100111 => 011000 => [2,1,4] => 1011000 => 2
101000 => 010111 => [2,2,1,1,1] => 1010111 => 2
101001 => 010110 => [2,2,1,2] => 1010110 => 3
101010 => 010101 => [2,2,2,1] => 1010101 => 3
101011 => 010100 => [2,2,3] => 1010100 => 3
101100 => 010011 => [2,3,1,1] => 1010011 => 2
101101 => 010010 => [2,3,2] => 1010010 => 3
101110 => 010001 => [2,4,1] => 1010001 => 2
101111 => 010000 => [2,5] => 1010000 => 2
110000 => 001111 => [3,1,1,1,1] => 1001111 => 1
110001 => 001110 => [3,1,1,2] => 1001110 => 2
110010 => 001101 => [3,1,2,1] => 1001101 => 2
110011 => 001100 => [3,1,3] => 1001100 => 2
110100 => 001011 => [3,2,1,1] => 1001011 => 2
110101 => 001010 => [3,2,2] => 1001010 => 3
110110 => 001001 => [3,3,1] => 1001001 => 2
110111 => 001000 => [3,4] => 1001000 => 2
111000 => 000111 => [4,1,1,1] => 1000111 => 1
111001 => 000110 => [4,1,2] => 1000110 => 2
111010 => 000101 => [4,2,1] => 1000101 => 2
111011 => 000100 => [4,3] => 1000100 => 2
111100 => 000011 => [5,1,1] => 1000011 => 1
111101 => 000010 => [5,2] => 1000010 => 2
111110 => 000001 => [6,1] => 1000001 => 1
111111 => 000000 => [7] => 1000000 => 1
0000000 => 1111111 => [1,1,1,1,1,1,1,1] => 11111111 => 0
0000001 => 1111110 => [1,1,1,1,1,1,2] => 11111110 => 1
0000010 => 1111101 => [1,1,1,1,1,2,1] => 11111101 => 1
0000011 => 1111100 => [1,1,1,1,1,3] => 11111100 => 1
0000100 => 1111011 => [1,1,1,1,2,1,1] => 11111011 => 1
0000101 => 1111010 => [1,1,1,1,2,2] => 11111010 => 2
0000110 => 1111001 => [1,1,1,1,3,1] => 11111001 => 1
0000111 => 1111000 => [1,1,1,1,4] => 11111000 => 1
0001000 => 1110111 => [1,1,1,2,1,1,1] => 11110111 => 1
0001001 => 1110110 => [1,1,1,2,1,2] => 11110110 => 2
0001010 => 1110101 => [1,1,1,2,2,1] => 11110101 => 2
0001011 => 1110100 => [1,1,1,2,3] => 11110100 => 2
0001100 => 1110011 => [1,1,1,3,1,1] => 11110011 => 1
0001101 => 1110010 => [1,1,1,3,2] => 11110010 => 2
0001110 => 1110001 => [1,1,1,4,1] => 11110001 => 1
0001111 => 1110000 => [1,1,1,5] => 11110000 => 1
0010000 => 1101111 => [1,1,2,1,1,1,1] => 11101111 => 1
0010001 => 1101110 => [1,1,2,1,1,2] => 11101110 => 2
0010010 => 1101101 => [1,1,2,1,2,1] => 11101101 => 2
0010011 => 1101100 => [1,1,2,1,3] => 11101100 => 2
0010100 => 1101011 => [1,1,2,2,1,1] => 11101011 => 2
0010101 => 1101010 => [1,1,2,2,2] => 11101010 => 3
0010110 => 1101001 => [1,1,2,3,1] => 11101001 => 2
0010111 => 1101000 => [1,1,2,4] => 11101000 => 2
0011000 => 1100111 => [1,1,3,1,1,1] => 11100111 => 1
0011001 => 1100110 => [1,1,3,1,2] => 11100110 => 2
0011010 => 1100101 => [1,1,3,2,1] => 11100101 => 2
0011011 => 1100100 => [1,1,3,3] => 11100100 => 2
0011100 => 1100011 => [1,1,4,1,1] => 11100011 => 1
0011101 => 1100010 => [1,1,4,2] => 11100010 => 2
0011110 => 1100001 => [1,1,5,1] => 11100001 => 1
0011111 => 1100000 => [1,1,6] => 11100000 => 1
0100000 => 1011111 => [1,2,1,1,1,1,1] => 11011111 => 1
0100001 => 1011110 => [1,2,1,1,1,2] => 11011110 => 2
0100010 => 1011101 => [1,2,1,1,2,1] => 11011101 => 2
0100011 => 1011100 => [1,2,1,1,3] => 11011100 => 2
0100100 => 1011011 => [1,2,1,2,1,1] => 11011011 => 2
0100101 => 1011010 => [1,2,1,2,2] => 11011010 => 3
0100110 => 1011001 => [1,2,1,3,1] => 11011001 => 2
0100111 => 1011000 => [1,2,1,4] => 11011000 => 2
0101000 => 1010111 => [1,2,2,1,1,1] => 11010111 => 2
0101001 => 1010110 => [1,2,2,1,2] => 11010110 => 3
0101010 => 1010101 => [1,2,2,2,1] => 11010101 => 3
0101011 => 1010100 => [1,2,2,3] => 11010100 => 3
0101100 => 1010011 => [1,2,3,1,1] => 11010011 => 2
0101101 => 1010010 => [1,2,3,2] => 11010010 => 3
0101110 => 1010001 => [1,2,4,1] => 11010001 => 2
0101111 => 1010000 => [1,2,5] => 11010000 => 2
0110000 => 1001111 => [1,3,1,1,1,1] => 11001111 => 1
0110001 => 1001110 => [1,3,1,1,2] => 11001110 => 2
