,1,1,1] => 1
0010100 => 1101011 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => 2
0010101 => 1101010 => [1,1,2,2,2] => [2,2,2,1,1] => 3
0010110 => 1101001 => [1,1,2,3,1] => [3,2,1,1,1] => 1
0010111 => 1101000 => [1,1,2,4] => [4,2,1,1] => 2
0011000 => 1100111 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 0
0011001 => 1100110 => [1,1,3,1,2] => [3,2,1,1,1] => 1
0011010 => 1100101 => [1,1,3,2,1] => [3,2,1,1,1] => 1
0011011 => 1100100 => [1,1,3,3] => [3,3,1,1] => 0
0011100 => 1100011 => [1,1,4,1,1] => [4,1,1,1,1] => 1
0011101 => 1100010 => [1,1,4,2] => [4,2,1,1] => 2
0011110 => 1100001 => [1,1,5,1] => [5,1,1,1] => 0
0011111 => 1100000 => [1,1,6] => [6,1,1] => 1
0100000 => 1011111 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
0100001 => 1011110 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => 2
0100010 => 1011101 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => 2
0100011 => 1011100 => [1,2,1,1,3] => [3,2,1,1,1] => 1
0100100 => 1011011 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => 2
0100101 => 1011010 => [1,2,1,2,2] => [2,2,2,1,1] => 3
0100110 => 1011001 => [1,2,1,3,1] => [3,2,1,1,1] => 1
0100111 => 1011000 => [1,2,1,4] => [4,2,1,1] => 2
0101000 => 1010111 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => 2
0101001 => 1010110 => [1,2,2,1,2] => [2,2,2,1,1] => 3
0101010 => 1010101 => [1,2,2,2,1] => [2,2,2,1,1] => 3
0101011 => 1010100 => [1,2,2,3] => [3,2,2,1] => 2
0101100 => 1010011 => [1,2,3,1,1] => [3,2,1,1,1] => 1
0101101 => 1010010 => [1,2,3,2] => [3,2,2,1] => 2
0101110 => 1010001 => [1,2,4,1] => [4,2,1,1] => 2
0101111 => 1010000 => [1,2,5] => [5,2,1] => 1
0110000 => 1001111 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 0
0110001 => 1001110 => [1,3,1,1,2] => [3,2,1,1,1] => 1
0110010 => 1001101 => [1,3,1,2,1] => [3,2,1,1,1] => 1
0110011 => 1001100 => [1,3,1,3] => [3,3,1,1] => 0
0110100 => 1001011 => [1,3,2,1,1] => [3,2,1,1,1] => 1
0110101 => 1001010 => [1,3,2,2] => [3,2,2,1] => 2
0110110 => 1001001 => [1,3,3,1] => [3,3,1,1] => 0
0110111 => 1001000 => [1,3,4] => [4,3,1] => 1
0111000 => 1000111 => [1,4,1,1,1] => [4,1,1,1,1] => 1
0111001 => 1000110 => [1,4,1,2] => [4,2,1,1] => 2
0111010 => 1000101 => [1,4,2,1] => [4,2,1,1] => 2
0111011 => 1000100 => [1,4,3] => [4,3,1] => 1
0111100 => 1000011 => [1,5,1,1] => [5,1,1,1] => 0
0111101 => 1000010 => [1,5,2] => [5,2,1] => 1
0111110 => 1000001 => [1,6,1] => [6,1,1] => 1
0111111 => 1000000 => [1,7] => [7,1] => 0
1000000 => 0111111 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
1000001 => 0111110 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 2
1000010 => 0111101 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => 2
1000011 => 0111100 => [2,1,1,1,3] => [3,2,1,1,1] => 1
1000100 => 0111011 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => 2
1000101 => 0111010 => [2,1,1,2,2] => [2,2,2,1,1] => 3
1000110 => 0111001 => [2,1,1,3,1] => [3,2,1,1,1] => 1
1000111 => 0111000 => [2,1,1,4] => [4,2,1,1] => 2
1001000 => 0110111 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => 2
1001001 => 0110110 => [2,1,2,1,2] => [2,2,2,1,1] => 3
1001010 => 0110101 => [2,1,2,2,1] => [2,2,2,1,1] => 3
1001011 => 0110100 => [2,1,2,3] => [3,2,2,1] => 2
1001100 => 0110011 => [2,1,3,1,1] => [3,2,1,1,1] => 1
1001101 => 0110010 => [2,1,3,2] => [3,2,2,1] => 2
1001110 => 0110001 => [2,1,4,1] => [4,2,1,1] => 2
1001111 => 0110000 => [2,1,5] => [5,2,1] => 1
1010000 => 0101111 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
1010001 => 0101110 => [2,2,1,1,2] => [2,2,2,1,1] => 3
1010010 => 0101101 => [2,2,1,2,1] => [2,2,2,1,1] => 3
1010011 => 0101100 => [2,2,1,3] => [3,2,2,1] => 2
1010100 => 0101011 => [2,2,2,1,1] => [2,2,2,1,1] => 3
1010101 => 0101010 => [2,2,2,2] => [2,2,2,2] => 4
1010110 => 0101001 => [2,2,3,1] => [3,2,2,1] => 2
1010111 => 0101000 => [2,2,4] => [4,2,2] => 3
1011000 => 0100111 => [2,3,1,1,1] => [3,2,1,1,1] => 1
1011001 => 0100110 => [2,3,1,2] => [3,2,2,1] => 2
1011010 => 0100101 => [2,3,2,1] => [3,2,2,1] => 2
1011011 => 0100100 => [2,3,3] => [3,3,2] => 1
1011100 => 0100011 => [2,4,1,1] => [4,2,1,1] => 2
1011101 => 0100010 => [2,4,2] => [4,2,2] => 3
1011110 => 0100001 => [2,5,1] => [5,2,1] => 1
1011111 => 0100000 => [2,6] => [6,2] => 2
1100000 => 0011111 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
1100001 => 0011110 => [3,1,1,1,2] => [3,2,1,1,1] => 1
1100010 => 0011101 => [3,1,1,2,1] => [3,2,1,1,1] => 1
1100011 => 0011100 => [3,1,1,3] => [3,3,1,1] => 0
1100100 => 0011011 => [3,1,2,1,1] => [3,2,1,1,1] => 1
1100101 => 0011010 => [3,1,2,2] => [3,2,2,1] => 2
1100110 => 0011001 => [3,1,3,1] => [3,3,1,1] => 0
1100111 => 0011000 => [3,1,4] => [4,3,1] => 1
1101000 => 0010111 => [3,2,1,1,1] => [3,2,1,1,1] => 1
1101001 => 0010110 => [3,2,1,2] => [3,2,2,1] => 2
1101010 => 0010101 => [3,2,2,1] => [3,2,2,1] => 2
1101011 => 0010100 => [3,2,3] => [3,3,2] => 1
1101100 => 0010011 => [3,3,1,1] => [3,3,1,1] => 0
1101101 => 0010010 => [3,3,2] => [3,3,2] => 1
1101110 => 0010001 => [3,4,1] => [4,3,1] => 1
1101111 => 0010000 => [3,5] => [5,3] => 0
1110000 => 0001111 => [4,1,1,1,1] => [4,1,1,1,1] => 1
1110001 => 0001110 => [4,1,1,2] => [4,2,1,1] => 2
1110010 => 0001101 => [4,1,2,1] => [4,2,1,1] => 2
1110011 => 0001100 => [4,1,3] => [4,3,1] => 1
1110100 => 0001011 => [4,2,1,1] => [4,2,1,1] => 2
1110101 => 0001010 => [4,2,2] => [4,2,2] => 3
1110110 => 0001001 => [4,3,1] => [4,3,1] => 1
1110111 => 0001000 => [4,4] => [4,4] => 2
1111000 => 0000111 => [5,1,1,1] => [5,1,1,1] => 0
1111001 => 0000110 => [5,1,2] => [5,2,1] => 1
1111010 => 0000101 => [5,2,1] => [5,2,1] => 1
1111011 => 0000100 => [5,3] => [5,3] => 0
1111100 => 0000011 => [6,1,1] => [6,1,1] => 1
1111101 => 0000010 => [6,2] => [6,2] => 2
1111110 => 0000001 => [7,1] => [7,1] => 0
1111111 => 0000000 => [8] => [8] => 1
00000000 => 11111111 => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
00000001 => 11111110 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => 1
00000010 => 11111101 => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => 1
00000011 => 11111100 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 0
00000100 => 11111011 => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => 1
00000101 => 11111010 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => 2
00000110 => 11111001 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 0
00000111 => 11111000 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 1
00001000 => 11110111 => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => 1
00001001 => 11110110 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => 2
00001010 => 11110101 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => 2
00001011 => 11110100 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => 1
00001100 => 11110011 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 0
00001101 => 11110010 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => 1
00001110 => 11110001 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 1
00001111 => 11110000 => [1,1,1,1,5] => [5,1,1,1,1] => 0
00010000 => 11101111 => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
00010001 => 11101110 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => 2
00010010 => 11101101 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => 2
00010011 => 11101100 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => 1
00010100 => 11101011 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => 2
00010101 => 11101010 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => 3
00010110 => 11101001 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => 1
00010111 => 11101000 => [1,1,1,2,4] => [4,2,1,1,1] => 2
00011000 => 11100111 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 0
00011001 => 11100110 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => 1
00011010 => 11100101 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => 1
00011011 => 11100100 => [1,1,1,3,3] => [3,3,1,1,1] => 0
00011100 => 11100011 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => 1
00011101 => 11100010 => [1,1,1,4,2] => [4,2,1,1,1] => 2
00011110 => 11100001 => [1,1,1,5,1] => [5,1,1,1,1] => 0
