Identifier
Mp00224:
Binary words
—runsort⟶
Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Images
0 => 0 => [2] => [2]
1 => 1 => [1,1] => [1,1]
00 => 00 => [3] => [3]
01 => 01 => [2,1] => [1,2]
10 => 01 => [2,1] => [1,2]
11 => 11 => [1,1,1] => [1,1,1]
000 => 000 => [4] => [4]
001 => 001 => [3,1] => [1,3]
010 => 001 => [3,1] => [1,3]
011 => 011 => [2,1,1] => [1,2,1]
100 => 001 => [3,1] => [1,3]
101 => 011 => [2,1,1] => [1,2,1]
110 => 011 => [2,1,1] => [1,2,1]
111 => 111 => [1,1,1,1] => [1,1,1,1]
0000 => 0000 => [5] => [5]
0001 => 0001 => [4,1] => [1,4]
0010 => 0001 => [4,1] => [1,4]
0011 => 0011 => [3,1,1] => [1,3,1]
0100 => 0001 => [4,1] => [1,4]
0101 => 0101 => [2,2,1] => [1,2,2]
0110 => 0011 => [3,1,1] => [1,3,1]
0111 => 0111 => [2,1,1,1] => [1,2,1,1]
1000 => 0001 => [4,1] => [1,4]
1001 => 0011 => [3,1,1] => [1,3,1]
1010 => 0011 => [3,1,1] => [1,3,1]
1011 => 0111 => [2,1,1,1] => [1,2,1,1]
1100 => 0011 => [3,1,1] => [1,3,1]
1101 => 0111 => [2,1,1,1] => [1,2,1,1]
1110 => 0111 => [2,1,1,1] => [1,2,1,1]
1111 => 1111 => [1,1,1,1,1] => [1,1,1,1,1]
00000 => 00000 => [6] => [6]
00001 => 00001 => [5,1] => [1,5]
00010 => 00001 => [5,1] => [1,5]
00011 => 00011 => [4,1,1] => [1,4,1]
00100 => 00001 => [5,1] => [1,5]
00101 => 00101 => [3,2,1] => [1,3,2]
00110 => 00011 => [4,1,1] => [1,4,1]
00111 => 00111 => [3,1,1,1] => [1,3,1,1]
01000 => 00001 => [5,1] => [1,5]
01001 => 00101 => [3,2,1] => [1,3,2]
01010 => 00101 => [3,2,1] => [1,3,2]
01011 => 01011 => [2,2,1,1] => [1,2,2,1]
01100 => 00011 => [4,1,1] => [1,4,1]
01101 => 01011 => [2,2,1,1] => [1,2,2,1]
01110 => 00111 => [3,1,1,1] => [1,3,1,1]
01111 => 01111 => [2,1,1,1,1] => [1,2,1,1,1]
10000 => 00001 => [5,1] => [1,5]
10001 => 00011 => [4,1,1] => [1,4,1]
10010 => 00011 => [4,1,1] => [1,4,1]
10011 => 00111 => [3,1,1,1] => [1,3,1,1]
10100 => 00011 => [4,1,1] => [1,4,1]
10101 => 01011 => [2,2,1,1] => [1,2,2,1]
10110 => 00111 => [3,1,1,1] => [1,3,1,1]
10111 => 01111 => [2,1,1,1,1] => [1,2,1,1,1]
11000 => 00011 => [4,1,1] => [1,4,1]
11001 => 00111 => [3,1,1,1] => [1,3,1,1]
11010 => 00111 => [3,1,1,1] => [1,3,1,1]
11011 => 01111 => [2,1,1,1,1] => [1,2,1,1,1]
11100 => 00111 => [3,1,1,1] => [1,3,1,1]
11101 => 01111 => [2,1,1,1,1] => [1,2,1,1,1]
11110 => 01111 => [2,1,1,1,1] => [1,2,1,1,1]
11111 => 11111 => [1,1,1,1,1,1] => [1,1,1,1,1,1]
000000 => 000000 => [7] => [7]
000001 => 000001 => [6,1] => [1,6]
000010 => 000001 => [6,1] => [1,6]
000011 => 000011 => [5,1,1] => [1,5,1]
000100 => 000001 => [6,1] => [1,6]
000101 => 000101 => [4,2,1] => [1,4,2]
000110 => 000011 => [5,1,1] => [1,5,1]
000111 => 000111 => [4,1,1,1] => [1,4,1,1]
001000 => 000001 => [6,1] => [1,6]
001001 => 001001 => [3,3,1] => [1,3,3]
001010 => 000101 => [4,2,1] => [1,4,2]
001011 => 001011 => [3,2,1,1] => [1,3,2,1]
001100 => 000011 => [5,1,1] => [1,5,1]
001101 => 001101 => [3,1,2,1] => [1,3,1,2]
001110 => 000111 => [4,1,1,1] => [1,4,1,1]
001111 => 001111 => [3,1,1,1,1] => [1,3,1,1,1]
010000 => 000001 => [6,1] => [1,6]