0110010 => 1001101 => [1,3,1,2,1] => 11001101 => 2
0110011 => 1001100 => [1,3,1,3] => 11001100 => 2
0110100 => 1001011 => [1,3,2,1,1] => 11001011 => 2
0110101 => 1001010 => [1,3,2,2] => 11001010 => 3
0110110 => 1001001 => [1,3,3,1] => 11001001 => 2
0110111 => 1001000 => [1,3,4] => 11001000 => 2
0111000 => 1000111 => [1,4,1,1,1] => 11000111 => 1
0111001 => 1000110 => [1,4,1,2] => 11000110 => 2
0111010 => 1000101 => [1,4,2,1] => 11000101 => 2
0111011 => 1000100 => [1,4,3] => 11000100 => 2
0111100 => 1000011 => [1,5,1,1] => 11000011 => 1
0111101 => 1000010 => [1,5,2] => 11000010 => 2
0111110 => 1000001 => [1,6,1] => 11000001 => 1
0111111 => 1000000 => [1,7] => 11000000 => 1
1000000 => 0111111 => [2,1,1,1,1,1,1] => 10111111 => 1
1000001 => 0111110 => [2,1,1,1,1,2] => 10111110 => 2
1000010 => 0111101 => [2,1,1,1,2,1] => 10111101 => 2
1000011 => 0111100 => [2,1,1,1,3] => 10111100 => 2
1000100 => 0111011 => [2,1,1,2,1,1] => 10111011 => 2
1000101 => 0111010 => [2,1,1,2,2] => 10111010 => 3
1000110 => 0111001 => [2,1,1,3,1] => 10111001 => 2
1000111 => 0111000 => [2,1,1,4] => 10111000 => 2
1001000 => 0110111 => [2,1,2,1,1,1] => 10110111 => 2
1001001 => 0110110 => [2,1,2,1,2] => 10110110 => 3
1001010 => 0110101 => [2,1,2,2,1] => 10110101 => 3
1001011 => 0110100 => [2,1,2,3] => 10110100 => 3
1001100 => 0110011 => [2,1,3,1,1] => 10110011 => 2
1001101 => 0110010 => [2,1,3,2] => 10110010 => 3
1001110 => 0110001 => [2,1,4,1] => 10110001 => 2
1001111 => 0110000 => [2,1,5] => 10110000 => 2
1010000 => 0101111 => [2,2,1,1,1,1] => 10101111 => 2
1010001 => 0101110 => [2,2,1,1,2] => 10101110 => 3
1010010 => 0101101 => [2,2,1,2,1] => 10101101 => 3
1010011 => 0101100 => [2,2,1,3] => 10101100 => 3
1010100 => 0101011 => [2,2,2,1,1] => 10101011 => 3
1010101 => 0101010 => [2,2,2,2] => 10101010 => 4
1010110 => 0101001 => [2,2,3,1] => 10101001 => 3
1010111 => 0101000 => [2,2,4] => 10101000 => 3
1011000 => 0100111 => [2,3,1,1,1] => 10100111 => 2
1011001 => 0100110 => [2,3,1,2] => 10100110 => 3
1011010 => 0100101 => [2,3,2,1] => 10100101 => 3
1011011 => 0100100 => [2,3,3] => 10100100 => 3
1011100 => 0100011 => [2,4,1,1] => 10100011 => 2
1011101 => 0100010 => [2,4,2] => 10100010 => 3
1011110 => 0100001 => [2,5,1] => 10100001 => 2
1011111 => 0100000 => [2,6] => 10100000 => 2
1100000 => 0011111 => [3,1,1,1,1,1] => 10011111 => 1
1100001 => 0011110 => [3,1,1,1,2] => 10011110 => 2
1100010 => 0011101 => [3,1,1,2,1] => 10011101 => 2
1100011 => 0011100 => [3,1,1,3] => 10011100 => 2
1100100 => 0011011 => [3,1,2,1,1] => 10011011 => 2
1100101 => 0011010 => [3,1,2,2] => 10011010 => 3
1100110 => 0011001 => [3,1,3,1] => 10011001 => 2
1100111 => 0011000 => [3,1,4] => 10011000 => 2
1101000 => 0010111 => [3,2,1,1,1] => 10010111 => 2
1101001 => 0010110 => [3,2,1,2] => 10010110 => 3
1101010 => 0010101 => [3,2,2,1] => 10010101 => 3
1101011 => 0010100 => [3,2,3] => 10010100 => 3
1101100 => 0010011 => [3,3,1,1] => 10010011 => 2
1101101 => 0010010 => [3,3,2] => 10010010 => 3
1101110 => 0010001 => [3,4,1] => 10010001 => 2
1101111 => 0010000 => [3,5] => 10010000 => 2
1110000 => 0001111 => [4,1,1,1,1] => 10001111 => 1
1110001 => 0001110 => [4,1,1,2] => 10001110 => 2
1110010 => 0001101 => [4,1,2,1] => 10001101 => 2
1110011 => 0001100 => [4,1,3] => 10001100 => 2
1110100 => 0001011 => [4,2,1,1] => 10001011 => 2
1110101 => 0001010 => [4,2,2] => 10001010 => 3
1110110 => 0001001 => [4,3,1] => 10001001 => 2
1110111 => 0001000 => [4,4] => 10001000 => 2
1111000 => 0000111 => [5,1,1,1] => 10000111 => 1
1111001 => 0000110 => [5,1,2] => 10000110 => 2
1111010 => 0000101 => [5,2,1] => 10000101 => 2
1111011 => 0000100 => [5,3] => 10000100 => 2
1111100 => 0000011 => [6,1,1] => 10000011 => 1