00011111 => 11100000 => [1,1,1,6] => [6,1,1,1] => 1
00100000 => 11011111 => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
00100001 => 11011110 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => 2
00100010 => 11011101 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => 2
00100011 => 11011100 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => 1
00100100 => 11011011 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => 2
00100101 => 11011010 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => 3
00100110 => 11011001 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => 1
00100111 => 11011000 => [1,1,2,1,4] => [4,2,1,1,1] => 2
00101000 => 11010111 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => 2
00101001 => 11010110 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => 3
00101010 => 11010101 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => 3
00101011 => 11010100 => [1,1,2,2,3] => [3,2,2,1,1] => 2
00101100 => 11010011 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => 1
00101101 => 11010010 => [1,1,2,3,2] => [3,2,2,1,1] => 2
00101110 => 11010001 => [1,1,2,4,1] => [4,2,1,1,1] => 2
00101111 => 11010000 => [1,1,2,5] => [5,2,1,1] => 1
00110000 => 11001111 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 0
00110001 => 11001110 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => 1
00110010 => 11001101 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => 1
00110011 => 11001100 => [1,1,3,1,3] => [3,3,1,1,1] => 0
00110100 => 11001011 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => 1
00110101 => 11001010 => [1,1,3,2,2] => [3,2,2,1,1] => 2
00110110 => 11001001 => [1,1,3,3,1] => [3,3,1,1,1] => 0
00110111 => 11001000 => [1,1,3,4] => [4,3,1,1] => 1
00111000 => 11000111 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => 1
00111001 => 11000110 => [1,1,4,1,2] => [4,2,1,1,1] => 2
00111010 => 11000101 => [1,1,4,2,1] => [4,2,1,1,1] => 2
00111011 => 11000100 => [1,1,4,3] => [4,3,1,1] => 1
00111100 => 11000011 => [1,1,5,1,1] => [5,1,1,1,1] => 0
00111101 => 11000010 => [1,1,5,2] => [5,2,1,1] => 1
00111110 => 11000001 => [1,1,6,1] => [6,1,1,1] => 1
00111111 => 11000000 => [1,1,7] => [7,1,1] => 0
01000000 => 10111111 => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
01000001 => 10111110 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 2
01000010 => 10111101 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => 2
01000011 => 10111100 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => 1
01000100 => 10111011 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => 2
01000101 => 10111010 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => 3
01000110 => 10111001 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => 1
01000111 => 10111000 => [1,2,1,1,4] => [4,2,1,1,1] => 2
01001000 => 10110111 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => 2
01001001 => 10110110 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => 3
01001010 => 10110101 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => 3
01001011 => 10110100 => [1,2,1,2,3] => [3,2,2,1,1] => 2
01001100 => 10110011 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => 1
01001101 => 10110010 => [1,2,1,3,2] => [3,2,2,1,1] => 2
01001110 => 10110001 => [1,2,1,4,1] => [4,2,1,1,1] => 2
01001111 => 10110000 => [1,2,1,5] => [5,2,1,1] => 1
01010000 => 10101111 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => 2
01010001 => 10101110 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => 3
01010010 => 10101101 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => 3
01010011 => 10101100 => [1,2,2,1,3] => [3,2,2,1,1] => 2
01010100 => 10101011 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => 3
01010101 => 10101010 => [1,2,2,2,2] => [2,2,2,2,1] => 4
01010110 => 10101001 => [1,2,2,3,1] => [3,2,2,1,1] => 2
01010111 => 10101000 => [1,2,2,4] => [4,2,2,1] => 3
01011000 => 10100111 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => 1
01011001 => 10100110 => [1,2,3,1,2] => [3,2,2,1,1] => 2
01011010 => 10100101 => [1,2,3,2,1] => [3,2,2,1,1] => 2
01011011 => 10100100 => [1,2,3,3] => [3,3,2,1] => 1
01011100 => 10100011 => [1,2,4,1,1] => [4,2,1,1,1] => 2
01011101 => 10100010 => [1,2,4,2] => [4,2,2,1] => 3
01011110 => 10100001 => [1,2,5,1] => [5,2,1,1] => 1
01011111 => 10100000 => [1,2,6] => [6,2,1] => 2
01100000 => 10011111 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
01100001 => 10011110 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => 1
01100010 => 10011101 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => 1
01100011 => 10011100 => [1,3,1,1,3] => [3,3,1,1,1] => 0
01100100 => 10011011 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => 1
01100101 => 10011010 => [1,3,1,2,2] => [3,2,2,1,1] => 2
01100110 => 10011001 => [1,3,1,3,1] => [3,3,1,1,1] => 0
01100111 => 10011000 => [1,3,1,4] => [4,3,1,1] => 1
01101000 => 10010111 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => 1
01101001 => 10010110 => [1,3,2,1,2] => [3,2,2,1,1] => 2
01101010 => 10010101 => [1,3,2,2,1] => [3,2,2,1,1] => 2
01101011 => 10010100 => [1,3,2,3] => [3,3,2,1] => 1
01101100 => 10010011 => [1,3,3,1,1] => [3,3,1,1,1] => 0
01101101 => 10010010 => [1,3,3,2] => [3,3,2,1] => 1
01101110 => 10010001 => [1,3,4,1] => [4,3,1,1] => 1
01101111 => 10010000 => [1,3,5] => [5,3,1] => 0
01110000 => 10001111 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 1
01110001 => 10001110 => [1,4,1,1,2] => [4,2,1,1,1] => 2
01110010 => 10001101 => [1,4,1,2,1] => [4,2,1,1,1] => 2
01110011 => 10001100 => [1,4,1,3] => [4,3,1,1] => 1
01110100 => 10001011 => [1,4,2,1,1] => [4,2,1,1,1] => 2
01110101 => 10001010 => [1,4,2,2] => [4,2,2,1] => 3
01110110 => 10001001 => [1,4,3,1] => [4,3,1,1] => 1
01110111 => 10001000 => [1,4,4] => [4,4,1] => 2
01111000 => 10000111 => [1,5,1,1,1] => [5,1,1,1,1] => 0
01111001 => 10000110 => [1,5,1,2] => [5,2,1,1] => 1
01111010 => 10000101 => [1,5,2,1] => [5,2,1,1] => 1
01111011 => 10000100 => [1,5,3] => [5,3,1] => 0
01111100 => 10000011 => [1,6,1,1] => [6,1,1,1] => 1
01111101 => 10000010 => [1,6,2] => [6,2,1] => 2
01111110 => 10000001 => [1,7,1] => [7,1,1] => 0
01111111 => 10000000 => [1,8] => [8,1] => 1
10000000 => 01111111 => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
10000001 => 01111110 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 2
10000010 => 01111101 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 2
10000011 => 01111100 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => 1
10000100 => 01111011 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => 2
10000101 => 01111010 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => 3
10000110 => 01111001 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => 1
10000111 => 01111000 => [2,1,1,1,4] => [4,2,1,1,1] => 2
10001000 => 01110111 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => 2
10001001 => 01110110 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => 3
10001010 => 01110101 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => 3
10001011 => 01110100 => [2,1,1,2,3] => [3,2,2,1,1] => 2
10001100 => 01110011 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => 1
10001101 => 01110010 => [2,1,1,3,2] => [3,2,2,1,1] => 2
10001110 => 01110001 => [2,1,1,4,1] => [4,2,1,1,1] => 2
10001111 => 01110000 => [2,1,1,5] => [5,2,1,1] => 1
10010000 => 01101111 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => 2
10010001 => 01101110 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => 3
10010010 => 01101101 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => 3
10010011 => 01101100 => [2,1,2,1,3] => [3,2,2,1,1] => 2
10010100 => 01101011 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => 3
10010101 => 01101010 => [2,1,2,2,2] => [2,2,2,2,1] => 4
10010110 => 01101001 => [2,1,2,3,1] => [3,2,2,1,1] => 2
10010111 => 01101000 => [2,1,2,4] => [4,2,2,1] => 3
10011000 => 01100111 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => 1
10011001 => 01100110 => [2,1,3,1,2] => [3,2,2,1,1] => 2
10011010 => 01100101 => [2,1,3,2,1] => [3,2,2,1,1] => 2
10011011 => 01100100 => [2,1,3,3] => [3,3,2,1] => 1
