100111 => [1,3,1,1,1] => [3,1,1,1,1] => 1
101000 => [1,2,4] => [2,4,1] => 1
101001 => [1,2,3,1] => [2,3,1,1] => 1
101010 => [1,2,2,2] => [2,2,2,1] => 1
101011 => [1,2,2,1,1] => [2,2,1,1,1] => 1
101100 => [1,2,1,3] => [2,1,3,1] => 1
101101 => [1,2,1,2,1] => [2,1,2,1,1] => 1
101110 => [1,2,1,1,2] => [2,1,1,2,1] => 1
101111 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 1
110000 => [1,1,5] => [1,5,1] => 1
110001 => [1,1,4,1] => [1,4,1,1] => 1
110010 => [1,1,3,2] => [1,3,2,1] => 1
110011 => [1,1,3,1,1] => [1,3,1,1,1] => 1
110100 => [1,1,2,3] => [1,2,3,1] => 1
110101 => [1,1,2,2,1] => [1,2,2,1,1] => 1
110110 => [1,1,2,1,2] => [1,2,1,2,1] => 1
110111 => [1,1,2,1,1,1] => [1,2,1,1,1,1] => 1
111000 => [1,1,1,4] => [1,1,4,1] => 1
111001 => [1,1,1,3,1] => [1,1,3,1,1] => 1
111010 => [1,1,1,2,2] => [1,1,2,2,1] => 1
111011 => [1,1,1,2,1,1] => [1,1,2,1,1,1] => 1
111100 => [1,1,1,1,3] => [1,1,1,3,1] => 1
111101 => [1,1,1,1,2,1] => [1,1,1,2,1,1] => 1
111110 => [1,1,1,1,1,2] => [1,1,1,1,2,1] => 1
111111 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
0000001 => [7,1] => [1,7] => 7
0001000 => [4,4] => [4,4] => 4
0001101 => [4,1,2,1] => [1,2,1,4] => 4
0010010 => [3,3,2] => [3,2,3] => 3
0010011 => [3,3,1,1] => [3,1,1,3] => 3
0010100 => [3,2,3] => [2,3,3] => 3
0010101 => [3,2,2,1] => [2,2,1,3] => 3
0010110 => [3,2,1,2] => [2,1,2,3] => 3
0011000 => [3,1,4] => [1,4,3] => 3
0011001 => [3,1,3,1] => [1,3,1,3] => 3
0011010 => [3,1,2,2] => [1,2,2,3] => 3
0011100 => [3,1,1,3] => [1,1,3,3] => 3
0100100 => [2,3,3] => [3,3,2] => 2
0100101 => [2,3,2,1] => [3,2,1,2] => 2
0100110 => [2,3,1,2] => [3,1,2,2] => 2
0101000 => [2,2,4] => [2,4,2] => 2
0101001 => [2,2,3,1] => [2,3,1,2] => 2
0101010 => [2,2,2,2] => [2,2,2,2] => 2
0101011 => [2,2,2,1,1] => [2,2,1,1,2] => 2
0101100 => [2,2,1,3] => [2,1,3,2] => 2
0101101 => [2,2,1,2,1] => [2,1,2,1,2] => 2
0101110 => [2,2,1,1,2] => [2,1,1,2,2] => 2
0101111 => [2,2,1,1,1,1] => [2,1,1,1,1,2] => 2
0110000 => [2,1,5] => [1,5,2] => 2
0110001 => [2,1,4,1] => [1,4,1,2] => 2
0110010 => [2,1,3,2] => [1,3,2,2] => 2
0110011 => [2,1,3,1,1] => [1,3,1,1,2] => 2
0110100 => [2,1,2,3] => [1,2,3,2] => 2
0110101 => [2,1,2,2,1] => [1,2,2,1,2] => 2
0110110 => [2,1,2,1,2] => [1,2,1,2,2] => 2
0110111 => [2,1,2,1,1,1] => [1,2,1,1,1,2] => 2
0111001 => [2,1,1,3,1] => [1,1,3,1,2] => 2
0111010 => [2,1,1,2,2] => [1,1,2,2,2] => 2
0111011 => [2,1,1,2,1,1] => [1,1,2,1,1,2] => 2