1111101 => 0000010 => [6,2] => 10000010 => 2
1111110 => 0000001 => [7,1] => 10000001 => 1
1111111 => 0000000 => [8] => 10000000 => 1
00000000 => 11111111 => [1,1,1,1,1,1,1,1,1] => 111111111 => 0
00000001 => 11111110 => [1,1,1,1,1,1,1,2] => 111111110 => 1
00000010 => 11111101 => [1,1,1,1,1,1,2,1] => 111111101 => 1
00000011 => 11111100 => [1,1,1,1,1,1,3] => 111111100 => 1
00000100 => 11111011 => [1,1,1,1,1,2,1,1] => 111111011 => 1
00000101 => 11111010 => [1,1,1,1,1,2,2] => 111111010 => 2
00000110 => 11111001 => [1,1,1,1,1,3,1] => 111111001 => 1
00000111 => 11111000 => [1,1,1,1,1,4] => 111111000 => 1
00001000 => 11110111 => [1,1,1,1,2,1,1,1] => 111110111 => 1
00001001 => 11110110 => [1,1,1,1,2,1,2] => 111110110 => 2
00001010 => 11110101 => [1,1,1,1,2,2,1] => 111110101 => 2
00001011 => 11110100 => [1,1,1,1,2,3] => 111110100 => 2
00001100 => 11110011 => [1,1,1,1,3,1,1] => 111110011 => 1
00001101 => 11110010 => [1,1,1,1,3,2] => 111110010 => 2
00001110 => 11110001 => [1,1,1,1,4,1] => 111110001 => 1
00001111 => 11110000 => [1,1,1,1,5] => 111110000 => 1
00010000 => 11101111 => [1,1,1,2,1,1,1,1] => 111101111 => 1
00010001 => 11101110 => [1,1,1,2,1,1,2] => 111101110 => 2
00010010 => 11101101 => [1,1,1,2,1,2,1] => 111101101 => 2
00010011 => 11101100 => [1,1,1,2,1,3] => 111101100 => 2
00010100 => 11101011 => [1,1,1,2,2,1,1] => 111101011 => 2
00010101 => 11101010 => [1,1,1,2,2,2] => 111101010 => 3
00010110 => 11101001 => [1,1,1,2,3,1] => 111101001 => 2
00010111 => 11101000 => [1,1,1,2,4] => 111101000 => 2
00011000 => 11100111 => [1,1,1,3,1,1,1] => 111100111 => 1
00011001 => 11100110 => [1,1,1,3,1,2] => 111100110 => 2
00011010 => 11100101 => [1,1,1,3,2,1] => 111100101 => 2
00011011 => 11100100 => [1,1,1,3,3] => 111100100 => 2
00011100 => 11100011 => [1,1,1,4,1,1] => 111100011 => 1
00011101 => 11100010 => [1,1,1,4,2] => 111100010 => 2
00011110 => 11100001 => [1,1,1,5,1] => 111100001 => 1
00011111 => 11100000 => [1,1,1,6] => 111100000 => 1
00100000 => 11011111 => [1,1,2,1,1,1,1,1] => 111011111 => 1
00100001 => 11011110 => [1,1,2,1,1,1,2] => 111011110 => 2
00100010 => 11011101 => [1,1,2,1,1,2,1] => 111011101 => 2
00100011 => 11011100 => [1,1,2,1,1,3] => 111011100 => 2
00100100 => 11011011 => [1,1,2,1,2,1,1] => 111011011 => 2
00100101 => 11011010 => [1,1,2,1,2,2] => 111011010 => 3
00100110 => 11011001 => [1,1,2,1,3,1] => 111011001 => 2
00100111 => 11011000 => [1,1,2,1,4] => 111011000 => 2
00101000 => 11010111 => [1,1,2,2,1,1,1] => 111010111 => 2
00101001 => 11010110 => [1,1,2,2,1,2] => 111010110 => 3
00101010 => 11010101 => [1,1,2,2,2,1] => 111010101 => 3
00101011 => 11010100 => [1,1,2,2,3] => 111010100 => 3
00101100 => 11010011 => [1,1,2,3,1,1] => 111010011 => 2
00101101 => 11010010 => [1,1,2,3,2] => 111010010 => 3
00101110 => 11010001 => [1,1,2,4,1] => 111010001 => 2
00101111 => 11010000 => [1,1,2,5] => 111010000 => 2
00110000 => 11001111 => [1,1,3,1,1,1,1] => 111001111 => 1
00110001 => 11001110 => [1,1,3,1,1,2] => 111001110 => 2
00110010 => 11001101 => [1,1,3,1,2,1] => 111001101 => 2
00110011 => 11001100 => [1,1,3,1,3] => 111001100 => 2
00110100 => 11001011 => [1,1,3,2,1,1] => 111001011 => 2
00110101 => 11001010 => [1,1,3,2,2] => 111001010 => 3
00110110 => 11001001 => [1,1,3,3,1] => 111001001 => 2
00110111 => 11001000 => [1,1,3,4] => 111001000 => 2
00111000 => 11000111 => [1,1,4,1,1,1] => 111000111 => 1
00111001 => 11000110 => [1,1,4,1,2] => 111000110 => 2
00111010 => 11000101 => [1,1,4,2,1] => 111000101 => 2
00111011 => 11000100 => [1,1,4,3] => 111000100 => 2
00111100 => 11000011 => [1,1,5,1,1] => 111000011 => 1
00111101 => 11000010 => [1,1,5,2] => 111000010 => 2
00111110 => 11000001 => [1,1,6,1] => 111000001 => 1