010001 => 000101 => [4,2,1] => [1,4,2]
010010 => 000101 => [4,2,1] => [1,4,2]
010011 => 001101 => [3,1,2,1] => [1,3,1,2]
010100 => 000101 => [4,2,1] => [1,4,2]
010101 => 010101 => [2,2,2,1] => [1,2,2,2]
010110 => 001011 => [3,2,1,1] => [1,3,2,1]
010111 => 010111 => [2,2,1,1,1] => [1,2,2,1,1]
011000 => 000011 => [5,1,1] => [1,5,1]
011001 => 001011 => [3,2,1,1] => [1,3,2,1]
011010 => 001011 => [3,2,1,1] => [1,3,2,1]
011011 => 011011 => [2,1,2,1,1] => [1,2,1,2,1]
011100 => 000111 => [4,1,1,1] => [1,4,1,1]
011101 => 010111 => [2,2,1,1,1] => [1,2,2,1,1]
011110 => 001111 => [3,1,1,1,1] => [1,3,1,1,1]
011111 => 011111 => [2,1,1,1,1,1] => [1,2,1,1,1,1]
100000 => 000001 => [6,1] => [1,6]
100001 => 000011 => [5,1,1] => [1,5,1]
100010 => 000011 => [5,1,1] => [1,5,1]
100011 => 000111 => [4,1,1,1] => [1,4,1,1]
100100 => 000011 => [5,1,1] => [1,5,1]
100101 => 001011 => [3,2,1,1] => [1,3,2,1]
100110 => 000111 => [4,1,1,1] => [1,4,1,1]
>>> Load all 1887 entries. <<<
100111 => 001111 => [3,1,1,1,1] => [1,3,1,1,1]
101000 => 000011 => [5,1,1] => [1,5,1]
101001 => 001011 => [3,2,1,1] => [1,3,2,1]
101010 => 001011 => [3,2,1,1] => [1,3,2,1]
101011 => 010111 => [2,2,1,1,1] => [1,2,2,1,1]
101100 => 000111 => [4,1,1,1] => [1,4,1,1]
101101 => 010111 => [2,2,1,1,1] => [1,2,2,1,1]
101110 => 001111 => [3,1,1,1,1] => [1,3,1,1,1]
101111 => 011111 => [2,1,1,1,1,1] => [1,2,1,1,1,1]
110000 => 000011 => [5,1,1] => [1,5,1]
110001 => 000111 => [4,1,1,1] => [1,4,1,1]
110010 => 000111 => [4,1,1,1] => [1,4,1,1]
110011 => 001111 => [3,1,1,1,1] => [1,3,1,1,1]
110100 => 000111 => [4,1,1,1] => [1,4,1,1]
110101 => 010111 => [2,2,1,1,1] => [1,2,2,1,1]
110110 => 001111 => [3,1,1,1,1] => [1,3,1,1,1]
110111 => 011111 => [2,1,1,1,1,1] => [1,2,1,1,1,1]
111000 => 000111 => [4,1,1,1] => [1,4,1,1]
111001 => 001111 => [3,1,1,1,1] => [1,3,1,1,1]
111010 => 001111 => [3,1,1,1,1] => [1,3,1,1,1]
111011 => 011111 => [2,1,1,1,1,1] => [1,2,1,1,1,1]
111100 => 001111 => [3,1,1,1,1] => [1,3,1,1,1]
111101 => 011111 => [2,1,1,1,1,1] => [1,2,1,1,1,1]
111110 => 011111 => [2,1,1,1,1,1] => [1,2,1,1,1,1]
111111 => 111111 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1]
0000000 => 0000000 => [8] => [8]
0000001 => 0000001 => [7,1] => [1,7]
0000010 => 0000001 => [7,1] => [1,7]
0000011 => 0000011 => [6,1,1] => [1,6,1]
0000100 => 0000001 => [7,1] => [1,7]
0000101 => 0000101 => [5,2,1] => [1,5,2]
0000110 => 0000011 => [6,1,1] => [1,6,1]
0000111 => 0000111 => [5,1,1,1] => [1,5,1,1]
0001000 => 0000001 => [7,1] => [1,7]
0001001 => 0001001 => [4,3,1] => [1,4,3]
0001010 => 0000101 => [5,2,1] => [1,5,2]
0001011 => 0001011 => [4,2,1,1] => [1,4,2,1]
0001100 => 0000011 => [6,1,1] => [1,6,1]
0001101 => 0001101 => [4,1,2,1] => [1,4,1,2]
0001110 => 0000111 => [5,1,1,1] => [1,5,1,1]
0001111 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
0010000 => 0000001 => [7,1] => [1,7]
0010001 => 0001001 => [4,3,1] => [1,4,3]
0010010 => 0001001 => [4,3,1] => [1,4,3]
0010011 => 0010011 => [3,3,1,1] => [1,3,3,1]
0010100 => 0000101 => [5,2,1] => [1,5,2]