10011100 => 01100011 => [2,1,4,1,1] => [4,2,1,1,1] => 2
10011101 => 01100010 => [2,1,4,2] => [4,2,2,1] => 3
10011110 => 01100001 => [2,1,5,1] => [5,2,1,1] => 1
10011111 => 01100000 => [2,1,6] => [6,2,1] => 2
10100000 => 01011111 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 2
10100001 => 01011110 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => 3
10100010 => 01011101 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => 3
10100011 => 01011100 => [2,2,1,1,3] => [3,2,2,1,1] => 2
10100100 => 01011011 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => 3
10100101 => 01011010 => [2,2,1,2,2] => [2,2,2,2,1] => 4
10100110 => 01011001 => [2,2,1,3,1] => [3,2,2,1,1] => 2
10100111 => 01011000 => [2,2,1,4] => [4,2,2,1] => 3
10101000 => 01010111 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
10101001 => 01010110 => [2,2,2,1,2] => [2,2,2,2,1] => 4
10101010 => 01010101 => [2,2,2,2,1] => [2,2,2,2,1] => 4
10101011 => 01010100 => [2,2,2,3] => [3,2,2,2] => 3
10101100 => 01010011 => [2,2,3,1,1] => [3,2,2,1,1] => 2
10101101 => 01010010 => [2,2,3,2] => [3,2,2,2] => 3
10101110 => 01010001 => [2,2,4,1] => [4,2,2,1] => 3
10101111 => 01010000 => [2,2,5] => [5,2,2] => 2
10110000 => 01001111 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => 1
10110001 => 01001110 => [2,3,1,1,2] => [3,2,2,1,1] => 2
10110010 => 01001101 => [2,3,1,2,1] => [3,2,2,1,1] => 2
10110011 => 01001100 => [2,3,1,3] => [3,3,2,1] => 1
10110100 => 01001011 => [2,3,2,1,1] => [3,2,2,1,1] => 2
10110101 => 01001010 => [2,3,2,2] => [3,2,2,2] => 3
10110110 => 01001001 => [2,3,3,1] => [3,3,2,1] => 1
10110111 => 01001000 => [2,3,4] => [4,3,2] => 2
10111000 => 01000111 => [2,4,1,1,1] => [4,2,1,1,1] => 2
10111001 => 01000110 => [2,4,1,2] => [4,2,2,1] => 3
10111010 => 01000101 => [2,4,2,1] => [4,2,2,1] => 3
10111011 => 01000100 => [2,4,3] => [4,3,2] => 2
10111100 => 01000011 => [2,5,1,1] => [5,2,1,1] => 1
10111101 => 01000010 => [2,5,2] => [5,2,2] => 2
10111110 => 01000001 => [2,6,1] => [6,2,1] => 2
10111111 => 01000000 => [2,7] => [7,2] => 1
11000000 => 00111111 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
11000001 => 00111110 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => 1
11000010 => 00111101 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => 1
11000011 => 00111100 => [3,1,1,1,3] => [3,3,1,1,1] => 0
11000100 => 00111011 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => 1
11000101 => 00111010 => [3,1,1,2,2] => [3,2,2,1,1] => 2
11000110 => 00111001 => [3,1,1,3,1] => [3,3,1,1,1] => 0
11000111 => 00111000 => [3,1,1,4] => [4,3,1,1] => 1
11001000 => 00110111 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => 1
11001001 => 00110110 => [3,1,2,1,2] => [3,2,2,1,1] => 2
11001010 => 00110101 => [3,1,2,2,1] => [3,2,2,1,1] => 2
11001011 => 00110100 => [3,1,2,3] => [3,3,2,1] => 1
11001100 => 00110011 => [3,1,3,1,1] => [3,3,1,1,1] => 0
11001101 => 00110010 => [3,1,3,2] => [3,3,2,1] => 1
11001110 => 00110001 => [3,1,4,1] => [4,3,1,1] => 1
11001111 => 00110000 => [3,1,5] => [5,3,1] => 0
11010000 => 00101111 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => 1
11010001 => 00101110 => [3,2,1,1,2] => [3,2,2,1,1] => 2
11010010 => 00101101 => [3,2,1,2,1] => [3,2,2,1,1] => 2
11010011 => 00101100 => [3,2,1,3] => [3,3,2,1] => 1
11010100 => 00101011 => [3,2,2,1,1] => [3,2,2,1,1] => 2
11010101 => 00101010 => [3,2,2,2] => [3,2,2,2] => 3
11010110 => 00101001 => [3,2,3,1] => [3,3,2,1] => 1
11010111 => 00101000 => [3,2,4] => [4,3,2] => 2
11011000 => 00100111 => [3,3,1,1,1] => [3,3,1,1,1] => 0
11011001 => 00100110 => [3,3,1,2] => [3,3,2,1] => 1
11011010 => 00100101 => [3,3,2,1] => [3,3,2,1] => 1
11011011 => 00100100 => [3,3,3] => [3,3,3] => 0
11011100 => 00100011 => [3,4,1,1] => [4,3,1,1] => 1
11011101 => 00100010 => [3,4,2] => [4,3,2] => 2
11011110 => 00100001 => [3,5,1] => [5,3,1] => 0
11011111 => 00100000 => [3,6] => [6,3] => 1
11100000 => 00011111 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 1
11100001 => 00011110 => [4,1,1,1,2] => [4,2,1,1,1] => 2
11100010 => 00011101 => [4,1,1,2,1] => [4,2,1,1,1] => 2
11100011 => 00011100 => [4,1,1,3] => [4,3,1,1] => 1
11100100 => 00011011 => [4,1,2,1,1] => [4,2,1,1,1] => 2
11100101 => 00011010 => [4,1,2,2] => [4,2,2,1] => 3
11100110 => 00011001 => [4,1,3,1] => [4,3,1,1] => 1
11100111 => 00011000 => [4,1,4] => [4,4,1] => 2
11101000 => 00010111 => [4,2,1,1,1] => [4,2,1,1,1] => 2
11101001 => 00010110 => [4,2,1,2] => [4,2,2,1] => 3
11101010 => 00010101 => [4,2,2,1] => [4,2,2,1] => 3
11101011 => 00010100 => [4,2,3] => [4,3,2] => 2
11101100 => 00010011 => [4,3,1,1] => [4,3,1,1] => 1
11101101 => 00010010 => [4,3,2] => [4,3,2] => 2
11101110 => 00010001 => [4,4,1] => [4,4,1] => 2
11101111 => 00010000 => [4,5] => [5,4] => 1
11110000 => 00001111 => [5,1,1,1,1] => [5,1,1,1,1] => 0
11110001 => 00001110 => [5,1,1,2] => [5,2,1,1] => 1
11110010 => 00001101 => [5,1,2,1] => [5,2,1,1] => 1
11110011 => 00001100 => [5,1,3] => [5,3,1] => 0
11110100 => 00001011 => [5,2,1,1] => [5,2,1,1] => 1
11110101 => 00001010 => [5,2,2] => [5,2,2] => 2
11110110 => 00001001 => [5,3,1] => [5,3,1] => 0
11110111 => 00001000 => [5,4] => [5,4] => 1
11111000 => 00000111 => [6,1,1,1] => [6,1,1,1] => 1
11111001 => 00000110 => [6,1,2] => [6,2,1] => 2
11111010 => 00000101 => [6,2,1] => [6,2,1] => 2
11111011 => 00000100 => [6,3] => [6,3] => 1
11111100 => 00000011 => [7,1,1] => [7,1,1] => 0
11111101 => 00000010 => [7,2] => [7,2] => 1
11111110 => 00000001 => [8,1] => [8,1] => 1
11111111 => 00000000 => [9] => [9] => 0
000000000 => 111111111 => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
000000001 => 111111110 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => 1
000000010 => 111111101 => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => 1
000000011 => 111111100 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => 0
000000100 => 111111011 => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => 1
000000101 => 111111010 => [1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => 2
000000110 => 111111001 => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => 0
000000111 => 111111000 => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 1
000001000 => 111110111 => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
000001001 => 111110110 => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => 2
000001010 => 111110101 => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => 2
000001011 => 111110100 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => 1
000001100 => 111110011 => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => 0
000001101 => 111110010 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => 1
000001110 => 111110001 => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => 1
000001111 => 111110000 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 0
000010000 => 111101111 => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
000010001 => 111101110 => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => 2
000010010 => 111101101 => [1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => 2
000010011 => 111101100 => [1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => 1
000010100 => 111101011 => [1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => 2
000010101 => 111101010 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => 3
000010110 => 111101001 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => 1
000010111 => 111101000 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => 2
000011000 => 111100111 => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => 0
000011001 => 111100110 => [1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => 1
000011010 => 111100101 => [1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => 1
000011011 => 111100100 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => 0
000011100 => 111100011 => [1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => 1
000011101 => 111100010 => [1,1,1,1,4,2] => [4,2,1,1,1,1] => 2
000011110 => 111100001 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => 0
000011111 => 111100000 => [1,1,1,1,6] => [6,1,1,1,1] => 1