00111111 => 11000000 => [1,1,7] => 111000000 => 1
01000000 => 10111111 => [1,2,1,1,1,1,1,1] => 110111111 => 1
01000001 => 10111110 => [1,2,1,1,1,1,2] => 110111110 => 2
01000010 => 10111101 => [1,2,1,1,1,2,1] => 110111101 => 2
01000011 => 10111100 => [1,2,1,1,1,3] => 110111100 => 2
01000100 => 10111011 => [1,2,1,1,2,1,1] => 110111011 => 2
01000101 => 10111010 => [1,2,1,1,2,2] => 110111010 => 3
01000110 => 10111001 => [1,2,1,1,3,1] => 110111001 => 2
01000111 => 10111000 => [1,2,1,1,4] => 110111000 => 2
01001000 => 10110111 => [1,2,1,2,1,1,1] => 110110111 => 2
01001001 => 10110110 => [1,2,1,2,1,2] => 110110110 => 3
01001010 => 10110101 => [1,2,1,2,2,1] => 110110101 => 3
01001011 => 10110100 => [1,2,1,2,3] => 110110100 => 3
01001100 => 10110011 => [1,2,1,3,1,1] => 110110011 => 2
01001101 => 10110010 => [1,2,1,3,2] => 110110010 => 3
01001110 => 10110001 => [1,2,1,4,1] => 110110001 => 2
01001111 => 10110000 => [1,2,1,5] => 110110000 => 2
01010000 => 10101111 => [1,2,2,1,1,1,1] => 110101111 => 2
01010001 => 10101110 => [1,2,2,1,1,2] => 110101110 => 3
01010010 => 10101101 => [1,2,2,1,2,1] => 110101101 => 3
01010011 => 10101100 => [1,2,2,1,3] => 110101100 => 3
01010100 => 10101011 => [1,2,2,2,1,1] => 110101011 => 3
01010101 => 10101010 => [1,2,2,2,2] => 110101010 => 4
01010110 => 10101001 => [1,2,2,3,1] => 110101001 => 3
01010111 => 10101000 => [1,2,2,4] => 110101000 => 3
01011000 => 10100111 => [1,2,3,1,1,1] => 110100111 => 2
01011001 => 10100110 => [1,2,3,1,2] => 110100110 => 3
01011010 => 10100101 => [1,2,3,2,1] => 110100101 => 3
01011011 => 10100100 => [1,2,3,3] => 110100100 => 3
01011100 => 10100011 => [1,2,4,1,1] => 110100011 => 2
01011101 => 10100010 => [1,2,4,2] => 110100010 => 3
01011110 => 10100001 => [1,2,5,1] => 110100001 => 2
01011111 => 10100000 => [1,2,6] => 110100000 => 2
01100000 => 10011111 => [1,3,1,1,1,1,1] => 110011111 => 1
01100001 => 10011110 => [1,3,1,1,1,2] => 110011110 => 2
01100010 => 10011101 => [1,3,1,1,2,1] => 110011101 => 2
01100011 => 10011100 => [1,3,1,1,3] => 110011100 => 2
01100100 => 10011011 => [1,3,1,2,1,1] => 110011011 => 2
01100101 => 10011010 => [1,3,1,2,2] => 110011010 => 3
01100110 => 10011001 => [1,3,1,3,1] => 110011001 => 2
01100111 => 10011000 => [1,3,1,4] => 110011000 => 2
01101000 => 10010111 => [1,3,2,1,1,1] => 110010111 => 2
01101001 => 10010110 => [1,3,2,1,2] => 110010110 => 3
01101010 => 10010101 => [1,3,2,2,1] => 110010101 => 3
01101011 => 10010100 => [1,3,2,3] => 110010100 => 3
01101100 => 10010011 => [1,3,3,1,1] => 110010011 => 2
01101101 => 10010010 => [1,3,3,2] => 110010010 => 3
01101110 => 10010001 => [1,3,4,1] => 110010001 => 2
01101111 => 10010000 => [1,3,5] => 110010000 => 2
01110000 => 10001111 => [1,4,1,1,1,1] => 110001111 => 1
01110001 => 10001110 => [1,4,1,1,2] => 110001110 => 2
01110010 => 10001101 => [1,4,1,2,1] => 110001101 => 2
01110011 => 10001100 => [1,4,1,3] => 110001100 => 2
01110100 => 10001011 => [1,4,2,1,1] => 110001011 => 2
01110101 => 10001010 => [1,4,2,2] => 110001010 => 3
01110110 => 10001001 => [1,4,3,1] => 110001001 => 2
01110111 => 10001000 => [1,4,4] => 110001000 => 2
01111000 => 10000111 => [1,5,1,1,1] => 110000111 => 1
01111001 => 10000110 => [1,5,1,2] => 110000110 => 2
01111010 => 10000101 => [1,5,2,1] => 110000101 => 2
01111011 => 10000100 => [1,5,3] => 110000100 => 2
01111100 => 10000011 => [1,6,1,1] => 110000011 => 1
01111101 => 10000010 => [1,6,2] => 110000010 => 2
01111110 => 10000001 => [1,7,1] => 110000001 => 1
01111111 => 10000000 => [1,8] => 110000000 => 1
10000000 => 01111111 => [2,1,1,1,1,1,1,1] => 101111111 => 1
10000001 => 01111110 => [2,1,1,1,1,1,2] => 101111110 => 2
10000010 => 01111101 => [2,1,1,1,1,2,1] => 101111101 => 2