0010101 => 0010101 => [3,2,2,1] => [1,3,2,2]
0010110 => 0001011 => [4,2,1,1] => [1,4,2,1]
0010111 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
0011000 => 0000011 => [6,1,1] => [1,6,1]
0011001 => 0010011 => [3,3,1,1] => [1,3,3,1]
0011010 => 0001101 => [4,1,2,1] => [1,4,1,2]
0011011 => 0011011 => [3,1,2,1,1] => [1,3,1,2,1]
0011100 => 0000111 => [5,1,1,1] => [1,5,1,1]
0011101 => 0011101 => [3,1,1,2,1] => [1,3,1,1,2]
0011110 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
0011111 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
0100000 => 0000001 => [7,1] => [1,7]
0100001 => 0000101 => [5,2,1] => [1,5,2]
0100010 => 0000101 => [5,2,1] => [1,5,2]
0100011 => 0001101 => [4,1,2,1] => [1,4,1,2]
0100100 => 0000101 => [5,2,1] => [1,5,2]
0100101 => 0010101 => [3,2,2,1] => [1,3,2,2]
0100110 => 0001101 => [4,1,2,1] => [1,4,1,2]
0100111 => 0011101 => [3,1,1,2,1] => [1,3,1,1,2]
0101000 => 0000101 => [5,2,1] => [1,5,2]
0101001 => 0010101 => [3,2,2,1] => [1,3,2,2]
0101010 => 0010101 => [3,2,2,1] => [1,3,2,2]
0101011 => 0101011 => [2,2,2,1,1] => [1,2,2,2,1]
0101100 => 0001011 => [4,2,1,1] => [1,4,2,1]
0101101 => 0101011 => [2,2,2,1,1] => [1,2,2,2,1]
0101110 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
0101111 => 0101111 => [2,2,1,1,1,1] => [1,2,2,1,1,1]
0110000 => 0000011 => [6,1,1] => [1,6,1]
0110001 => 0001011 => [4,2,1,1] => [1,4,2,1]
0110010 => 0001011 => [4,2,1,1] => [1,4,2,1]
0110011 => 0011011 => [3,1,2,1,1] => [1,3,1,2,1]
0110100 => 0001011 => [4,2,1,1] => [1,4,2,1]
0110101 => 0101011 => [2,2,2,1,1] => [1,2,2,2,1]
0110110 => 0011011 => [3,1,2,1,1] => [1,3,1,2,1]
0110111 => 0110111 => [2,1,2,1,1,1] => [1,2,1,2,1,1]
0111000 => 0000111 => [5,1,1,1] => [1,5,1,1]
0111001 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
0111010 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
0111011 => 0110111 => [2,1,2,1,1,1] => [1,2,1,2,1,1]
0111100 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
0111101 => 0101111 => [2,2,1,1,1,1] => [1,2,2,1,1,1]
0111110 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
0111111 => 0111111 => [2,1,1,1,1,1,1] => [1,2,1,1,1,1,1]
1000000 => 0000001 => [7,1] => [1,7]
1000001 => 0000011 => [6,1,1] => [1,6,1]
1000010 => 0000011 => [6,1,1] => [1,6,1]
1000011 => 0000111 => [5,1,1,1] => [1,5,1,1]
1000100 => 0000011 => [6,1,1] => [1,6,1]
1000101 => 0001011 => [4,2,1,1] => [1,4,2,1]
1000110 => 0000111 => [5,1,1,1] => [1,5,1,1]
1000111 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1001000 => 0000011 => [6,1,1] => [1,6,1]
1001001 => 0010011 => [3,3,1,1] => [1,3,3,1]
1001010 => 0001011 => [4,2,1,1] => [1,4,2,1]
1001011 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
1001100 => 0000111 => [5,1,1,1] => [1,5,1,1]
1001101 => 0011011 => [3,1,2,1,1] => [1,3,1,2,1]
1001110 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1001111 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
1010000 => 0000011 => [6,1,1] => [1,6,1]
1010001 => 0001011 => [4,2,1,1] => [1,4,2,1]