000100000 => 111011111 => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
000100001 => 111011110 => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => 2
000100010 => 111011101 => [1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => 2
000100011 => 111011100 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => 1
000100100 => 111011011 => [1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => 2
000100101 => 111011010 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => 3
000100110 => 111011001 => [1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => 1
000100111 => 111011000 => [1,1,1,2,1,4] => [4,2,1,1,1,1] => 2
000101000 => 111010111 => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => 2
000101001 => 111010110 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => 3
000101010 => 111010101 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => 3
000101011 => 111010100 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => 2
000101100 => 111010011 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => 1
000101101 => 111010010 => [1,1,1,2,3,2] => [3,2,2,1,1,1] => 2
000101110 => 111010001 => [1,1,1,2,4,1] => [4,2,1,1,1,1] => 2
000101111 => 111010000 => [1,1,1,2,5] => [5,2,1,1,1] => 1
000110000 => 111001111 => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
000110001 => 111001110 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => 1
000110010 => 111001101 => [1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => 1
000110011 => 111001100 => [1,1,1,3,1,3] => [3,3,1,1,1,1] => 0
000110100 => 111001011 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => 1
000110101 => 111001010 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => 2
000110110 => 111001001 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => 0
000110111 => 111001000 => [1,1,1,3,4] => [4,3,1,1,1] => 1
000111000 => 111000111 => [1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => 1
000111001 => 111000110 => [1,1,1,4,1,2] => [4,2,1,1,1,1] => 2
000111010 => 111000101 => [1,1,1,4,2,1] => [4,2,1,1,1,1] => 2
000111011 => 111000100 => [1,1,1,4,3] => [4,3,1,1,1] => 1
000111100 => 111000011 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => 0
000111101 => 111000010 => [1,1,1,5,2] => [5,2,1,1,1] => 1
000111110 => 111000001 => [1,1,1,6,1] => [6,1,1,1,1] => 1
000111111 => 111000000 => [1,1,1,7] => [7,1,1,1] => 0
001000000 => 110111111 => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
001000001 => 110111110 => [1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 2
001000010 => 110111101 => [1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 2
001000011 => 110111100 => [1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => 1
001000100 => 110111011 => [1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 2
001000101 => 110111010 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => 3
001000110 => 110111001 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => 1
001000111 => 110111000 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => 2
001001000 => 110110111 => [1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 2
001001001 => 110110110 => [1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => 3
001001010 => 110110101 => [1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => 3
001001011 => 110110100 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => 2
001001100 => 110110011 => [1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => 1
001001101 => 110110010 => [1,1,2,1,3,2] => [3,2,2,1,1,1] => 2
001001110 => 110110001 => [1,1,2,1,4,1] => [4,2,1,1,1,1] => 2
001001111 => 110110000 => [1,1,2,1,5] => [5,2,1,1,1] => 1
001010000 => 110101111 => [1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2
001010001 => 110101110 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => 3
001010010 => 110101101 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => 3
001010011 => 110101100 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => 2
001010100 => 110101011 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => 3
001010101 => 110101010 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => 4
001010110 => 110101001 => [1,1,2,2,3,1] => [3,2,2,1,1,1] => 2
001010111 => 110101000 => [1,1,2,2,4] => [4,2,2,1,1] => 3
001011000 => 110100111 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => 1
001011001 => 110100110 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => 2
001011010 => 110100101 => [1,1,2,3,2,1] => [3,2,2,1,1,1] => 2
001011011 => 110100100 => [1,1,2,3,3] => [3,3,2,1,1] => 1
001011100 => 110100011 => [1,1,2,4,1,1] => [4,2,1,1,1,1] => 2
001011101 => 110100010 => [1,1,2,4,2] => [4,2,2,1,1] => 3
001011110 => 110100001 => [1,1,2,5,1] => [5,2,1,1,1] => 1
001011111 => 110100000 => [1,1,2,6] => [6,2,1,1] => 2
001100000 => 110011111 => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
001100001 => 110011110 => [1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => 1
001100010 => 110011101 => [1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => 1
001100011 => 110011100 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => 0
001100100 => 110011011 => [1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => 1
001100101 => 110011010 => [1,1,3,1,2,2] => [3,2,2,1,1,1] => 2
001100110 => 110011001 => [1,1,3,1,3,1] => [3,3,1,1,1,1] => 0
001100111 => 110011000 => [1,1,3,1,4] => [4,3,1,1,1] => 1
001101000 => 110010111 => [1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => 1
001101001 => 110010110 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => 2
001101010 => 110010101 => [1,1,3,2,2,1] => [3,2,2,1,1,1] => 2
001101011 => 110010100 => [1,1,3,2,3] => [3,3,2,1,1] => 1
001101100 => 110010011 => [1,1,3,3,1,1] => [3,3,1,1,1,1] => 0
001101101 => 110010010 => [1,1,3,3,2] => [3,3,2,1,1] => 1
001101110 => 110010001 => [1,1,3,4,1] => [4,3,1,1,1] => 1
001101111 => 110010000 => [1,1,3,5] => [5,3,1,1] => 0
001110000 => 110001111 => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => 1
001110001 => 110001110 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => 2
001110010 => 110001101 => [1,1,4,1,2,1] => [4,2,1,1,1,1] => 2
001110011 => 110001100 => [1,1,4,1,3] => [4,3,1,1,1] => 1
001110100 => 110001011 => [1,1,4,2,1,1] => [4,2,1,1,1,1] => 2
001110101 => 110001010 => [1,1,4,2,2] => [4,2,2,1,1] => 3
001110110 => 110001001 => [1,1,4,3,1] => [4,3,1,1,1] => 1
001110111 => 110001000 => [1,1,4,4] => [4,4,1,1] => 2
001111000 => 110000111 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => 0
001111001 => 110000110 => [1,1,5,1,2] => [5,2,1,1,1] => 1
001111010 => 110000101 => [1,1,5,2,1] => [5,2,1,1,1] => 1
001111011 => 110000100 => [1,1,5,3] => [5,3,1,1] => 0
001111100 => 110000011 => [1,1,6,1,1] => [6,1,1,1,1] => 1
001111101 => 110000010 => [1,1,6,2] => [6,2,1,1] => 2
001111110 => 110000001 => [1,1,7,1] => [7,1,1,1] => 0
001111111 => 110000000 => [1,1,8] => [8,1,1] => 1
010000000 => 101111111 => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
010000001 => 101111110 => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 2
010000010 => 101111101 => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 2
010000011 => 101111100 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => 1
010000100 => 101111011 => [1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 2
010000101 => 101111010 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => 3
010000110 => 101111001 => [1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => 1
010000111 => 101111000 => [1,2,1,1,1,4] => [4,2,1,1,1,1] => 2
010001000 => 101110111 => [1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 2
010001001 => 101110110 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => 3
010001010 => 101110101 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => 3
010001011 => 101110100 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => 2
010001100 => 101110011 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => 1
010001101 => 101110010 => [1,2,1,1,3,2] => [3,2,2,1,1,1] => 2
010001110 => 101110001 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => 2
010001111 => 101110000 => [1,2,1,1,5] => [5,2,1,1,1] => 1
