100111 => 011000 => [2,1,4] => [1,4,2] => 2
101000 => 010111 => [2,2,1,1,1] => [2,1,1,1,2] => 2
101001 => 010110 => [2,2,1,2] => [2,1,2,2] => 2
101010 => 010101 => [2,2,2,1] => [2,2,1,2] => 2
101011 => 010100 => [2,2,3] => [2,3,2] => 2
101100 => 010011 => [2,3,1,1] => [3,1,1,2] => 2
101101 => 010010 => [2,3,2] => [3,2,2] => 2
101110 => 010001 => [2,4,1] => [4,1,2] => 2
101111 => 010000 => [2,5] => [5,2] => 2
110000 => 001111 => [3,1,1,1,1] => [1,1,1,1,3] => 3
110001 => 001110 => [3,1,1,2] => [1,1,2,3] => 3
110010 => 001101 => [3,1,2,1] => [1,2,1,3] => 3
110011 => 001100 => [3,1,3] => [1,3,3] => 3
110100 => 001011 => [3,2,1,1] => [2,1,1,3] => 3
110101 => 001010 => [3,2,2] => [2,2,3] => 3
110110 => 001001 => [3,3,1] => [3,1,3] => 3
110111 => 001000 => [3,4] => [4,3] => 3
111000 => 000111 => [4,1,1,1] => [1,1,1,4] => 4
111001 => 000110 => [4,1,2] => [1,2,4] => 4
111010 => 000101 => [4,2,1] => [2,1,4] => 4
111011 => 000100 => [4,3] => [3,4] => 4
111100 => 000011 => [5,1,1] => [1,1,5] => 5
111101 => 000010 => [5,2] => [2,5] => 5
111110 => 000001 => [6,1] => [1,6] => 6
111111 => 000000 => [7] => [7] => 7
0000000 => 1111111 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
0000001 => 1111110 => [1,1,1,1,1,1,2] => [1,1,1,1,1,2,1] => 1
0000010 => 1111101 => [1,1,1,1,1,2,1] => [1,1,1,1,2,1,1] => 1
0000011 => 1111100 => [1,1,1,1,1,3] => [1,1,1,1,3,1] => 1
0000100 => 1111011 => [1,1,1,1,2,1,1] => [1,1,1,2,1,1,1] => 1
0000101 => 1111010 => [1,1,1,1,2,2] => [1,1,1,2,2,1] => 1
0000110 => 1111001 => [1,1,1,1,3,1] => [1,1,1,3,1,1] => 1
0001000 => 1110111 => [1,1,1,2,1,1,1] => [1,1,2,1,1,1,1] => 1
0001001 => 1110110 => [1,1,1,2,1,2] => [1,1,2,1,2,1] => 1
0001010 => 1110101 => [1,1,1,2,2,1] => [1,1,2,2,1,1] => 1
0001011 => 1110100 => [1,1,1,2,3] => [1,1,2,3,1] => 1
0001100 => 1110011 => [1,1,1,3,1,1] => [1,1,3,1,1,1] => 1
0001101 => 1110010 => [1,1,1,3,2] => [1,1,3,2,1] => 1
0001111 => 1110000 => [1,1,1,5] => [1,1,5,1] => 1
0010000 => 1101111 => [1,1,2,1,1,1,1] => [1,2,1,1,1,1,1] => 1
0010001 => 1101110 => [1,1,2,1,1,2] => [1,2,1,1,2,1] => 1
0010010 => 1101101 => [1,1,2,1,2,1] => [1,2,1,2,1,1] => 1
0010011 => 1101100 => [1,1,2,1,3] => [1,2,1,3,1] => 1
0010100 => 1101011 => [1,1,2,2,1,1] => [1,2,2,1,1,1] => 1
0010101 => 1101010 => [1,1,2,2,2] => [1,2,2,2,1] => 1
0010110 => 1101001 => [1,1,2,3,1] => [1,2,3,1,1] => 1
0010111 => 1101000 => [1,1,2,4] => [1,2,4,1] => 1
0011000 => 1100111 => [1,1,3,1,1,1] => [1,3,1,1,1,1] => 1
0011001 => 1100110 => [1,1,3,1,2] => [1,3,1,2,1] => 1
0011010 => 1100101 => [1,1,3,2,1] => [1,3,2,1,1] => 1
0011011 => 1100100 => [1,1,3,3] => [1,3,3,1] => 1
0011101 => 1100010 => [1,1,4,2] => [1,4,2,1] => 1
0011110 => 1100001 => [1,1,5,1] => [1,5,1,1] => 1
0011111 => 1100000 => [1,1,6] => [1,6,1] => 1
0100001 => 1011110 => [1,2,1,1,1,2] => [2,1,1,1,2,1] => 1
0100010 => 1011101 => [1,2,1,1,2,1] => [2,1,1,2,1,1] => 1