0111100 => [2,1,1,1,3] => [1,1,1,3,2] => 2
0111101 => [2,1,1,1,2,1] => [1,1,1,2,1,2] => 2
0111110 => [2,1,1,1,1,2] => [1,1,1,1,2,2] => 2
1000000 => [1,7] => [7,1] => 1
1000001 => [1,6,1] => [6,1,1] => 1
1000010 => [1,5,2] => [5,2,1] => 1
1000011 => [1,5,1,1] => [5,1,1,1] => 1
1000100 => [1,4,3] => [4,3,1] => 1
1000110 => [1,4,1,2] => [4,1,2,1] => 1
1001000 => [1,3,4] => [3,4,1] => 1
1001001 => [1,3,3,1] => [3,3,1,1] => 1
1001010 => [1,3,2,2] => [3,2,2,1] => 1
1001100 => [1,3,1,3] => [3,1,3,1] => 1
1010010 => [1,2,3,2] => [2,3,2,1] => 1
1010011 => [1,2,3,1,1] => [2,3,1,1,1] => 1
1010100 => [1,2,2,3] => [2,2,3,1] => 1
1010101 => [1,2,2,2,1] => [2,2,2,1,1] => 1
1010110 => [1,2,2,1,2] => [2,2,1,2,1] => 1
1010111 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => 1
1011000 => [1,2,1,4] => [2,1,4,1] => 1
1011001 => [1,2,1,3,1] => [2,1,3,1,1] => 1
1011010 => [1,2,1,2,2] => [2,1,2,2,1] => 1
1011011 => [1,2,1,2,1,1] => [2,1,2,1,1,1] => 1
1011100 => [1,2,1,1,3] => [2,1,1,3,1] => 1
1011101 => [1,2,1,1,2,1] => [2,1,1,2,1,1] => 1
1011110 => [1,2,1,1,1,2] => [2,1,1,1,2,1] => 1
1100000 => [1,1,6] => [1,6,1] => 1
1100001 => [1,1,5,1] => [1,5,1,1] => 1
1100010 => [1,1,4,2] => [1,4,2,1] => 1
1100100 => [1,1,3,3] => [1,3,3,1] => 1
1100101 => [1,1,3,2,1] => [1,3,2,1,1] => 1
1100110 => [1,1,3,1,2] => [1,3,1,2,1] => 1
1100111 => [1,1,3,1,1,1] => [1,3,1,1,1,1] => 1
1101000 => [1,1,2,4] => [1,2,4,1] => 1
1101001 => [1,1,2,3,1] => [1,2,3,1,1] => 1
1101010 => [1,1,2,2,2] => [1,2,2,2,1] => 1
1101011 => [1,1,2,2,1,1] => [1,2,2,1,1,1] => 1
1101100 => [1,1,2,1,3] => [1,2,1,3,1] => 1
1101101 => [1,1,2,1,2,1] => [1,2,1,2,1,1] => 1
1101110 => [1,1,2,1,1,2] => [1,2,1,1,2,1] => 1
1101111 => [1,1,2,1,1,1,1] => [1,2,1,1,1,1,1] => 1
1110000 => [1,1,1,5] => [1,1,5,1] => 1
1110010 => [1,1,1,3,2] => [1,1,3,2,1] => 1
1110011 => [1,1,1,3,1,1] => [1,1,3,1,1,1] => 1
1110100 => [1,1,1,2,3] => [1,1,2,3,1] => 1
1110101 => [1,1,1,2,2,1] => [1,1,2,2,1,1] => 1
1110110 => [1,1,1,2,1,2] => [1,1,2,1,2,1] => 1
1110111 => [1,1,1,2,1,1,1] => [1,1,2,1,1,1,1] => 1
1111001 => [1,1,1,1,3,1] => [1,1,1,3,1,1] => 1
1111010 => [1,1,1,1,2,2] => [1,1,1,2,2,1] => 1
1111011 => [1,1,1,1,2,1,1] => [1,1,1,2,1,1,1] => 1
1111100 => [1,1,1,1,1,3] => [1,1,1,1,3,1] => 1
1111101 => [1,1,1,1,1,2,1] => [1,1,1,1,2,1,1] => 1
1111110 => [1,1,1,1,1,1,2] => [1,1,1,1,1,2,1] => 1
1111111 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
