100111 => [1,3,1,1,1] => 1
101000 => [1,2,4] => 4
101001 => [1,2,3,1] => 1
101010 => [1,2,2,2] => 2
101011 => [1,2,2,1,1] => 1
101100 => [1,2,1,3] => 3
101101 => [1,2,1,2,1] => 1
101110 => [1,2,1,1,2] => 2
101111 => [1,2,1,1,1,1] => 1
110000 => [1,1,5] => 5
110001 => [1,1,4,1] => 1
110010 => [1,1,3,2] => 2
110011 => [1,1,3,1,1] => 1
110100 => [1,1,2,3] => 3
110101 => [1,1,2,2,1] => 1
110110 => [1,1,2,1,2] => 2
110111 => [1,1,2,1,1,1] => 1
111000 => [1,1,1,4] => 4
111001 => [1,1,1,3,1] => 1
111010 => [1,1,1,2,2] => 2
111011 => [1,1,1,2,1,1] => 1
111100 => [1,1,1,1,3] => 3
111101 => [1,1,1,1,2,1] => 1
111110 => [1,1,1,1,1,2] => 2
111111 => [1,1,1,1,1,1,1] => 1
0000001 => [7,1] => 1
0000011 => [6,1,1] => 1
0000101 => [5,2,1] => 1
0000111 => [5,1,1,1] => 1
0001000 => [4,4] => 4
0001001 => [4,3,1] => 1
0001101 => [4,1,2,1] => 1
0010001 => [3,4,1] => 1
0010010 => [3,3,2] => 2
0010011 => [3,3,1,1] => 1
0010100 => [3,2,3] => 3
0010101 => [3,2,2,1] => 1
0010110 => [3,2,1,2] => 2
0011001 => [3,1,3,1] => 1
0011010 => [3,1,2,2] => 2
0011100 => [3,1,1,3] => 3
0100010 => [2,4,2] => 2
0100100 => [2,3,3] => 3
0100101 => [2,3,2,1] => 1
0100110 => [2,3,1,2] => 2
0100111 => [2,3,1,1,1] => 1
0101001 => [2,2,3,1] => 1
0101010 => [2,2,2,2] => 2
0101011 => [2,2,2,1,1] => 1
0101100 => [2,2,1,3] => 3
0101101 => [2,2,1,2,1] => 1
0101110 => [2,2,1,1,2] => 2
0101111 => [2,2,1,1,1,1] => 1
0110001 => [2,1,4,1] => 1
0110010 => [2,1,3,2] => 2
0110011 => [2,1,3,1,1] => 1
0110100 => [2,1,2,3] => 3
0110101 => [2,1,2,2,1] => 1
0110110 => [2,1,2,1,2] => 2
0110111 => [2,1,2,1,1,1] => 1
0111001 => [2,1,1,3,1] => 1
0111010 => [2,1,1,2,2] => 2
0111011 => [2,1,1,2,1,1] => 1
0111101 => [2,1,1,1,2,1] => 1
0111110 => [2,1,1,1,1,2] => 2
1000000 => [1,7] => 7
1000001 => [1,6,1] => 1
1000010 => [1,5,2] => 2
1000011 => [1,5,1,1] => 1
1000100 => [1,4,3] => 3
1000101 => [1,4,2,1] => 1
1000110 => [1,4,1,2] => 2
1001001 => [1,3,3,1] => 1
1001010 => [1,3,2,2] => 2
1001011 => [1,3,2,1,1] => 1
1001100 => [1,3,1,3] => 3
1001101 => [1,3,1,2,1] => 1
1001110 => [1,3,1,1,2] => 2
1001111 => [1,3,1,1,1,1] => 1
1010001 => [1,2,4,1] => 1
1010010 => [1,2,3,2] => 2
1010011 => [1,2,3,1,1] => 1
1010100 => [1,2,2,3] => 3
1010101 => [1,2,2,2,1] => 1
1010110 => [1,2,2,1,2] => 2
1010111 => [1,2,2,1,1,1] => 1
1011000 => [1,2,1,4] => 4
1011001 => [1,2,1,3,1] => 1
1011010 => [1,2,1,2,2] => 2
1011011 => [1,2,1,2,1,1] => 1
1011101 => [1,2,1,1,2,1] => 1
1011110 => [1,2,1,1,1,2] => 2
1011111 => [1,2,1,1,1,1,1] => 1
1100001 => [1,1,5,1] => 1
1100100 => [1,1,3,3] => 3
1100101 => [1,1,3,2,1] => 1
1100110 => [1,1,3,1,2] => 2
1100111 => [1,1,3,1,1,1] => 1
1101001 => [1,1,2,3,1] => 1
1101010 => [1,1,2,2,2] => 2