0100011 => 1011100 => [1,2,1,1,3] => [2,1,1,3,1] => 1
0100100 => 1011011 => [1,2,1,2,1,1] => [2,1,2,1,1,1] => 1
0100101 => 1011010 => [1,2,1,2,2] => [2,1,2,2,1] => 1
0100110 => 1011001 => [1,2,1,3,1] => [2,1,3,1,1] => 1
0100111 => 1011000 => [1,2,1,4] => [2,1,4,1] => 1
0101000 => 1010111 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => 1
0101001 => 1010110 => [1,2,2,1,2] => [2,2,1,2,1] => 1
0101010 => 1010101 => [1,2,2,2,1] => [2,2,2,1,1] => 1
0101011 => 1010100 => [1,2,2,3] => [2,2,3,1] => 1
0101100 => 1010011 => [1,2,3,1,1] => [2,3,1,1,1] => 1
0101101 => 1010010 => [1,2,3,2] => [2,3,2,1] => 1
0110011 => 1001100 => [1,3,1,3] => [3,1,3,1] => 1
0110101 => 1001010 => [1,3,2,2] => [3,2,2,1] => 1
0110110 => 1001001 => [1,3,3,1] => [3,3,1,1] => 1
0110111 => 1001000 => [1,3,4] => [3,4,1] => 1
0111001 => 1000110 => [1,4,1,2] => [4,1,2,1] => 1
0111011 => 1000100 => [1,4,3] => [4,3,1] => 1
0111100 => 1000011 => [1,5,1,1] => [5,1,1,1] => 1
0111101 => 1000010 => [1,5,2] => [5,2,1] => 1
0111110 => 1000001 => [1,6,1] => [6,1,1] => 1
0111111 => 1000000 => [1,7] => [7,1] => 1
1000001 => 0111110 => [2,1,1,1,1,2] => [1,1,1,1,2,2] => 2
1000010 => 0111101 => [2,1,1,1,2,1] => [1,1,1,2,1,2] => 2
1000011 => 0111100 => [2,1,1,1,3] => [1,1,1,3,2] => 2
1000100 => 0111011 => [2,1,1,2,1,1] => [1,1,2,1,1,2] => 2
1000101 => 0111010 => [2,1,1,2,2] => [1,1,2,2,2] => 2
1000110 => 0111001 => [2,1,1,3,1] => [1,1,3,1,2] => 2
1001000 => 0110111 => [2,1,2,1,1,1] => [1,2,1,1,1,2] => 2
1001001 => 0110110 => [2,1,2,1,2] => [1,2,1,2,2] => 2
1001010 => 0110101 => [2,1,2,2,1] => [1,2,2,1,2] => 2
1001011 => 0110100 => [2,1,2,3] => [1,2,3,2] => 2
1001100 => 0110011 => [2,1,3,1,1] => [1,3,1,1,2] => 2
1001101 => 0110010 => [2,1,3,2] => [1,3,2,2] => 2
1001110 => 0110001 => [2,1,4,1] => [1,4,1,2] => 2
1001111 => 0110000 => [2,1,5] => [1,5,2] => 2
1010000 => 0101111 => [2,2,1,1,1,1] => [2,1,1,1,1,2] => 2
1010001 => 0101110 => [2,2,1,1,2] => [2,1,1,2,2] => 2
1010010 => 0101101 => [2,2,1,2,1] => [2,1,2,1,2] => 2
1010011 => 0101100 => [2,2,1,3] => [2,1,3,2] => 2
1010100 => 0101011 => [2,2,2,1,1] => [2,2,1,1,2] => 2
1010101 => 0101010 => [2,2,2,2] => [2,2,2,2] => 2
1010110 => 0101001 => [2,2,3,1] => [2,3,1,2] => 2
1010111 => 0101000 => [2,2,4] => [2,4,2] => 2
1011001 => 0100110 => [2,3,1,2] => [3,1,2,2] => 2
1011010 => 0100101 => [2,3,2,1] => [3,2,1,2] => 2
1011011 => 0100100 => [2,3,3] => [3,3,2] => 2
1100011 => 0011100 => [3,1,1,3] => [1,1,3,3] => 3
1100101 => 0011010 => [3,1,2,2] => [1,2,2,3] => 3
1100110 => 0011001 => [3,1,3,1] => [1,3,1,3] => 3
1100111 => 0011000 => [3,1,4] => [1,4,3] => 3
1101001 => 0010110 => [3,2,1,2] => [2,1,2,3] => 3
1101010 => 0010101 => [3,2,2,1] => [2,2,1,3] => 3
1101011 => 0010100 => [3,2,3] => [2,3,3] => 3
1101100 => 0010011 => [3,3,1,1] => [3,1,1,3] => 3
1101101 => 0010010 => [3,3,2] => [3,2,3] => 3