00000001 => [8,1] => [1,8] => 8
00110001 => [3,1,4,1] => [1,4,1,3] => 3
01100000 => [2,1,6] => [1,6,2] => 2
01100001 => [2,1,5,1] => [1,5,1,2] => 2
01100010 => [2,1,4,2] => [1,4,2,2] => 2
10000000 => [1,8] => [8,1] => 1
10000001 => [1,7,1] => [7,1,1] => 1
10000010 => [1,6,2] => [6,2,1] => 1
10011000 => [1,3,1,4] => [3,1,4,1] => 1
10101000 => [1,2,2,4] => [2,2,4,1] => 1
10110000 => [1,2,1,5] => [2,1,5,1] => 1
11000000 => [1,1,7] => [1,7,1] => 1
11000001 => [1,1,6,1] => [1,6,1,1] => 1
11000010 => [1,1,5,2] => [1,5,2,1] => 1
11000100 => [1,1,4,3] => [1,4,3,1] => 1
11000111 => [1,1,4,1,1,1] => [1,4,1,1,1,1] => 1
11001000 => [1,1,3,4] => [1,3,4,1] => 1
11001011 => [1,1,3,2,1,1] => [1,3,2,1,1,1] => 1
11001101 => [1,1,3,1,2,1] => [1,3,1,2,1,1] => 1
11001110 => [1,1,3,1,1,2] => [1,3,1,1,2,1] => 1
11010000 => [1,1,2,5] => [1,2,5,1] => 1
11010110 => [1,1,2,2,1,2] => [1,2,2,1,2,1] => 1
11011010 => [1,1,2,1,2,2] => [1,2,1,2,2,1] => 1
11011100 => [1,1,2,1,1,3] => [1,2,1,1,3,1] => 1
11100000 => [1,1,1,6] => [1,1,6,1] => 1
11101100 => [1,1,1,2,1,3] => [1,1,2,1,3,1] => 1
11110100 => [1,1,1,1,2,3] => [1,1,1,2,3,1] => 1
11111000 => [1,1,1,1,1,4] => [1,1,1,1,4,1] => 1
000000001 => [9,1] => [1,9] => 9
000010000 => [5,5] => [5,5] => 5
000100011 => [4,4,1,1] => [4,1,1,4] => 4
000100110 => [4,3,1,2] => [3,1,2,4] => 4
000101100 => [4,2,1,3] => [2,1,3,4] => 4
000111000 => [4,1,1,4] => [1,1,4,4] => 4
001000101 => [3,4,2,1] => [4,2,1,3] => 3
001001010 => [3,3,2,2] => [3,2,2,3] => 3
001001111 => [3,3,1,1,1,1] => [3,1,1,1,1,3] => 3
001010100 => [3,2,2,3] => [2,2,3,3] => 3
001011011 => [3,2,1,2,1,1] => [2,1,2,1,1,3] => 3
001011110 => [3,2,1,1,1,2] => [2,1,1,1,2,3] => 3
001110011 => [3,1,1,3,1,1] => [1,1,3,1,1,3] => 3
001110110 => [3,1,1,2,1,2] => [1,1,2,1,2,3] => 3
001111100 => [3,1,1,1,1,3] => [1,1,1,1,3,3] => 3
010001001 => [2,4,3,1] => [4,3,1,2] => 2
010010010 => [2,3,3,2] => [3,3,2,2] => 2
010010111 => [2,3,2,1,1,1] => [3,2,1,1,1,2] => 2
010011101 => [2,3,1,1,2,1] => [3,1,1,2,1,2] => 2
010101011 => [2,2,2,2,1,1] => [2,2,2,1,1,2] => 2
010101110 => [2,2,2,1,1,2] => [2,2,1,1,2,2] => 2
010110101 => [2,2,1,2,2,1] => [2,1,2,2,1,2] => 2
010111010 => [2,2,1,1,2,2] => [2,1,1,2,2,2] => 2
010111111 => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,2] => 2
011000001 => [2,1,6,1] => [1,6,1,2] => 2
011100101 => [2,1,1,3,2,1] => [1,1,3,2,1,2] => 2
011101010 => [2,1,1,2,2,2] => [1,1,2,2,2,2] => 2