1101011 => [1,1,2,2,1,1] => 1
1101101 => [1,1,2,1,2,1] => 1
1101110 => [1,1,2,1,1,2] => 2
1101111 => [1,1,2,1,1,1,1] => 1
1110010 => [1,1,1,3,2] => 2
1110011 => [1,1,1,3,1,1] => 1
1110101 => [1,1,1,2,2,1] => 1
1110110 => [1,1,1,2,1,2] => 2
1110111 => [1,1,1,2,1,1,1] => 1
1111001 => [1,1,1,1,3,1] => 1
1111010 => [1,1,1,1,2,2] => 2
1111011 => [1,1,1,1,2,1,1] => 1
1111101 => [1,1,1,1,1,2,1] => 1
1111111 => [1,1,1,1,1,1,1,1] => 1
00000001 => [8,1] => 1
00000011 => [7,1,1] => 1
00000101 => [6,2,1] => 1
00110001 => [3,1,4,1] => 1
01010001 => [2,2,4,1] => 1
01100001 => [2,1,5,1] => 1
10000000 => [1,8] => 8
10000001 => [1,7,1] => 1
10000010 => [1,6,2] => 2
10000011 => [1,6,1,1] => 1
10000101 => [1,5,2,1] => 1
10000110 => [1,5,1,2] => 2
10001001 => [1,4,3,1] => 1
10001010 => [1,4,2,2] => 2
10001100 => [1,4,1,3] => 3
10001111 => [1,4,1,1,1,1] => 1
10010001 => [1,3,4,1] => 1
10010111 => [1,3,2,1,1,1] => 1
10011011 => [1,3,1,2,1,1] => 1
10011101 => [1,3,1,1,2,1] => 1
10100001 => [1,2,5,1] => 1
10101101 => [1,2,2,1,2,1] => 1
10110101 => [1,2,1,2,2,1] => 1
10111001 => [1,2,1,1,3,1] => 1
11000001 => [1,1,6,1] => 1
11011001 => [1,1,2,1,3,1] => 1
11101001 => [1,1,1,2,3,1] => 1
11110001 => [1,1,1,1,4,1] => 1
000000001 => [9,1] => 1
000000011 => [8,1,1] => 1
000010000 => [5,5] => 5
000100011 => [4,4,1,1] => 1
000100110 => [4,3,1,2] => 2
000101100 => [4,2,1,3] => 3
000111000 => [4,1,1,4] => 4
001001010 => [3,3,2,2] => 2
001001111 => [3,3,1,1,1,1] => 1
001010100 => [3,2,2,3] => 3
001011011 => [3,2,1,2,1,1] => 1
001011110 => [3,2,1,1,1,2] => 2
001101000 => [3,1,2,4] => 4
001110011 => [3,1,1,3,1,1] => 1
001110110 => [3,1,1,2,1,2] => 2
001111100 => [3,1,1,1,1,3] => 3
010100100 => [2,2,3,3] => 3
010101011 => [2,2,2,2,1,1] => 1
010101110 => [2,2,2,1,1,2] => 2
010111010 => [2,2,1,1,2,2] => 2
010111111 => [2,2,1,1,1,1,1,1] => 1
011000001 => [2,1,6,1] => 1
011001000 => [2,1,3,4] => 4
011010011 => [2,1,2,3,1,1] => 1
011010110 => [2,1,2,2,1,2] => 2
011011100 => [2,1,2,1,1,3] => 3
011101010 => [2,1,1,2,2,2] => 2
011101111 => [2,1,1,2,1,1,1,1] => 1
011110100 => [2,1,1,1,2,3] => 3
011111011 => [2,1,1,1,1,2,1,1] => 1
011111110 => [2,1,1,1,1,1,1,2] => 2
100000000 => [1,9] => 9
100000001 => [1,8,1] => 1
100000011 => [1,7,1,1] => 1
100000101 => [1,6,2,1] => 1
100000110 => [1,6,1,2] => 2
100001001 => [1,5,3,1] => 1
100001111 => [1,5,1,1,1,1] => 1
100010001 => [1,4,4,1] => 1
100011101 => [1,4,1,1,2,1] => 1
100100001 => [1,3,5,1] => 1
100111001 => [1,3,1,1,3,1] => 1
101000001 => [1,2,6,1] => 1
101110001 => [1,2,1,1,4,1] => 1
110000001 => [1,1,7,1] => 1
110001000 => [1,1,4,4] => 4
110010011 => [1,1,3,3,1,1] => 1
110010110 => [1,1,3,2,1,2] => 2