1110010 => 0001101 => [4,1,2,1] => [1,2,1,4] => 4
1110111 => 0001000 => [4,4] => [4,4] => 4
1111110 => 0000001 => [7,1] => [1,7] => 7
00000111 => 11111000 => [1,1,1,1,1,4] => [1,1,1,1,4,1] => 1
00001011 => 11110100 => [1,1,1,1,2,3] => [1,1,1,2,3,1] => 1
00010011 => 11101100 => [1,1,1,2,1,3] => [1,1,2,1,3,1] => 1
00011111 => 11100000 => [1,1,1,6] => [1,1,6,1] => 1
00100011 => 11011100 => [1,1,2,1,1,3] => [1,2,1,1,3,1] => 1
00100101 => 11011010 => [1,1,2,1,2,2] => [1,2,1,2,2,1] => 1
00101001 => 11010110 => [1,1,2,2,1,2] => [1,2,2,1,2,1] => 1
00101111 => 11010000 => [1,1,2,5] => [1,2,5,1] => 1
00110001 => 11001110 => [1,1,3,1,1,2] => [1,3,1,1,2,1] => 1
00110010 => 11001101 => [1,1,3,1,2,1] => [1,3,1,2,1,1] => 1
00110100 => 11001011 => [1,1,3,2,1,1] => [1,3,2,1,1,1] => 1
00110111 => 11001000 => [1,1,3,4] => [1,3,4,1] => 1
00111000 => 11000111 => [1,1,4,1,1,1] => [1,4,1,1,1,1] => 1
00111011 => 11000100 => [1,1,4,3] => [1,4,3,1] => 1
00111101 => 11000010 => [1,1,5,2] => [1,5,2,1] => 1
00111110 => 11000001 => [1,1,6,1] => [1,6,1,1] => 1
00111111 => 11000000 => [1,1,7] => [1,7,1] => 1
01001111 => 10110000 => [1,2,1,5] => [2,1,5,1] => 1
01010111 => 10101000 => [1,2,2,4] => [2,2,4,1] => 1
01100111 => 10011000 => [1,3,1,4] => [3,1,4,1] => 1
01111101 => 10000010 => [1,6,2] => [6,2,1] => 1
01111110 => 10000001 => [1,7,1] => [7,1,1] => 1
01111111 => 10000000 => [1,8] => [8,1] => 1
10011101 => 01100010 => [2,1,4,2] => [1,4,2,2] => 2
10011110 => 01100001 => [2,1,5,1] => [1,5,1,2] => 2
10011111 => 01100000 => [2,1,6] => [1,6,2] => 2
11001110 => 00110001 => [3,1,4,1] => [1,4,1,3] => 3
11111110 => 00000001 => [8,1] => [1,8] => 8
000000000 => 111111111 => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
000001010 => 111110101 => [1,1,1,1,1,2,2,1] => [1,1,1,1,2,2,1,1] => 1
000001111 => 111110000 => [1,1,1,1,1,5] => [1,1,1,1,5,1] => 1
000100010 => 111011101 => [1,1,1,2,1,1,2,1] => [1,1,2,1,1,2,1,1] => 1
000101000 => 111010111 => [1,1,1,2,2,1,1,1] => [1,1,2,2,1,1,1,1] => 1
000110110 => 111001001 => [1,1,1,3,3,1] => [1,1,3,3,1,1] => 1
000111111 => 111000000 => [1,1,1,7] => [1,1,7,1] => 1
001000111 => 110111000 => [1,1,2,1,1,4] => [1,2,1,1,4,1] => 1
001011111 => 110100000 => [1,1,2,6] => [1,2,6,1] => 1
001100011 => 110011100 => [1,1,3,1,1,3] => [1,3,1,1,3,1] => 1
001101111 => 110010000 => [1,1,3,5] => [1,3,5,1] => 1
001110001 => 110001110 => [1,1,4,1,1,2] => [1,4,1,1,2,1] => 1
001110111 => 110001000 => [1,1,4,4] => [1,4,4,1] => 1
001111000 => 110000111 => [1,1,5,1,1,1] => [1,5,1,1,1,1] => 1
001111011 => 110000100 => [1,1,5,3] => [1,5,3,1] => 1
001111101 => 110000010 => [1,1,6,2] => [1,6,2,1] => 1
001111110 => 110000001 => [1,1,7,1] => [1,7,1,1] => 1
001111111 => 110000000 => [1,1,8] => [1,8,1] => 1
010000010 => 101111101 => [1,2,1,1,1,1,2,1] => [2,1,1,1,1,2,1,1] => 1