010010000 => 101101111 => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2
010010001 => 101101110 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => 3
010010010 => 101101101 => [1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => 3
010010011 => 101101100 => [1,2,1,2,1,3] => [3,2,2,1,1,1] => 2
010010100 => 101101011 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => 3
010010101 => 101101010 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => 4
010010110 => 101101001 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => 2
010010111 => 101101000 => [1,2,1,2,4] => [4,2,2,1,1] => 3
010011000 => 101100111 => [1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => 1
010011001 => 101100110 => [1,2,1,3,1,2] => [3,2,2,1,1,1] => 2
010011010 => 101100101 => [1,2,1,3,2,1] => [3,2,2,1,1,1] => 2
010011011 => 101100100 => [1,2,1,3,3] => [3,3,2,1,1] => 1
010011100 => 101100011 => [1,2,1,4,1,1] => [4,2,1,1,1,1] => 2
010011101 => 101100010 => [1,2,1,4,2] => [4,2,2,1,1] => 3
010011110 => 101100001 => [1,2,1,5,1] => [5,2,1,1,1] => 1
010011111 => 101100000 => [1,2,1,6] => [6,2,1,1] => 2
010100000 => 101011111 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2
010100001 => 101011110 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => 3
010100010 => 101011101 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => 3
010100011 => 101011100 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => 2
010100100 => 101011011 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => 3
010100101 => 101011010 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => 4
010100110 => 101011001 => [1,2,2,1,3,1] => [3,2,2,1,1,1] => 2
010100111 => 101011000 => [1,2,2,1,4] => [4,2,2,1,1] => 3
010101000 => 101010111 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => 3
010101001 => 101010110 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => 4
010101010 => 101010101 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => 4
010101011 => 101010100 => [1,2,2,2,3] => [3,2,2,2,1] => 3
010101100 => 101010011 => [1,2,2,3,1,1] => [3,2,2,1,1,1] => 2
010101101 => 101010010 => [1,2,2,3,2] => [3,2,2,2,1] => 3
010101110 => 101010001 => [1,2,2,4,1] => [4,2,2,1,1] => 3
010101111 => 101010000 => [1,2,2,5] => [5,2,2,1] => 2
010110000 => 101001111 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => 1
010110001 => 101001110 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => 2
010110010 => 101001101 => [1,2,3,1,2,1] => [3,2,2,1,1,1] => 2
010110011 => 101001100 => [1,2,3,1,3] => [3,3,2,1,1] => 1
010110100 => 101001011 => [1,2,3,2,1,1] => [3,2,2,1,1,1] => 2
010110101 => 101001010 => [1,2,3,2,2] => [3,2,2,2,1] => 3
010110110 => 101001001 => [1,2,3,3,1] => [3,3,2,1,1] => 1
010110111 => 101001000 => [1,2,3,4] => [4,3,2,1] => 2
010111000 => 101000111 => [1,2,4,1,1,1] => [4,2,1,1,1,1] => 2
010111001 => 101000110 => [1,2,4,1,2] => [4,2,2,1,1] => 3
010111010 => 101000101 => [1,2,4,2,1] => [4,2,2,1,1] => 3
010111011 => 101000100 => [1,2,4,3] => [4,3,2,1] => 2
010111100 => 101000011 => [1,2,5,1,1] => [5,2,1,1,1] => 1
010111101 => 101000010 => [1,2,5,2] => [5,2,2,1] => 2
010111110 => 101000001 => [1,2,6,1] => [6,2,1,1] => 2
010111111 => 101000000 => [1,2,7] => [7,2,1] => 1
011000000 => 100111111 => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
011000001 => 100111110 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => 1
011000010 => 100111101 => [1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => 1
011000011 => 100111100 => [1,3,1,1,1,3] => [3,3,1,1,1,1] => 0
011000100 => 100111011 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => 1
011000101 => 100111010 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => 2
011000110 => 100111001 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => 0
011000111 => 100111000 => [1,3,1,1,4] => [4,3,1,1,1] => 1
011001000 => 100110111 => [1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => 1
011001001 => 100110110 => [1,3,1,2,1,2] => [3,2,2,1,1,1] => 2
011001010 => 100110101 => [1,3,1,2,2,1] => [3,2,2,1,1,1] => 2
011001011 => 100110100 => [1,3,1,2,3] => [3,3,2,1,1] => 1
011001100 => 100110011 => [1,3,1,3,1,1] => [3,3,1,1,1,1] => 0
011001101 => 100110010 => [1,3,1,3,2] => [3,3,2,1,1] => 1
011001110 => 100110001 => [1,3,1,4,1] => [4,3,1,1,1] => 1
011001111 => 100110000 => [1,3,1,5] => [5,3,1,1] => 0
011010000 => 100101111 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => 1
011010001 => 100101110 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => 2
011010010 => 100101101 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => 2
011010011 => 100101100 => [1,3,2,1,3] => [3,3,2,1,1] => 1
011010100 => 100101011 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => 2
011010101 => 100101010 => [1,3,2,2,2] => [3,2,2,2,1] => 3
011010110 => 100101001 => [1,3,2,3,1] => [3,3,2,1,1] => 1
011010111 => 100101000 => [1,3,2,4] => [4,3,2,1] => 2
011011000 => 100100111 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => 0
011011001 => 100100110 => [1,3,3,1,2] => [3,3,2,1,1] => 1
011011010 => 100100101 => [1,3,3,2,1] => [3,3,2,1,1] => 1
011011011 => 100100100 => [1,3,3,3] => [3,3,3,1] => 0
011011100 => 100100011 => [1,3,4,1,1] => [4,3,1,1,1] => 1
011011101 => 100100010 => [1,3,4,2] => [4,3,2,1] => 2
011011110 => 100100001 => [1,3,5,1] => [5,3,1,1] => 0
011011111 => 100100000 => [1,3,6] => [6,3,1] => 1
011100000 => 100011111 => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => 1
011100001 => 100011110 => [1,4,1,1,1,2] => [4,2,1,1,1,1] => 2
011100010 => 100011101 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => 2
011100011 => 100011100 => [1,4,1,1,3] => [4,3,1,1,1] => 1
011100100 => 100011011 => [1,4,1,2,1,1] => [4,2,1,1,1,1] => 2
011100101 => 100011010 => [1,4,1,2,2] => [4,2,2,1,1] => 3
011100110 => 100011001 => [1,4,1,3,1] => [4,3,1,1,1] => 1
011100111 => 100011000 => [1,4,1,4] => [4,4,1,1] => 2
011101000 => 100010111 => [1,4,2,1,1,1] => [4,2,1,1,1,1] => 2
011101001 => 100010110 => [1,4,2,1,2] => [4,2,2,1,1] => 3
011101010 => 100010101 => [1,4,2,2,1] => [4,2,2,1,1] => 3
011101011 => 100010100 => [1,4,2,3] => [4,3,2,1] => 2
011101100 => 100010011 => [1,4,3,1,1] => [4,3,1,1,1] => 1
011101101 => 100010010 => [1,4,3,2] => [4,3,2,1] => 2
011101110 => 100010001 => [1,4,4,1] => [4,4,1,1] => 2
011101111 => 100010000 => [1,4,5] => [5,4,1] => 1
011110000 => 100001111 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => 0
011110001 => 100001110 => [1,5,1,1,2] => [5,2,1,1,1] => 1
011110010 => 100001101 => [1,5,1,2,1] => [5,2,1,1,1] => 1
011110011 => 100001100 => [1,5,1,3] => [5,3,1,1] => 0
011110100 => 100001011 => [1,5,2,1,1] => [5,2,1,1,1] => 1
011110101 => 100001010 => [1,5,2,2] => [5,2,2,1] => 2
011110110 => 100001001 => [1,5,3,1] => [5,3,1,1] => 0
011110111 => 100001000 => [1,5,4] => [5,4,1] => 1
011111000 => 100000111 => [1,6,1,1,1] => [6,1,1,1,1] => 1
011111001 => 100000110 => [1,6,1,2] => [6,2,1,1] => 2
011111010 => 100000101 => [1,6,2,1] => [6,2,1,1] => 2
011111011 => 100000100 => [1,6,3] => [6,3,1] => 1
011111100 => 100000011 => [1,7,1,1] => [7,1,1,1] => 0
011111101 => 100000010 => [1,7,2] => [7,2,1] => 1
011111110 => 100000001 => [1,8,1] => [8,1,1] => 1
011111111 => 100000000 => [1,9] => [9,1] => 0
100000000 => 011111111 => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
100000001 => 011111110 => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 2
100000010 => 011111101 => [2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 2
100000011 => 011111100 => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => 1
100000100 => 011111011 => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 2
100000101 => 011111010 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => 3
100000110 => 011111001 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => 1
100000111 => 011111000 => [2,1,1,1,1,4] => [4,2,1,1,1,1] => 2
100001000 => 011110111 => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 2
100001001 => 011110110 => [2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => 3
100001010 => 011110101 => [2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => 3