011101111 => [2,1,1,2,1,1,1,1] => [1,1,2,1,1,1,1,2] => 2
011111011 => [2,1,1,1,1,2,1,1] => [1,1,1,1,2,1,1,2] => 2
011111110 => [2,1,1,1,1,1,1,2] => [1,1,1,1,1,1,2,2] => 2
100000000 => [1,9] => [9,1] => 1
100000001 => [1,8,1] => [8,1,1] => 1
100010001 => [1,4,4,1] => [4,4,1,1] => 1
100100111 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => 1
100101101 => [1,3,2,1,2,1] => [3,2,1,2,1,1] => 1
100111001 => [1,3,1,1,3,1] => [3,1,1,3,1,1] => 1
101010101 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => 1
101011111 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
101100000 => [1,2,1,6] => [2,1,6,1] => 1
101101001 => [1,2,1,2,3,1] => [2,1,2,3,1,1] => 1
101110111 => [1,2,1,1,2,1,1,1] => [2,1,1,2,1,1,1,1] => 1
101111101 => [1,2,1,1,1,1,2,1] => [2,1,1,1,1,2,1,1] => 1
110000000 => [1,1,8] => [1,8,1] => 1
110000001 => [1,1,7,1] => [1,7,1,1] => 1
110000010 => [1,1,6,2] => [1,6,2,1] => 1
110000100 => [1,1,5,3] => [1,5,3,1] => 1
110000111 => [1,1,5,1,1,1] => [1,5,1,1,1,1] => 1
110001000 => [1,1,4,4] => [1,4,4,1] => 1
110001110 => [1,1,4,1,1,2] => [1,4,1,1,2,1] => 1
110010000 => [1,1,3,5] => [1,3,5,1] => 1
110011100 => [1,1,3,1,1,3] => [1,3,1,1,3,1] => 1
110100000 => [1,1,2,6] => [1,2,6,1] => 1
110111000 => [1,1,2,1,1,4] => [1,2,1,1,4,1] => 1
111000000 => [1,1,1,7] => [1,1,7,1] => 1
111001001 => [1,1,1,3,3,1] => [1,1,3,3,1,1] => 1
111010111 => [1,1,1,2,2,1,1,1] => [1,1,2,2,1,1,1,1] => 1
111011101 => [1,1,1,2,1,1,2,1] => [1,1,2,1,1,2,1,1] => 1
111110000 => [1,1,1,1,1,5] => [1,1,1,1,5,1] => 1
111110101 => [1,1,1,1,1,2,2,1] => [1,1,1,1,2,2,1,1] => 1
111111111 => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
1100000001 => [1,1,8,1] => [1,8,1,1] => 1
1000000000 => [1,10] => [10,1] => 1
=> [1] => [1] => 1
0000000001 => [10,1] => [1,10] => 10
00101010011 => [3,2,2,3,1,1] => [2,2,3,1,1,3] => 3
00100101011 => [3,3,2,2,1,1] => [3,2,2,1,1,3] => 3
01111111110 => [2,1,1,1,1,1,1,1,1,2] => [1,1,1,1,1,1,1,1,2,2] => 2
10101001001 => [1,2,2,3,3,1] => [2,2,3,3,1,1] => 1
10010010101 => [1,3,3,2,2,1] => [3,3,2,2,1,1] => 1
10010101001 => [1,3,2,2,3,1] => [3,2,2,3,1,1] => 1
10000100001 => [1,5,5,1] => [5,5,1,1] => 1
01001010101 => [2,3,2,2,2,1] => [3,2,2,2,1,2] => 2
01000100010 => [2,4,4,2] => [4,4,2,2] => 2
01000010001 => [2,5,4,1] => [5,4,1,2] => 2
01010100101 => [2,2,2,3,2,1] => [2,2,3,2,1,2] => 2
01010101010 => [2,2,2,2,2,2] => [2,2,2,2,2,2] => 2