010001000 => 101110111 => [1,2,1,1,2,1,1,1] => [2,1,1,2,1,1,1,1] => 1
010010110 => 101101001 => [1,2,1,2,3,1] => [2,1,2,3,1,1] => 1
010011111 => 101100000 => [1,2,1,6] => [2,1,6,1] => 1
010100000 => 101011111 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
010101010 => 101010101 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => 1
011000110 => 100111001 => [1,3,1,1,3,1] => [3,1,1,3,1,1] => 1
011010010 => 100101101 => [1,3,2,1,2,1] => [3,2,1,2,1,1] => 1
011011000 => 100100111 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => 1
011101110 => 100010001 => [1,4,4,1] => [4,4,1,1] => 1
011111110 => 100000001 => [1,8,1] => [8,1,1] => 1
011111111 => 100000000 => [1,9] => [9,1] => 1
100000001 => 011111110 => [2,1,1,1,1,1,1,2] => [1,1,1,1,1,1,2,2] => 2
100000100 => 011111011 => [2,1,1,1,1,2,1,1] => [1,1,1,1,2,1,1,2] => 2
100010000 => 011101111 => [2,1,1,2,1,1,1,1] => [1,1,2,1,1,1,1,2] => 2
100010101 => 011101010 => [2,1,1,2,2,2] => [1,1,2,2,2,2] => 2
100011010 => 011100101 => [2,1,1,3,2,1] => [1,1,3,2,1,2] => 2
100111110 => 011000001 => [2,1,6,1] => [1,6,1,2] => 2
101000000 => 010111111 => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,2] => 2
101000101 => 010111010 => [2,2,1,1,2,2] => [2,1,1,2,2,2] => 2
101001010 => 010110101 => [2,2,1,2,2,1] => [2,1,2,2,1,2] => 2
101010001 => 010101110 => [2,2,2,1,1,2] => [2,2,1,1,2,2] => 2
101010100 => 010101011 => [2,2,2,2,1,1] => [2,2,2,1,1,2] => 2
101100010 => 010011101 => [2,3,1,1,2,1] => [3,1,1,2,1,2] => 2
101101000 => 010010111 => [2,3,2,1,1,1] => [3,2,1,1,1,2] => 2
101101101 => 010010010 => [2,3,3,2] => [3,3,2,2] => 2
101110110 => 010001001 => [2,4,3,1] => [4,3,1,2] => 2
110000011 => 001111100 => [3,1,1,1,1,3] => [1,1,1,1,3,3] => 3
110001001 => 001110110 => [3,1,1,2,1,2] => [1,1,2,1,2,3] => 3
110001100 => 001110011 => [3,1,1,3,1,1] => [1,1,3,1,1,3] => 3
110100001 => 001011110 => [3,2,1,1,1,2] => [2,1,1,1,2,3] => 3
110100100 => 001011011 => [3,2,1,2,1,1] => [2,1,2,1,1,3] => 3
110101011 => 001010100 => [3,2,2,3] => [2,2,3,3] => 3
110110000 => 001001111 => [3,3,1,1,1,1] => [3,1,1,1,1,3] => 3
110110101 => 001001010 => [3,3,2,2] => [3,2,2,3] => 3
110111010 => 001000101 => [3,4,2,1] => [4,2,1,3] => 3
111000111 => 000111000 => [4,1,1,4] => [1,1,4,4] => 4
111010011 => 000101100 => [4,2,1,3] => [2,1,3,4] => 4
111011001 => 000100110 => [4,3,1,2] => [3,1,2,4] => 4
111011100 => 000100011 => [4,4,1,1] => [4,1,1,4] => 4
111101111 => 000010000 => [5,5] => [5,5] => 5
111111110 => 000000001 => [9,1] => [1,9] => 9
1111111110 => 0000000001 => [10,1] => [1,10] => 10
10000000100 => 01111111011 => [2,1,1,1,1,1,1,2,1,1] => [1,1,1,1,1,1,2,1,1,2] => 2
10000010000 => 01111101111 => [2,1,1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1,1,2] => 2
10001001010 => 01110110101 => [2,1,1,2,1,2,2,1] => [1,1,2,1,2,2,1,2] => 2
10111101110 => 01000010001 => [2,5,4,1] => [5,4,1,2] => 2