100001011 => 011110100 => [2,1,1,1,2,3] => [3,2,2,1,1,1] => 2
100001100 => 011110011 => [2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => 1
100001101 => 011110010 => [2,1,1,1,3,2] => [3,2,2,1,1,1] => 2
100001110 => 011110001 => [2,1,1,1,4,1] => [4,2,1,1,1,1] => 2
100001111 => 011110000 => [2,1,1,1,5] => [5,2,1,1,1] => 1
100010000 => 011101111 => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2
100010001 => 011101110 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => 3
100010010 => 011101101 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => 3
100010011 => 011101100 => [2,1,1,2,1,3] => [3,2,2,1,1,1] => 2
100010100 => 011101011 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => 3
100010101 => 011101010 => [2,1,1,2,2,2] => [2,2,2,2,1,1] => 4
100010110 => 011101001 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => 2
100010111 => 011101000 => [2,1,1,2,4] => [4,2,2,1,1] => 3
100011000 => 011100111 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => 1
100011001 => 011100110 => [2,1,1,3,1,2] => [3,2,2,1,1,1] => 2
100011010 => 011100101 => [2,1,1,3,2,1] => [3,2,2,1,1,1] => 2
100011011 => 011100100 => [2,1,1,3,3] => [3,3,2,1,1] => 1
100011100 => 011100011 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => 2
100011101 => 011100010 => [2,1,1,4,2] => [4,2,2,1,1] => 3
100011110 => 011100001 => [2,1,1,5,1] => [5,2,1,1,1] => 1
100011111 => 011100000 => [2,1,1,6] => [6,2,1,1] => 2
100100000 => 011011111 => [2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2
100100001 => 011011110 => [2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => 3
100100010 => 011011101 => [2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => 3
100100011 => 011011100 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => 2
100100100 => 011011011 => [2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => 3
100100101 => 011011010 => [2,1,2,1,2,2] => [2,2,2,2,1,1] => 4
100100110 => 011011001 => [2,1,2,1,3,1] => [3,2,2,1,1,1] => 2
100100111 => 011011000 => [2,1,2,1,4] => [4,2,2,1,1] => 3
100101000 => 011010111 => [2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => 3
100101001 => 011010110 => [2,1,2,2,1,2] => [2,2,2,2,1,1] => 4
100101010 => 011010101 => [2,1,2,2,2,1] => [2,2,2,2,1,1] => 4
100101011 => 011010100 => [2,1,2,2,3] => [3,2,2,2,1] => 3
100101100 => 011010011 => [2,1,2,3,1,1] => [3,2,2,1,1,1] => 2
100101101 => 011010010 => [2,1,2,3,2] => [3,2,2,2,1] => 3
100101110 => 011010001 => [2,1,2,4,1] => [4,2,2,1,1] => 3
100101111 => 011010000 => [2,1,2,5] => [5,2,2,1] => 2
100110000 => 011001111 => [2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => 1
100110001 => 011001110 => [2,1,3,1,1,2] => [3,2,2,1,1,1] => 2
100110010 => 011001101 => [2,1,3,1,2,1] => [3,2,2,1,1,1] => 2
100110011 => 011001100 => [2,1,3,1,3] => [3,3,2,1,1] => 1
100110100 => 011001011 => [2,1,3,2,1,1] => [3,2,2,1,1,1] => 2
100110101 => 011001010 => [2,1,3,2,2] => [3,2,2,2,1] => 3
100110110 => 011001001 => [2,1,3,3,1] => [3,3,2,1,1] => 1
100110111 => 011001000 => [2,1,3,4] => [4,3,2,1] => 2
100111000 => 011000111 => [2,1,4,1,1,1] => [4,2,1,1,1,1] => 2
100111001 => 011000110 => [2,1,4,1,2] => [4,2,2,1,1] => 3
100111010 => 011000101 => [2,1,4,2,1] => [4,2,2,1,1] => 3
100111011 => 011000100 => [2,1,4,3] => [4,3,2,1] => 2
100111100 => 011000011 => [2,1,5,1,1] => [5,2,1,1,1] => 1
100111101 => 011000010 => [2,1,5,2] => [5,2,2,1] => 2
100111110 => 011000001 => [2,1,6,1] => [6,2,1,1] => 2
100111111 => 011000000 => [2,1,7] => [7,2,1] => 1
101000000 => 010111111 => [2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2
101000001 => 010111110 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => 3
101000010 => 010111101 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => 3
101000011 => 010111100 => [2,2,1,1,1,3] => [3,2,2,1,1,1] => 2
101000100 => 010111011 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => 3
101000101 => 010111010 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => 4
101000110 => 010111001 => [2,2,1,1,3,1] => [3,2,2,1,1,1] => 2
101000111 => 010111000 => [2,2,1,1,4] => [4,2,2,1,1] => 3
101001000 => 010110111 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => 3
101001001 => 010110110 => [2,2,1,2,1,2] => [2,2,2,2,1,1] => 4
101001010 => 010110101 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => 4
101001011 => 010110100 => [2,2,1,2,3] => [3,2,2,2,1] => 3
101001100 => 010110011 => [2,2,1,3,1,1] => [3,2,2,1,1,1] => 2
101001101 => 010110010 => [2,2,1,3,2] => [3,2,2,2,1] => 3
101001110 => 010110001 => [2,2,1,4,1] => [4,2,2,1,1] => 3
101001111 => 010110000 => [2,2,1,5] => [5,2,2,1] => 2
101010000 => 010101111 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 3
101010001 => 010101110 => [2,2,2,1,1,2] => [2,2,2,2,1,1] => 4
101010010 => 010101101 => [2,2,2,1,2,1] => [2,2,2,2,1,1] => 4
101010011 => 010101100 => [2,2,2,1,3] => [3,2,2,2,1] => 3
101010100 => 010101011 => [2,2,2,2,1,1] => [2,2,2,2,1,1] => 4
101010101 => 010101010 => [2,2,2,2,2] => [2,2,2,2,2] => 5
101010110 => 010101001 => [2,2,2,3,1] => [3,2,2,2,1] => 3
101010111 => 010101000 => [2,2,2,4] => [4,2,2,2] => 4
101011000 => 010100111 => [2,2,3,1,1,1] => [3,2,2,1,1,1] => 2
101011001 => 010100110 => [2,2,3,1,2] => [3,2,2,2,1] => 3
101011010 => 010100101 => [2,2,3,2,1] => [3,2,2,2,1] => 3
101011011 => 010100100 => [2,2,3,3] => [3,3,2,2] => 2
101011100 => 010100011 => [2,2,4,1,1] => [4,2,2,1,1] => 3
101011101 => 010100010 => [2,2,4,2] => [4,2,2,2] => 4
101011110 => 010100001 => [2,2,5,1] => [5,2,2,1] => 2
101011111 => 010100000 => [2,2,6] => [6,2,2] => 3
101100000 => 010011111 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1
101100001 => 010011110 => [2,3,1,1,1,2] => [3,2,2,1,1,1] => 2
101100010 => 010011101 => [2,3,1,1,2,1] => [3,2,2,1,1,1] => 2
101100011 => 010011100 => [2,3,1,1,3] => [3,3,2,1,1] => 1
101100100 => 010011011 => [2,3,1,2,1,1] => [3,2,2,1,1,1] => 2
101100101 => 010011010 => [2,3,1,2,2] => [3,2,2,2,1] => 3
101100110 => 010011001 => [2,3,1,3,1] => [3,3,2,1,1] => 1
101100111 => 010011000 => [2,3,1,4] => [4,3,2,1] => 2
101101000 => 010010111 => [2,3,2,1,1,1] => [3,2,2,1,1,1] => 2
101101001 => 010010110 => [2,3,2,1,2] => [3,2,2,2,1] => 3
101101010 => 010010101 => [2,3,2,2,1] => [3,2,2,2,1] => 3
101101011 => 010010100 => [2,3,2,3] => [3,3,2,2] => 2
101101100 => 010010011 => [2,3,3,1,1] => [3,3,2,1,1] => 1
101101101 => 010010010 => [2,3,3,2] => [3,3,2,2] => 2
101101110 => 010010001 => [2,3,4,1] => [4,3,2,1] => 2
101101111 => 010010000 => [2,3,5] => [5,3,2] => 1
101110000 => 010001111 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => 2
101110001 => 010001110 => [2,4,1,1,2] => [4,2,2,1,1] => 3
101110010 => 010001101 => [2,4,1,2,1] => [4,2,2,1,1] => 3
101110011 => 010001100 => [2,4,1,3] => [4,3,2,1] => 2
101110100 => 010001011 => [2,4,2,1,1] => [4,2,2,1,1] => 3
101110101 => 010001010 => [2,4,2,2] => [4,2,2,2] => 4
101110110 => 010001001 => [2,4,3,1] => [4,3,2,1] => 2
101110111 => 010001000 => [2,4,4] => [4,4,2] => 3
101111000 => 010000111 => [2,5,1,1,1] => [5,2,1,1,1] => 1
101111001 => 010000110 => [2,5,1,2] => [5,2,2,1] => 2
101111010 => 010000101 => [2,5,2,1] => [5,2,2,1] => 2
101111011 => 010000100 => [2,5,3] => [5,3,2] => 1
101111100 => 010000011 => [2,6,1,1] => [6,2,1,1] => 2
101111101 => 010000010 => [2,6,2] => [6,2,2] => 3
101111110 => 010000001 => [2,7,1] => [7,2,1] => 1
101111111 => 010000000 => [2,8] => [8,2] => 2
110000000 => 001111111 => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
110000001 => 001111110 => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => 1
110000010 => 001111101 => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => 1
110000011 => 001111100 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => 0
110000100 => 001111011 => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => 1
110000101 => 001111010 => [3,1,1,1,2,2] => [3,2,2,1,1,1] => 2
110000110 => 001111001 => [3,1,1,1,3,1] => [3,3,1,1,1,1] => 0
110000111 => 001111000 => [3,1,1,1,4] => [4,3,1,1,1] => 1
110001000 => 001110111 => [3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => 1
110001001 => 001110110 => [3,1,1,2,1,2] => [3,2,2,1,1,1] => 2