00100010010 => [3,4,3,2] => [4,3,2,3] => 3
00100001001 => [3,5,3,1] => [5,3,1,3] => 3
00100100100 => [3,3,3,3] => [3,3,3,3] => 3
00010000101 => [4,5,2,1] => [5,2,1,4] => 4
00010001010 => [4,4,2,2] => [4,2,2,4] => 4
00010010100 => [4,3,2,3] => [3,2,3,4] => 4
00010101000 => [4,2,2,4] => [2,2,4,4] => 4
00000100000 => [6,6] => [6,6] => 6
01011111111 => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,2] => 2
01111111011 => [2,1,1,1,1,1,1,2,1,1] => [1,1,1,1,1,1,2,1,1,2] => 2
10111111101 => [1,2,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,2,1,1] => 1
11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
01010111011 => [2,2,2,1,1,2,1,1] => [2,2,1,1,2,1,1,2] => 2
01011011101 => [2,2,1,2,1,1,2,1] => [2,1,2,1,1,2,1,2] => 2
01011101110 => [2,2,1,1,2,1,1,2] => [2,1,1,2,1,1,2,2] => 2
01011101011 => [2,2,1,1,2,2,1,1] => [2,1,1,2,2,1,1,2] => 2
01110111010 => [2,1,1,2,1,1,2,2] => [1,1,2,1,1,2,2,2] => 2
01110110101 => [2,1,1,2,1,2,2,1] => [1,1,2,1,2,2,1,2] => 2
01110101110 => [2,1,1,2,2,1,1,2] => [1,1,2,2,1,1,2,2] => 2
01110101011 => [2,1,1,2,2,2,1,1] => [1,1,2,2,2,1,1,2] => 2
01111101111 => [2,1,1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1,1,2] => 2
10110101101 => [1,2,1,2,2,1,2,1] => [2,1,2,2,1,2,1,1] => 1
10111010101 => [1,2,1,1,2,2,2,1] => [2,1,1,2,2,2,1,1] => 1
10111110111 => [1,2,1,1,1,1,2,1,1,1] => [2,1,1,1,1,2,1,1,1,1] => 1
10101110101 => [1,2,2,1,1,2,2,1] => [2,2,1,1,2,2,1,1] => 1
10101011101 => [1,2,2,2,1,1,2,1] => [2,2,2,1,1,2,1,1] => 1
11101111101 => [1,1,1,2,1,1,1,1,2,1] => [1,1,2,1,1,1,1,2,1,1] => 1
11101110111 => [1,1,1,2,1,1,2,1,1,1] => [1,1,2,1,1,2,1,1,1,1] => 1
10101111111 => [1,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
00101111110 => [3,2,1,1,1,1,1,2] => [2,1,1,1,1,1,2,3] => 3
00111011110 => [3,1,1,2,1,1,1,2] => [1,1,2,1,1,1,2,3] => 3
00111110110 => [3,1,1,1,1,2,1,2] => [1,1,1,1,2,1,2,3] => 3
00111111100 => [3,1,1,1,1,1,1,3] => [1,1,1,1,1,1,3,3] => 3
01010101111 => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1,2] => 2
01011010111 => [2,2,1,2,2,1,1,1] => [2,1,2,2,1,1,1,2] => 2
10101010111 => [1,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1,1] => 1
01110111111 => [2,1,1,2,1,1,1,1,1,1] => [1,1,2,1,1,1,1,1,1,2] => 2
00011111000 => [4,1,1,1,1,4] => [1,1,1,1,4,4] => 4
00011100011 => [4,1,1,4,1,1] => [1,1,4,1,1,4] => 4
00010001111 => [4,4,1,1,1,1] => [4,1,1,1,1,4] => 4
01011111010 => [2,2,1,1,1,1,2,2] => [2,1,1,1,1,2,2,2] => 2