10000011 => 01111100 => [2,1,1,1,1,3] => 101111100 => 2
10000100 => 01111011 => [2,1,1,1,2,1,1] => 101111011 => 2
10000101 => 01111010 => [2,1,1,1,2,2] => 101111010 => 3
10000110 => 01111001 => [2,1,1,1,3,1] => 101111001 => 2
10000111 => 01111000 => [2,1,1,1,4] => 101111000 => 2
10001000 => 01110111 => [2,1,1,2,1,1,1] => 101110111 => 2
10001001 => 01110110 => [2,1,1,2,1,2] => 101110110 => 3
10001010 => 01110101 => [2,1,1,2,2,1] => 101110101 => 3
10001011 => 01110100 => [2,1,1,2,3] => 101110100 => 3
10001100 => 01110011 => [2,1,1,3,1,1] => 101110011 => 2
10001101 => 01110010 => [2,1,1,3,2] => 101110010 => 3
10001110 => 01110001 => [2,1,1,4,1] => 101110001 => 2
10001111 => 01110000 => [2,1,1,5] => 101110000 => 2
10010000 => 01101111 => [2,1,2,1,1,1,1] => 101101111 => 2
10010001 => 01101110 => [2,1,2,1,1,2] => 101101110 => 3
10010010 => 01101101 => [2,1,2,1,2,1] => 101101101 => 3
10010011 => 01101100 => [2,1,2,1,3] => 101101100 => 3
10010100 => 01101011 => [2,1,2,2,1,1] => 101101011 => 3
10010101 => 01101010 => [2,1,2,2,2] => 101101010 => 4
10010110 => 01101001 => [2,1,2,3,1] => 101101001 => 3
10010111 => 01101000 => [2,1,2,4] => 101101000 => 3
10011000 => 01100111 => [2,1,3,1,1,1] => 101100111 => 2
10011001 => 01100110 => [2,1,3,1,2] => 101100110 => 3
10011010 => 01100101 => [2,1,3,2,1] => 101100101 => 3
10011011 => 01100100 => [2,1,3,3] => 101100100 => 3
10011100 => 01100011 => [2,1,4,1,1] => 101100011 => 2
10011101 => 01100010 => [2,1,4,2] => 101100010 => 3
10011110 => 01100001 => [2,1,5,1] => 101100001 => 2
10011111 => 01100000 => [2,1,6] => 101100000 => 2
10100000 => 01011111 => [2,2,1,1,1,1,1] => 101011111 => 2
10100001 => 01011110 => [2,2,1,1,1,2] => 101011110 => 3
10100010 => 01011101 => [2,2,1,1,2,1] => 101011101 => 3
10100011 => 01011100 => [2,2,1,1,3] => 101011100 => 3
10100100 => 01011011 => [2,2,1,2,1,1] => 101011011 => 3
10100101 => 01011010 => [2,2,1,2,2] => 101011010 => 4
10100110 => 01011001 => [2,2,1,3,1] => 101011001 => 3
10100111 => 01011000 => [2,2,1,4] => 101011000 => 3
10101000 => 01010111 => [2,2,2,1,1,1] => 101010111 => 3
10101001 => 01010110 => [2,2,2,1,2] => 101010110 => 4
10101010 => 01010101 => [2,2,2,2,1] => 101010101 => 4
10101011 => 01010100 => [2,2,2,3] => 101010100 => 4
10101100 => 01010011 => [2,2,3,1,1] => 101010011 => 3
10101101 => 01010010 => [2,2,3,2] => 101010010 => 4
10101110 => 01010001 => [2,2,4,1] => 101010001 => 3
10101111 => 01010000 => [2,2,5] => 101010000 => 3
10110000 => 01001111 => [2,3,1,1,1,1] => 101001111 => 2
10110001 => 01001110 => [2,3,1,1,2] => 101001110 => 3
10110010 => 01001101 => [2,3,1,2,1] => 101001101 => 3
10110011 => 01001100 => [2,3,1,3] => 101001100 => 3
10110100 => 01001011 => [2,3,2,1,1] => 101001011 => 3
10110101 => 01001010 => [2,3,2,2] => 101001010 => 4
10110110 => 01001001 => [2,3,3,1] => 101001001 => 3
10110111 => 01001000 => [2,3,4] => 101001000 => 3
10111000 => 01000111 => [2,4,1,1,1] => 101000111 => 2
10111001 => 01000110 => [2,4,1,2] => 101000110 => 3
10111010 => 01000101 => [2,4,2,1] => 101000101 => 3
10111011 => 01000100 => [2,4,3] => 101000100 => 3
10111100 => 01000011 => [2,5,1,1] => 101000011 => 2
10111101 => 01000010 => [2,5,2] => 101000010 => 3
10111110 => 01000001 => [2,6,1] => 101000001 => 2
10111111 => 01000000 => [2,7] => 101000000 => 2
11000000 => 00111111 => [3,1,1,1,1,1,1] => 100111111 => 1
11000001 => 00111110 => [3,1,1,1,1,2] => 100111110 => 2
11000010 => 00111101 => [3,1,1,1,2,1] => 100111101 => 2
11000011 => 00111100 => [3,1,1,1,3] => 100111100 => 2
11000100 => 00111011 => [3,1,1,2,1,1] => 100111011 => 2
11000101 => 00111010 => [3,1,1,2,2] => 100111010 => 3
11000110 => 00111001 => [3,1,1,3,1] => 100111001 => 2