1010010 => 0001011 => [4,2,1,1] => [1,4,2,1]
1010011 => 0011011 => [3,1,2,1,1] => [1,3,1,2,1]
1010100 => 0001011 => [4,2,1,1] => [1,4,2,1]
1010101 => 0101011 => [2,2,2,1,1] => [1,2,2,2,1]
1010110 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
1010111 => 0101111 => [2,2,1,1,1,1] => [1,2,2,1,1,1]
1011000 => 0000111 => [5,1,1,1] => [1,5,1,1]
1011001 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
1011010 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
1011011 => 0110111 => [2,1,2,1,1,1] => [1,2,1,2,1,1]
1011100 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1011101 => 0101111 => [2,2,1,1,1,1] => [1,2,2,1,1,1]
1011110 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
1011111 => 0111111 => [2,1,1,1,1,1,1] => [1,2,1,1,1,1,1]
1100000 => 0000011 => [6,1,1] => [1,6,1]
1100001 => 0000111 => [5,1,1,1] => [1,5,1,1]
1100010 => 0000111 => [5,1,1,1] => [1,5,1,1]
1100011 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1100100 => 0000111 => [5,1,1,1] => [1,5,1,1]
1100101 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
1100110 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1100111 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
1101000 => 0000111 => [5,1,1,1] => [1,5,1,1]
1101001 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
1101010 => 0010111 => [3,2,1,1,1] => [1,3,2,1,1]
1101011 => 0101111 => [2,2,1,1,1,1] => [1,2,2,1,1,1]
1101100 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1101101 => 0101111 => [2,2,1,1,1,1] => [1,2,2,1,1,1]
1101110 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
1101111 => 0111111 => [2,1,1,1,1,1,1] => [1,2,1,1,1,1,1]
1110000 => 0000111 => [5,1,1,1] => [1,5,1,1]
1110001 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1110010 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1110011 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
1110100 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1110101 => 0101111 => [2,2,1,1,1,1] => [1,2,2,1,1,1]
1110110 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
1110111 => 0111111 => [2,1,1,1,1,1,1] => [1,2,1,1,1,1,1]
1111000 => 0001111 => [4,1,1,1,1] => [1,4,1,1,1]
1111001 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
1111010 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
1111011 => 0111111 => [2,1,1,1,1,1,1] => [1,2,1,1,1,1,1]
1111100 => 0011111 => [3,1,1,1,1,1] => [1,3,1,1,1,1]
1111101 => 0111111 => [2,1,1,1,1,1,1] => [1,2,1,1,1,1,1]
1111110 => 0111111 => [2,1,1,1,1,1,1] => [1,2,1,1,1,1,1]
1111111 => 1111111 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1]
00000000 => 00000000 => [9] => [9]
00000001 => 00000001 => [8,1] => [1,8]
00000010 => 00000001 => [8,1] => [1,8]
00000011 => 00000011 => [7,1,1] => [1,7,1]
00000100 => 00000001 => [8,1] => [1,8]
00000101 => 00000101 => [6,2,1] => [1,6,2]
00000110 => 00000011 => [7,1,1] => [1,7,1]
00000111 => 00000111 => [6,1,1,1] => [1,6,1,1]
00001000 => 00000001 => [8,1] => [1,8]
00001001 => 00001001 => [5,3,1] => [1,5,3]
00001010 => 00000101 => [6,2,1] => [1,6,2]