10001000000 => 01110111111 => [2,1,1,2,1,1,1,1,1,1] => [1,1,2,1,1,1,1,1,1,2] => 2
10001010100 => 01110101011 => [2,1,1,2,2,2,1,1] => [1,1,2,2,2,1,1,2] => 2
10100000000 => 01011111111 => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,2] => 2
10101011010 => 01010100101 => [2,2,2,3,2,1] => [2,2,3,2,1,2] => 2
=> => [1] => [1] => 1
0111111111 => 1000000000 => [1,10] => [10,1] => 1
11010101100 => 00101010011 => [3,2,2,3,1,1] => [2,2,3,1,1,3] => 3
11011010100 => 00100101011 => [3,3,2,2,1,1] => [3,2,2,1,1,3] => 3
0011111110 => 1100000001 => [1,1,8,1] => [1,8,1,1] => 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] => 1
10101010101 => 01010101010 => [2,2,2,2,2,2] => [2,2,2,2,2,2] => 2
10101000100 => 01010111011 => [2,2,2,1,1,2,1,1] => [2,2,1,1,2,1,1,2] => 2
10100010100 => 01011101011 => [2,2,1,1,2,2,1,1] => [2,1,1,2,2,1,1,2] => 2
01000101010 => 10111010101 => [1,2,1,1,2,2,2,1] => [2,1,1,2,2,2,1,1] => 1
01000001000 => 10111110111 => [1,2,1,1,1,1,2,1,1,1] => [2,1,1,1,1,2,1,1,1,1] => 1
01010001010 => 10101110101 => [1,2,2,1,1,2,2,1] => [2,2,1,1,2,2,1,1] => 1
01010100010 => 10101011101 => [1,2,2,2,1,1,2,1] => [2,2,2,1,1,2,1,1] => 1
00010000010 => 11101111101 => [1,1,1,2,1,1,1,1,2,1] => [1,1,2,1,1,1,1,2,1,1] => 1
00010001000 => 11101110111 => [1,1,1,2,1,1,2,1,1,1] => [1,1,2,1,1,2,1,1,1,1] => 1
10000000001 => 01111111110 => [2,1,1,1,1,1,1,1,1,2] => [1,1,1,1,1,1,1,1,2,2] => 2
10110101010 => 01001010101 => [2,3,2,2,2,1] => [3,2,2,2,1,2] => 2
10111011101 => 01000100010 => [2,4,4,2] => [4,4,2,2] => 2
11011101101 => 00100010010 => [3,4,3,2] => [4,3,2,3] => 3
11011011011 => 00100100100 => [3,3,3,3] => [3,3,3,3] => 3
11101111010 => 00010000101 => [4,5,2,1] => [5,2,1,4] => 4
11101110101 => 00010001010 => [4,4,2,2] => [4,2,2,4] => 4
11101101011 => 00010010100 => [4,3,2,3] => [3,2,3,4] => 4
11101010111 => 00010101000 => [4,2,2,4] => [2,2,4,4] => 4
11111011111 => 00000100000 => [6,6] => [6,6] => 6
11000000011 => 00111111100 => [3,1,1,1,1,1,1,3] => [1,1,1,1,1,1,3,3] => 3
10100101000 => 01011010111 => [2,2,1,2,2,1,1,1] => [2,1,2,2,1,1,1,2] => 2
10101010000 => 01010101111 => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1,2] => 2
11000001001 => 00111110110 => [3,1,1,1,1,2,1,2] => [1,1,1,1,2,1,2,3] => 3
11000100001 => 00111011110 => [3,1,1,2,1,1,1,2] => [1,1,2,1,1,1,2,3] => 3
11010000001 => 00101111110 => [3,2,1,1,1,1,1,2] => [2,1,1,1,1,1,2,3] => 3
01010101000 => 10101010111 => [1,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1,1] => 1
01010000000 => 10101111111 => [1,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
01000000010 => 10111111101 => [1,2,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,2,1,1] => 1
11101110000 => 00010001111 => [4,4,1,1,1,1] => [4,1,1,1,1,4] => 4
11100011100 => 00011100011 => [4,1,1,4,1,1] => [1,1,4,1,1,4] => 4
11100000111 => 00011111000 => [4,1,1,1,1,4] => [1,1,1,1,4,4] => 4