11000111 => 00111000 => [3,1,1,4] => 100111000 => 2
11001000 => 00110111 => [3,1,2,1,1,1] => 100110111 => 2
11001001 => 00110110 => [3,1,2,1,2] => 100110110 => 3
11001010 => 00110101 => [3,1,2,2,1] => 100110101 => 3
11001011 => 00110100 => [3,1,2,3] => 100110100 => 3
11001100 => 00110011 => [3,1,3,1,1] => 100110011 => 2
11001101 => 00110010 => [3,1,3,2] => 100110010 => 3
11001110 => 00110001 => [3,1,4,1] => 100110001 => 2
11001111 => 00110000 => [3,1,5] => 100110000 => 2
11010000 => 00101111 => [3,2,1,1,1,1] => 100101111 => 2
11010001 => 00101110 => [3,2,1,1,2] => 100101110 => 3
11010010 => 00101101 => [3,2,1,2,1] => 100101101 => 3
11010011 => 00101100 => [3,2,1,3] => 100101100 => 3
11010100 => 00101011 => [3,2,2,1,1] => 100101011 => 3
11010101 => 00101010 => [3,2,2,2] => 100101010 => 4
11010110 => 00101001 => [3,2,3,1] => 100101001 => 3
11010111 => 00101000 => [3,2,4] => 100101000 => 3
11011000 => 00100111 => [3,3,1,1,1] => 100100111 => 2
11011001 => 00100110 => [3,3,1,2] => 100100110 => 3
11011010 => 00100101 => [3,3,2,1] => 100100101 => 3
11011011 => 00100100 => [3,3,3] => 100100100 => 3
11011100 => 00100011 => [3,4,1,1] => 100100011 => 2
11011101 => 00100010 => [3,4,2] => 100100010 => 3
11011110 => 00100001 => [3,5,1] => 100100001 => 2
11011111 => 00100000 => [3,6] => 100100000 => 2
11100000 => 00011111 => [4,1,1,1,1,1] => 100011111 => 1
11100001 => 00011110 => [4,1,1,1,2] => 100011110 => 2
11100010 => 00011101 => [4,1,1,2,1] => 100011101 => 2
11100011 => 00011100 => [4,1,1,3] => 100011100 => 2
11100100 => 00011011 => [4,1,2,1,1] => 100011011 => 2
11100101 => 00011010 => [4,1,2,2] => 100011010 => 3
11100110 => 00011001 => [4,1,3,1] => 100011001 => 2
11100111 => 00011000 => [4,1,4] => 100011000 => 2
11101000 => 00010111 => [4,2,1,1,1] => 100010111 => 2
11101001 => 00010110 => [4,2,1,2] => 100010110 => 3
11101010 => 00010101 => [4,2,2,1] => 100010101 => 3
11101011 => 00010100 => [4,2,3] => 100010100 => 3
11101100 => 00010011 => [4,3,1,1] => 100010011 => 2
11101101 => 00010010 => [4,3,2] => 100010010 => 3
11101110 => 00010001 => [4,4,1] => 100010001 => 2
11101111 => 00010000 => [4,5] => 100010000 => 2
11110000 => 00001111 => [5,1,1,1,1] => 100001111 => 1
11110001 => 00001110 => [5,1,1,2] => 100001110 => 2
11110010 => 00001101 => [5,1,2,1] => 100001101 => 2
11110011 => 00001100 => [5,1,3] => 100001100 => 2
11110100 => 00001011 => [5,2,1,1] => 100001011 => 2
11110101 => 00001010 => [5,2,2] => 100001010 => 3
11110110 => 00001001 => [5,3,1] => 100001001 => 2
11110111 => 00001000 => [5,4] => 100001000 => 2
11111000 => 00000111 => [6,1,1,1] => 100000111 => 1
11111001 => 00000110 => [6,1,2] => 100000110 => 2
11111010 => 00000101 => [6,2,1] => 100000101 => 2
11111011 => 00000100 => [6,3] => 100000100 => 2
11111100 => 00000011 => [7,1,1] => 100000011 => 1
11111101 => 00000010 => [7,2] => 100000010 => 2
11111110 => 00000001 => [8,1] => 100000001 => 1
11111111 => 00000000 => [9] => 100000000 => 1
000000001 => 111111110 => [1,1,1,1,1,1,1,1,2] => 1111111110 => 1
000000010 => 111111101 => [1,1,1,1,1,1,1,2,1] => 1111111101 => 1
000011111 => 111100000 => [1,1,1,1,6] => 1111100000 => 1
000101111 => 111010000 => [1,1,1,2,5] => 1111010000 => 2
000110111 => 111001000 => [1,1,1,3,4] => 1111001000 => 2
000111011 => 111000100 => [1,1,1,4,3] => 1111000100 => 2
000111101 => 111000010 => [1,1,1,5,2] => 1111000010 => 2
000111110 => 111000001 => [1,1,1,6,1] => 1111000001 => 1
001000001 => 110111110 => [1,1,2,1,1,1,1,2] => 1110111110 => 2
001001111 => 110110000 => [1,1,2,1,5] => 1110110000 => 2
001010111 => 110101000 => [1,1,2,2,4] => 1110101000 => 3
001011011 => 110100100 => [1,1,2,3,3] => 1110100100 => 3
001011101 => 110100010 => [1,1,2,4,2] => 1110100010 => 3