110011100 => [1,1,3,1,1,3] => 3
110101010 => [1,1,2,2,2,2] => 2
110101111 => [1,1,2,2,1,1,1,1] => 1
110110100 => [1,1,2,1,2,3] => 3
110111011 => [1,1,2,1,1,2,1,1] => 1
110111110 => [1,1,2,1,1,1,1,2] => 2
111100001 => [1,1,1,1,5,1] => 1
111100100 => [1,1,1,1,3,3] => 3
111101011 => [1,1,1,1,2,2,1,1] => 1
111101110 => [1,1,1,1,2,1,1,2] => 2
111111010 => [1,1,1,1,1,1,2,2] => 2
111111111 => [1,1,1,1,1,1,1,1,1,1] => 1
1100000001 => [1,1,8,1] => 1
1010000001 => [1,2,7,1] => 1
1000001001 => [1,6,3,1] => 1
1000000101 => [1,7,2,1] => 1
1000000011 => [1,8,1,1] => 1
1000000000 => [1,10] => 10
11011111110 => [1,1,2,1,1,1,1,1,1,2] => 2
11110111110 => [1,1,1,1,2,1,1,1,1,2] => 2
11111101110 => [1,1,1,1,1,1,2,1,1,2] => 2
11010101110 => [1,1,2,2,2,1,1,2] => 2
11111111010 => [1,1,1,1,1,1,1,1,2,2] => 2
=> [1] => 1
0000000001 => [10,1] => 1
11010100100 => [1,1,2,2,3,3] => 3
11001010100 => [1,1,3,2,2,3] => 3
00101010011 => [3,2,2,3,1,1] => 1
00100101011 => [3,3,2,2,1,1] => 1
01111111110 => [2,1,1,1,1,1,1,1,1,2] => 2
01010101010 => [2,2,2,2,2,2] => 2
01010001000 => [2,2,4,4] => 4
00100100100 => [3,3,3,3] => 3
00101001000 => [3,2,3,4] => 4
00010001010 => [4,4,2,2] => 2
00010010100 => [4,3,2,3] => 3
00010101000 => [4,2,2,4] => 4
00000100000 => [6,6] => 6
01011111111 => [2,2,1,1,1,1,1,1,1,1] => 1
01111111011 => [2,1,1,1,1,1,1,2,1,1] => 1
11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
01010111011 => [2,2,2,1,1,2,1,1] => 1
01011101110 => [2,2,1,1,2,1,1,2] => 2
01011101011 => [2,2,1,1,2,2,1,1] => 1
01101110110 => [2,1,2,1,1,2,1,2] => 2
01101011011 => [2,1,2,2,1,2,1,1] => 1
01110111010 => [2,1,1,2,1,1,2,2] => 2
01110101110 => [2,1,1,2,2,1,1,2] => 2
01110101011 => [2,1,1,2,2,2,1,1] => 1
01111101111 => [2,1,1,1,1,2,1,1,1,1] => 1
11011101010 => [1,1,2,1,1,2,2,2] => 2
11011111011 => [1,1,2,1,1,1,1,2,1,1] => 1
11011010110 => [1,1,2,1,2,2,1,2] => 2
11010111010 => [1,1,2,2,1,1,2,2] => 2
11010101011 => [1,1,2,2,2,2,1,1] => 1
11011101111 => [1,1,2,1,1,2,1,1,1,1] => 1
11110111011 => [1,1,1,1,2,1,1,2,1,1] => 1
11110101111 => [1,1,1,1,2,2,1,1,1,1] => 1
00101111110 => [3,2,1,1,1,1,1,2] => 2
00111011110 => [3,1,1,2,1,1,1,2] => 2
00111110110 => [3,1,1,1,1,2,1,2] => 2
00111111100 => [3,1,1,1,1,1,1,3] => 3
01101010100 => [2,1,2,2,2,3] => 3
01101001010 => [2,1,2,3,2,2] => 2
01010101111 => [2,2,2,2,1,1,1,1] => 1
11011110100 => [1,1,2,1,1,1,2,3] => 3
01010110100 => [2,2,2,1,2,3] => 3
01110111111 => [2,1,1,2,1,1,1,1,1,1] => 1
11110001000 => [1,1,1,1,4,4] => 4
11000111000 => [1,1,4,1,1,4] => 4
11000100011 => [1,1,4,4,1,1] => 1
00011111000 => [4,1,1,1,1,4] => 4
00011100011 => [4,1,1,4,1,1] => 1
00010001111 => [4,4,1,1,1,1] => 1
01011111010 => [2,2,1,1,1,1,2,2] => 2