110001010 => 001110101 => [3,1,1,2,2,1] => [3,2,2,1,1,1] => 2
110001011 => 001110100 => [3,1,1,2,3] => [3,3,2,1,1] => 1
110001100 => 001110011 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => 0
110001101 => 001110010 => [3,1,1,3,2] => [3,3,2,1,1] => 1
110001110 => 001110001 => [3,1,1,4,1] => [4,3,1,1,1] => 1
110001111 => 001110000 => [3,1,1,5] => [5,3,1,1] => 0
110010000 => 001101111 => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => 1
110010001 => 001101110 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => 2
110010010 => 001101101 => [3,1,2,1,2,1] => [3,2,2,1,1,1] => 2
110010011 => 001101100 => [3,1,2,1,3] => [3,3,2,1,1] => 1
110010100 => 001101011 => [3,1,2,2,1,1] => [3,2,2,1,1,1] => 2
110010101 => 001101010 => [3,1,2,2,2] => [3,2,2,2,1] => 3
110010110 => 001101001 => [3,1,2,3,1] => [3,3,2,1,1] => 1
110010111 => 001101000 => [3,1,2,4] => [4,3,2,1] => 2
110011000 => 001100111 => [3,1,3,1,1,1] => [3,3,1,1,1,1] => 0
110011001 => 001100110 => [3,1,3,1,2] => [3,3,2,1,1] => 1
110011010 => 001100101 => [3,1,3,2,1] => [3,3,2,1,1] => 1
110011011 => 001100100 => [3,1,3,3] => [3,3,3,1] => 0
110011100 => 001100011 => [3,1,4,1,1] => [4,3,1,1,1] => 1
110011101 => 001100010 => [3,1,4,2] => [4,3,2,1] => 2
110011110 => 001100001 => [3,1,5,1] => [5,3,1,1] => 0
110011111 => 001100000 => [3,1,6] => [6,3,1] => 1
110100000 => 001011111 => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1
110100001 => 001011110 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => 2
110100010 => 001011101 => [3,2,1,1,2,1] => [3,2,2,1,1,1] => 2
110100011 => 001011100 => [3,2,1,1,3] => [3,3,2,1,1] => 1
110100100 => 001011011 => [3,2,1,2,1,1] => [3,2,2,1,1,1] => 2
110100101 => 001011010 => [3,2,1,2,2] => [3,2,2,2,1] => 3
110100110 => 001011001 => [3,2,1,3,1] => [3,3,2,1,1] => 1
110100111 => 001011000 => [3,2,1,4] => [4,3,2,1] => 2
110101000 => 001010111 => [3,2,2,1,1,1] => [3,2,2,1,1,1] => 2
110101001 => 001010110 => [3,2,2,1,2] => [3,2,2,2,1] => 3
110101010 => 001010101 => [3,2,2,2,1] => [3,2,2,2,1] => 3
110101011 => 001010100 => [3,2,2,3] => [3,3,2,2] => 2
110101100 => 001010011 => [3,2,3,1,1] => [3,3,2,1,1] => 1
110101101 => 001010010 => [3,2,3,2] => [3,3,2,2] => 2
110101110 => 001010001 => [3,2,4,1] => [4,3,2,1] => 2
110101111 => 001010000 => [3,2,5] => [5,3,2] => 1
110110000 => 001001111 => [3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
110110001 => 001001110 => [3,3,1,1,2] => [3,3,2,1,1] => 1
110110010 => 001001101 => [3,3,1,2,1] => [3,3,2,1,1] => 1
110110011 => 001001100 => [3,3,1,3] => [3,3,3,1] => 0
110110100 => 001001011 => [3,3,2,1,1] => [3,3,2,1,1] => 1
110110101 => 001001010 => [3,3,2,2] => [3,3,2,2] => 2
110110110 => 001001001 => [3,3,3,1] => [3,3,3,1] => 0
110110111 => 001001000 => [3,3,4] => [4,3,3] => 1
110111000 => 001000111 => [3,4,1,1,1] => [4,3,1,1,1] => 1
110111001 => 001000110 => [3,4,1,2] => [4,3,2,1] => 2
110111010 => 001000101 => [3,4,2,1] => [4,3,2,1] => 2
110111011 => 001000100 => [3,4,3] => [4,3,3] => 1
110111100 => 001000011 => [3,5,1,1] => [5,3,1,1] => 0
110111101 => 001000010 => [3,5,2] => [5,3,2] => 1
110111110 => 001000001 => [3,6,1] => [6,3,1] => 1
110111111 => 001000000 => [3,7] => [7,3] => 0
111000000 => 000111111 => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 1
111000001 => 000111110 => [4,1,1,1,1,2] => [4,2,1,1,1,1] => 2
111000010 => 000111101 => [4,1,1,1,2,1] => [4,2,1,1,1,1] => 2
111000011 => 000111100 => [4,1,1,1,3] => [4,3,1,1,1] => 1
111000100 => 000111011 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => 2
111000101 => 000111010 => [4,1,1,2,2] => [4,2,2,1,1] => 3
111000110 => 000111001 => [4,1,1,3,1] => [4,3,1,1,1] => 1
111000111 => 000111000 => [4,1,1,4] => [4,4,1,1] => 2
111001000 => 000110111 => [4,1,2,1,1,1] => [4,2,1,1,1,1] => 2
111001001 => 000110110 => [4,1,2,1,2] => [4,2,2,1,1] => 3
111001010 => 000110101 => [4,1,2,2,1] => [4,2,2,1,1] => 3
111001011 => 000110100 => [4,1,2,3] => [4,3,2,1] => 2
111001100 => 000110011 => [4,1,3,1,1] => [4,3,1,1,1] => 1
111001101 => 000110010 => [4,1,3,2] => [4,3,2,1] => 2
111001110 => 000110001 => [4,1,4,1] => [4,4,1,1] => 2
111001111 => 000110000 => [4,1,5] => [5,4,1] => 1
111010000 => 000101111 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => 2
111010001 => 000101110 => [4,2,1,1,2] => [4,2,2,1,1] => 3
111010010 => 000101101 => [4,2,1,2,1] => [4,2,2,1,1] => 3
111010011 => 000101100 => [4,2,1,3] => [4,3,2,1] => 2
111010100 => 000101011 => [4,2,2,1,1] => [4,2,2,1,1] => 3
111010101 => 000101010 => [4,2,2,2] => [4,2,2,2] => 4
111010110 => 000101001 => [4,2,3,1] => [4,3,2,1] => 2
111010111 => 000101000 => [4,2,4] => [4,4,2] => 3
111011000 => 000100111 => [4,3,1,1,1] => [4,3,1,1,1] => 1
111011001 => 000100110 => [4,3,1,2] => [4,3,2,1] => 2
111011010 => 000100101 => [4,3,2,1] => [4,3,2,1] => 2
111011011 => 000100100 => [4,3,3] => [4,3,3] => 1
111011100 => 000100011 => [4,4,1,1] => [4,4,1,1] => 2
111011101 => 000100010 => [4,4,2] => [4,4,2] => 3
111011110 => 000100001 => [4,5,1] => [5,4,1] => 1
111011111 => 000100000 => [4,6] => [6,4] => 2
111100000 => 000011111 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 0
111100001 => 000011110 => [5,1,1,1,2] => [5,2,1,1,1] => 1
111100010 => 000011101 => [5,1,1,2,1] => [5,2,1,1,1] => 1
111100011 => 000011100 => [5,1,1,3] => [5,3,1,1] => 0
111100100 => 000011011 => [5,1,2,1,1] => [5,2,1,1,1] => 1
111100101 => 000011010 => [5,1,2,2] => [5,2,2,1] => 2
111100110 => 000011001 => [5,1,3,1] => [5,3,1,1] => 0
111100111 => 000011000 => [5,1,4] => [5,4,1] => 1
111101000 => 000010111 => [5,2,1,1,1] => [5,2,1,1,1] => 1
111101001 => 000010110 => [5,2,1,2] => [5,2,2,1] => 2
111101010 => 000010101 => [5,2,2,1] => [5,2,2,1] => 2
111101011 => 000010100 => [5,2,3] => [5,3,2] => 1
111101100 => 000010011 => [5,3,1,1] => [5,3,1,1] => 0
111101101 => 000010010 => [5,3,2] => [5,3,2] => 1
111101110 => 000010001 => [5,4,1] => [5,4,1] => 1
111101111 => 000010000 => [5,5] => [5,5] => 0
111110000 => 000001111 => [6,1,1,1,1] => [6,1,1,1,1] => 1
111110001 => 000001110 => [6,1,1,2] => [6,2,1,1] => 2
111110010 => 000001101 => [6,1,2,1] => [6,2,1,1] => 2
111110011 => 000001100 => [6,1,3] => [6,3,1] => 1
111110100 => 000001011 => [6,2,1,1] => [6,2,1,1] => 2
111110101 => 000001010 => [6,2,2] => [6,2,2] => 3
111110110 => 000001001 => [6,3,1] => [6,3,1] => 1
111110111 => 000001000 => [6,4] => [6,4] => 2
111111000 => 000000111 => [7,1,1,1] => [7,1,1,1] => 0
111111001 => 000000110 => [7,1,2] => [7,2,1] => 1
111111010 => 000000101 => [7,2,1] => [7,2,1] => 1
111111011 => 000000100 => [7,3] => [7,3] => 0
111111100 => 000000011 => [8,1,1] => [8,1,1] => 1
111111101 => 000000010 => [8,2] => [8,2] => 2
111111110 => 000000001 => [9,1] => [9,1] => 0
111111111 => 000000000 => [10] => [10] => 1
1010101010 => 0101010101 => [2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
1011110000 => 0100001111 => [2,5,1,1,1,1] => [5,2,1,1,1,1] => 1
1111000010 => 0000111101 => [5,1,1,1,2,1] => [5,2,1,1,1,1] => 1
1111000100 => 0000111011 => [5,1,1,2,1,1] => [5,2,1,1,1,1] => 1
1111001000 => 0000110111 => [5,1,2,1,1,1] => [5,2,1,1,1,1] => 1
1111010000 => 0000101111 => [5,2,1,1,1,1] => [5,2,1,1,1,1] => 1
1111100000 => 0000011111 => [6,1,1,1,1,1] => [6,1,1,1,1,1] => 1
101010101010 => 010101010101 => [2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 6
1111111111 => 0000000000 => [11] => [11] => 0
1111111110 => 0000000001 => [10,1] => [10,1] => 1
1111000001 => 0000111110 => [5,1,1,1,1,2] => [5,2,1,1,1,1] => 1
1010000001 => 0101111110 => [2,2,1,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 3
1001011110 => 0110100001 => [2,1,2,5,1] => [5,2,2,1,1] => 2
1000011110 => 0111100001 => [2,1,1,1,5,1] => [5,2,1,1,1,1] => 1
1000001010 => 0111110101 => [2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1] => 3
1000000101 => 0111111010 => [2,1,1,1,1,1,2,2] => [2,2,2,1,1,1,1,1] => 3
1000000000 => 0111111111 => [2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1
10000000010 => 01111111101 => [2,1,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 2
11111111110 => 00000000001 => [11,1] => [11,1] => 0