001011110 => 110100001 => [1,1,2,5,1] => 1110100001 => 2
001100001 => 110011110 => [1,1,3,1,1,1,2] => 1110011110 => 2
001100111 => 110011000 => [1,1,3,1,4] => 1110011000 => 2
001101011 => 110010100 => [1,1,3,2,3] => 1110010100 => 3
001101101 => 110010010 => [1,1,3,3,2] => 1110010010 => 3
001101110 => 110010001 => [1,1,3,4,1] => 1110010001 => 2
001110011 => 110001100 => [1,1,4,1,3] => 1110001100 => 2
001110101 => 110001010 => [1,1,4,2,2] => 1110001010 => 3
001110110 => 110001001 => [1,1,4,3,1] => 1110001001 => 2
001111010 => 110000101 => [1,1,5,2,1] => 1110000101 => 2
010000001 => 101111110 => [1,2,1,1,1,1,1,2] => 1101111110 => 2
010001111 => 101110000 => [1,2,1,1,5] => 1101110000 => 2
010010111 => 101101000 => [1,2,1,2,4] => 1101101000 => 3
010011011 => 101100100 => [1,2,1,3,3] => 1101100100 => 3
010011101 => 101100010 => [1,2,1,4,2] => 1101100010 => 3
010011110 => 101100001 => [1,2,1,5,1] => 1101100001 => 2
010100111 => 101011000 => [1,2,2,1,4] => 1101011000 => 3
010101011 => 101010100 => [1,2,2,2,3] => 1101010100 => 4
010101101 => 101010010 => [1,2,2,3,2] => 1101010010 => 4
010101110 => 101010001 => [1,2,2,4,1] => 1101010001 => 3
010110001 => 101001110 => [1,2,3,1,1,2] => 1101001110 => 3
010110011 => 101001100 => [1,2,3,1,3] => 1101001100 => 3
010110101 => 101001010 => [1,2,3,2,2] => 1101001010 => 4
010110110 => 101001001 => [1,2,3,3,1] => 1101001001 => 3
010111010 => 101000101 => [1,2,4,2,1] => 1101000101 => 3
011000111 => 100111000 => [1,3,1,1,4] => 1100111000 => 2
011001011 => 100110100 => [1,3,1,2,3] => 1100110100 => 3
011001101 => 100110010 => [1,3,1,3,2] => 1100110010 => 3
011001110 => 100110001 => [1,3,1,4,1] => 1100110001 => 2
011010011 => 100101100 => [1,3,2,1,3] => 1100101100 => 3
011010101 => 100101010 => [1,3,2,2,2] => 1100101010 => 4
011010110 => 100101001 => [1,3,2,3,1] => 1100101001 => 3
011011001 => 100100110 => [1,3,3,1,2] => 1100100110 => 3
011011010 => 100100101 => [1,3,3,2,1] => 1100100101 => 3
011100110 => 100011001 => [1,4,1,3,1] => 1100011001 => 2
011101010 => 100010101 => [1,4,2,2,1] => 1100010101 => 3
011101101 => 100010010 => [1,4,3,2] => 1100010010 => 3
011110111 => 100001000 => [1,5,4] => 1100001000 => 2
100000001 => 011111110 => [2,1,1,1,1,1,1,2] => 1011111110 => 2
100000010 => 011111101 => [2,1,1,1,1,1,2,1] => 1011111101 => 2
100001111 => 011110000 => [2,1,1,1,5] => 1011110000 => 2
100010111 => 011101000 => [2,1,1,2,4] => 1011101000 => 3
100011011 => 011100100 => [2,1,1,3,3] => 1011100100 => 3
100011101 => 011100010 => [2,1,1,4,2] => 1011100010 => 3
100011110 => 011100001 => [2,1,1,5,1] => 1011100001 => 2
100100111 => 011011000 => [2,1,2,1,4] => 1011011000 => 3
100101011 => 011010100 => [2,1,2,2,3] => 1011010100 => 4
100101101 => 011010010 => [2,1,2,3,2] => 1011010010 => 4
100101110 => 011010001 => [2,1,2,4,1] => 1011010001 => 3
100110011 => 011001100 => [2,1,3,1,3] => 1011001100 => 3
100110101 => 011001010 => [2,1,3,2,2] => 1011001010 => 4
100110110 => 011001001 => [2,1,3,3,1] => 1011001001 => 3
100111010 => 011000101 => [2,1,4,2,1] => 1011000101 => 3
101000001 => 010111110 => [2,2,1,1,1,1,2] => 1010111110 => 3
101000111 => 010111000 => [2,2,1,1,4] => 1010111000 => 3
101001011 => 010110100 => [2,2,1,2,3] => 1010110100 => 4
101001101 => 010110010 => [2,2,1,3,2] => 1010110010 => 4
101001110 => 010110001 => [2,2,1,4,1] => 1010110001 => 3
101010011 => 010101100 => [2,2,2,1,3] => 1010101100 => 4
101010101 => 010101010 => [2,2,2,2,2] => 1010101010 => 5
101010110 => 010101001 => [2,2,2,3,1] => 1010101001 => 4
101011001 => 010100110 => [2,2,3,1,2] => 1010100110 => 4
101011010 => 010100101 => [2,2,3,2,1] => 1010100101 => 4
101100101 => 010011010 => [2,3,1,2,2] => 1010011010 => 4