10000000100 => 01111111011 => [2,1,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
10000010000 => 01111101111 => [2,1,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
10111011110 => 01000100001 => [2,4,5,1] => [5,4,2,1] => 2
10111101110 => 01000010001 => [2,5,4,1] => [5,4,2,1] => 2
10001000000 => 01110111111 => [2,1,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
11101011110 => 00010100001 => [4,2,5,1] => [5,4,2,1] => 2
11011101110 => 00100010001 => [3,4,4,1] => [4,4,3,1] => 2
10101010110 => 01010101001 => [2,2,2,2,3,1] => [3,2,2,2,2,1] => 4
11101101110 => 00010010001 => [4,3,4,1] => [4,4,3,1] => 2
10100000000 => 01011111111 => [2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
10101011010 => 01010100101 => [2,2,2,3,2,1] => [3,2,2,2,2,1] => 4
11101110110 => 00010001001 => [4,4,3,1] => [4,4,3,1] => 2
=> => [1] => [1] => 0
0111111111 => 1000000000 => [1,10] => [10,1] => 1
0111100001 => 1000011110 => [1,5,1,1,1,2] => [5,2,1,1,1,1] => 1
0000000001 => 1111111110 => [1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1] => 1
01111111111 => 10000000000 => [1,11] => [11,1] => 0
0111101001 => 1000010110 => [1,5,2,1,2] => [5,2,2,1,1] => 2
0101000001 => 1010111110 => [1,2,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 3
01000000001 => 10111111110 => [1,2,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 2
0101010101 => 1010101010 => [1,2,2,2,2,2] => [2,2,2,2,2,1] => 5
0100001111 => 1011110000 => [1,2,1,1,1,5] => [5,2,1,1,1,1] => 1
0010001111 => 1101110000 => [1,1,2,1,1,5] => [5,2,1,1,1,1] => 1
0001001111 => 1110110000 => [1,1,1,2,1,5] => [5,2,1,1,1,1] => 1
0000111101 => 1111000010 => [1,1,1,1,5,2] => [5,2,1,1,1,1] => 1
0000101111 => 1111010000 => [1,1,1,1,2,5] => [5,2,1,1,1,1] => 1
0000011111 => 1111100000 => [1,1,1,1,1,6] => [6,1,1,1,1,1] => 1
010101010101 => 101010101010 => [1,2,2,2,2,2,2] => [2,2,2,2,2,2,1] => 6
11010101010 => 00101010101 => [3,2,2,2,2,1] => [3,2,2,2,2,1] => 4
11010101100 => 00101010011 => [3,2,2,3,1,1] => [3,3,2,2,1,1] => 2
11011010100 => 00100101011 => [3,3,2,2,1,1] => [3,3,2,2,1,1] => 2
0000000000 => 1111111111 => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
0001100110 => 1110011001 => [1,1,1,3,1,3,1] => [3,3,1,1,1,1,1] => 0
0110000110 => 1001111001 => [1,3,1,1,1,3,1] => [3,3,1,1,1,1,1] => 0
0110011000 => 1001100111 => [1,3,1,3,1,1,1] => [3,3,1,1,1,1,1] => 0
0110011110 => 1001100001 => [1,3,1,5,1] => [5,3,1,1,1] => 0
0111100110 => 1000011001 => [1,5,1,3,1] => [5,3,1,1,1] => 0
0111111110 => 1000000001 => [1,9,1] => [9,1,1] => 0
000000000000 => 111111111111 => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
0010101000 => 1101010111 => [1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1] => 3
0001010100 => 1110101011 => [1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1] => 3
00101011011 => 11010100100 => [1,1,2,2,3,3] => [3,3,2,2,1,1] => 2
0010111100 => 1101000011 => [1,1,2,5,1,1] => [5,2,1,1,1,1] => 1
00101101011 => 11010010100 => [1,1,2,3,2,3] => [3,3,2,2,1,1] => 2
0011110100 => 1100001011 => [1,1,5,2,1,1] => [5,2,1,1,1,1] => 1
00110101011 => 11001010100 => [1,1,3,2,2,3] => [3,3,2,2,1,1] => 2
01010101011 => 10101010100 => [1,2,2,2,2,3] => [3,2,2,2,2,1] => 4
0000000010 => 1111111101 => [1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1] => 1
00000000000 => 11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 0
01111111110 => 10000000001 => [1,10,1] => [10,1,1] => 1
10101010101 => 01010101010 => [2,2,2,2,2,2] => [2,2,2,2,2,2] => 6
01000001000 => 10111110111 => [1,2,1,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
01000010000 => 10111101111 => [1,2,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00100001000 => 11011110111 => [1,1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00100010000 => 11011101111 => [1,1,2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00010000010 => 11101111101 => [1,1,1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00010000100 => 11101111011 => [1,1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00010001000 => 11101110111 => [1,1,1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00010010000 => 11101101111 => [1,1,1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00001000001 => 11110111110 => [1,1,1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 2
00001000010 => 11110111101 => [1,1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00001000100 => 11110111011 => [1,1,1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00001001000 => 11110110111 => [1,1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
00000000101 => 11111111010 => [1,1,1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1,1,1] => 2
11111111101 => 00000000010 => [10,2] => [10,2] => 2
00100000001 => 11011111110 => [1,1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 2
10000000001 => 01111111110 => [2,1,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 2
11111111111 => 00000000000 => [12] => [12] => 1
01011110111 => 10100001000 => [1,2,5,4] => [5,4,2,1] => 2
01101010101 => 10010101010 => [1,3,2,2,2,2] => [3,2,2,2,2,1] => 4
01110111101 => 10001000010 => [1,4,5,2] => [5,4,2,1] => 2
01111011101 => 10000100010 => [1,5,4,2] => [5,4,2,1] => 2
01111010111 => 10000101000 => [1,5,2,4] => [5,4,2,1] => 2
10110101010 => 01001010101 => [2,3,2,2,2,1] => [3,2,2,2,2,1] => 4
10111011101 => 01000100010 => [2,4,4,2] => [4,4,2,2] => 4
10111110111 => 01000001000 => [2,6,4] => [6,4,2] => 3
10101101010 => 01010010101 => [2,2,3,2,2,1] => [3,2,2,2,2,1] => 4
10101110111 => 01010001000 => [2,2,4,4] => [4,4,2,2] => 4
10111010111 => 01000101000 => [2,4,2,4] => [4,4,2,2] => 4
10111101111 => 01000010000 => [2,5,5] => [5,5,2] => 1
11011101101 => 00100010010 => [3,4,3,2] => [4,3,3,2] => 2
11011011101 => 00100100010 => [3,3,4,2] => [4,3,3,2] => 2
11011011011 => 00100100100 => [3,3,3,3] => [3,3,3,3] => 0
11011101011 => 00100010100 => [3,4,2,3] => [4,3,3,2] => 2
11011110111 => 00100001000 => [3,5,4] => [5,4,3] => 1
11010111011 => 00101000100 => [3,2,4,3] => [4,3,3,2] => 2
11010110111 => 00101001000 => [3,2,3,4] => [4,3,3,2] => 2
11011010111 => 00100101000 => [3,3,2,4] => [4,3,3,2] => 2
11011101111 => 00100010000 => [3,4,5] => [5,4,3] => 1
11101111010 => 00010000101 => [4,5,2,1] => [5,4,2,1] => 2
11101111101 => 00010000010 => [4,6,2] => [6,4,2] => 3
11101110101 => 00010001010 => [4,4,2,2] => [4,4,2,2] => 4
11101111011 => 00010000100 => [4,5,3] => [5,4,3] => 1
11101101101 => 00010010010 => [4,3,3,2] => [4,3,3,2] => 2
11101101011 => 00010010100 => [4,3,2,3] => [4,3,3,2] => 2
11101110111 => 00010001000 => [4,4,4] => [4,4,4] => 3
11101011101 => 00010100010 => [4,2,4,2] => [4,4,2,2] => 4
11101011011 => 00010100100 => [4,2,3,3] => [4,3,3,2] => 2
11101010111 => 00010101000 => [4,2,2,4] => [4,4,2,2] => 4
11101101111 => 00010010000 => [4,3,5] => [5,4,3] => 1
11110111101 => 00001000010 => [5,5,2] => [5,5,2] => 1
11110111011 => 00001000100 => [5,4,3] => [5,4,3] => 1
11110110111 => 00001001000 => [5,3,4] => [5,4,3] => 1
11110101111 => 00001010000 => [5,2,5] => [5,5,2] => 1
11111011111 => 00000100000 => [6,6] => [6,6] => 2
0111101111 => 1000010000 => [1,5,5] => [5,5,1] => 0
0011111111 => 1100000000 => [1,1,9] => [9,1,1] => 0
10101001011 => 01010110100 => [2,2,2,1,2,3] => [3,2,2,2,2,1] => 4
10010110101 => 01101001010 => [2,1,2,3,2,2] => [3,2,2,2,2,1] => 4
01010000000 => 10101111111 => [1,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 2
01000000010 => 10111111101 => [1,2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 2
10010101011 => 01101010100 => [2,1,2,2,2,3] => [3,2,2,2,2,1] => 4
11110101010 => 00001010101 => [5,2,2,2,1] => [5,2,2,2,1] => 3
0111011111 => 1000100000 => [1,4,6] => [6,4,1] => 2
11111011101 => 00000100010 => [6,4,2] => [6,4,2] => 3
00000010001 => 11111101110 => [1,1,1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 2
11101011010 => 00010100101 => [4,2,3,2,1] => [4,3,2,2,1] => 3
11101010110 => 00010101001 => [4,2,2,3,1] => [4,3,2,2,1] => 3
11101101010 => 00010010101 => [4,3,2,2,1] => [4,3,2,2,1] => 3
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Description
The number of even parts of a partition.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.