101100110 => 010011001 => [2,3,1,3,1] => 1010011001 => 3
101101001 => 010010110 => [2,3,2,1,2] => 1010010110 => 4
101101010 => 010010101 => [2,3,2,2,1] => 1010010101 => 4
101110001 => 010001110 => [2,4,1,1,2] => 1010001110 => 3
110000001 => 001111110 => [3,1,1,1,1,1,2] => 1001111110 => 2
110000111 => 001111000 => [3,1,1,1,4] => 1001111000 => 2
110001011 => 001110100 => [3,1,1,2,3] => 1001110100 => 3
110001110 => 001110001 => [3,1,1,4,1] => 1001110001 => 2
110010011 => 001101100 => [3,1,2,1,3] => 1001101100 => 3
110010101 => 001101010 => [3,1,2,2,2] => 1001101010 => 4
110010110 => 001101001 => [3,1,2,3,1] => 1001101001 => 3
110011001 => 001100110 => [3,1,3,1,2] => 1001100110 => 3
110011010 => 001100101 => [3,1,3,2,1] => 1001100101 => 3
110100001 => 001011110 => [3,2,1,1,1,2] => 1001011110 => 3
110100101 => 001011010 => [3,2,1,2,2] => 1001011010 => 4
110100110 => 001011001 => [3,2,1,3,1] => 1001011001 => 3
110101001 => 001010110 => [3,2,2,1,2] => 1001010110 => 4
110101010 => 001010101 => [3,2,2,2,1] => 1001010101 => 4
110110001 => 001001110 => [3,3,1,1,2] => 1001001110 => 3
111000001 => 000111110 => [4,1,1,1,1,2] => 1000111110 => 2
111000011 => 000111100 => [4,1,1,1,3] => 1000111100 => 2
111000101 => 000111010 => [4,1,1,2,2] => 1000111010 => 3
111001001 => 000110110 => [4,1,2,1,2] => 1000110110 => 3
111010001 => 000101110 => [4,2,1,1,2] => 1000101110 => 3
111100001 => 000011110 => [5,1,1,1,2] => 1000011110 => 2
111101001 => 000010110 => [5,2,1,2] => 1000010110 => 3
111110001 => 000001110 => [6,1,1,2] => 1000001110 => 2
111110101 => 000001010 => [6,2,2] => 1000001010 => 3
111111001 => 000000110 => [7,1,2] => 1000000110 => 2
111111011 => 000000100 => [7,3] => 1000000100 => 2
111111101 => 000000010 => [8,2] => 1000000010 => 2
111111111 => 000000000 => [10] => 1000000000 => 1
1010101010 => 0101010101 => [2,2,2,2,2,1] => 10101010101 => 5
1111111111 => 0000000000 => [11] => 10000000000 => 1
1111111101 => 0000000010 => [9,2] => 10000000010 => 2
1111000001 => 0000111110 => [5,1,1,1,1,2] => 10000111110 => 2
1110111011 => 0001000100 => [4,4,3] => 10001000100 => 3
1100000001 => 0011111110 => [3,1,1,1,1,1,1,2] => 10011111110 => 2
1010000001 => 0101111110 => [2,2,1,1,1,1,1,2] => 10101111110 => 3
10000111110 => 01111000001 => [2,1,1,1,6,1] => 101111000001 => 2
10101010110 => 01010101001 => [2,2,2,2,3,1] => 101010101001 => 5
10101011010 => 01010100101 => [2,2,2,3,2,1] => 101010100101 => 5
=> => [1] => 1 => 0
0100000001 => 1011111110 => [1,2,1,1,1,1,1,1,2] => 11011111110 => 2
0000000001 => 1111111110 => [1,1,1,1,1,1,1,1,1,2] => 11111111110 => 1
11010101010 => 00101010101 => [3,2,2,2,2,1] => 100101010101 => 5
00101010111 => 11010101000 => [1,1,2,2,2,4] => 111010101000 => 4
00101011011 => 11010100100 => [1,1,2,2,3,3] => 111010100100 => 4
00101101011 => 11010010100 => [1,1,2,3,2,3] => 111010010100 => 4
00110101011 => 11001010100 => [1,1,3,2,2,3] => 111001010100 => 4
01010101011 => 10101010100 => [1,2,2,2,2,3] => 110101010100 => 5
0000000010 => 1111111101 => [1,1,1,1,1,1,1,1,2,1] => 11111111101 => 1
10101010101 => 01010101010 => [2,2,2,2,2,2] => 101010101010 => 6
01101010101 => 10010101010 => [1,3,2,2,2,2] => 110010101010 => 5
10110101010 => 01001010101 => [2,3,2,2,2,1] => 101001010101 => 5
10101101010 => 01010010101 => [2,2,3,2,2,1] => 101010010101 => 5
10101001011 => 01010110100 => [2,2,2,1,2,3] => 101010110100 => 5
00111000111 => 11000111000 => [1,1,4,1,1,4] => 111000111000 => 2
10010110101 => 01101001010 => [2,1,2,3,2,2] => 101101001010 => 5
10010101011 => 01101010100 => [2,1,2,2,2,3] => 101101010100 => 5
00001110111 => 11110001000 => [1,1,1,1,4,4] => 111110001000 => 2
11100000111 => 00011111000 => [4,1,1,1,1,4] => 100011111000 => 2