00001011 => 00001011 => [5,2,1,1] => [1,5,2,1]
00001100 => 00000011 => [7,1,1] => [1,7,1]
00001101 => 00001101 => [5,1,2,1] => [1,5,1,2]
00001110 => 00000111 => [6,1,1,1] => [1,6,1,1]
00001111 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
00010000 => 00000001 => [8,1] => [1,8]
00010001 => 00010001 => [4,4,1] => [1,4,4]
00010010 => 00001001 => [5,3,1] => [1,5,3]
00010011 => 00010011 => [4,3,1,1] => [1,4,3,1]
00010100 => 00000101 => [6,2,1] => [1,6,2]
00010101 => 00010101 => [4,2,2,1] => [1,4,2,2]
00010110 => 00001011 => [5,2,1,1] => [1,5,2,1]
00010111 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
00011000 => 00000011 => [7,1,1] => [1,7,1]
00011001 => 00011001 => [4,1,3,1] => [1,4,1,3]
00011010 => 00001101 => [5,1,2,1] => [1,5,1,2]
00011011 => 00011011 => [4,1,2,1,1] => [1,4,1,2,1]
00011100 => 00000111 => [6,1,1,1] => [1,6,1,1]
00011101 => 00011101 => [4,1,1,2,1] => [1,4,1,1,2]
00011110 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
00011111 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
00100000 => 00000001 => [8,1] => [1,8]
00100001 => 00001001 => [5,3,1] => [1,5,3]
00100010 => 00001001 => [5,3,1] => [1,5,3]
00100011 => 00011001 => [4,1,3,1] => [1,4,1,3]
00100100 => 00001001 => [5,3,1] => [1,5,3]
00100101 => 00100101 => [3,3,2,1] => [1,3,3,2]
00100110 => 00010011 => [4,3,1,1] => [1,4,3,1]
00100111 => 00100111 => [3,3,1,1,1] => [1,3,3,1,1]
00101000 => 00000101 => [6,2,1] => [1,6,2]
00101001 => 00100101 => [3,3,2,1] => [1,3,3,2]
00101010 => 00010101 => [4,2,2,1] => [1,4,2,2]
00101011 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
00101100 => 00001011 => [5,2,1,1] => [1,5,2,1]
00101101 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
00101110 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
00101111 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
00110000 => 00000011 => [7,1,1] => [1,7,1]
00110001 => 00010011 => [4,3,1,1] => [1,4,3,1]
00110010 => 00010011 => [4,3,1,1] => [1,4,3,1]
00110011 => 00110011 => [3,1,3,1,1] => [1,3,1,3,1]
00110100 => 00001101 => [5,1,2,1] => [1,5,1,2]
00110101 => 00110101 => [3,1,2,2,1] => [1,3,1,2,2]
00110110 => 00011011 => [4,1,2,1,1] => [1,4,1,2,1]
00110111 => 00110111 => [3,1,2,1,1,1] => [1,3,1,2,1,1]
00111000 => 00000111 => [6,1,1,1] => [1,6,1,1]
00111001 => 00100111 => [3,3,1,1,1] => [1,3,3,1,1]
00111010 => 00011101 => [4,1,1,2,1] => [1,4,1,1,2]
00111011 => 00111011 => [3,1,1,2,1,1] => [1,3,1,1,2,1]
00111100 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
00111101 => 00111101 => [3,1,1,1,2,1] => [1,3,1,1,1,2]
00111110 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
00111111 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
01000000 => 00000001 => [8,1] => [1,8]
01000001 => 00000101 => [6,2,1] => [1,6,2]
01000010 => 00000101 => [6,2,1] => [1,6,2]
01000011 => 00001101 => [5,1,2,1] => [1,5,1,2]
01000100 => 00000101 => [6,2,1] => [1,6,2]
01000101 => 00010101 => [4,2,2,1] => [1,4,2,2]
01000110 => 00001101 => [5,1,2,1] => [1,5,1,2]
01000111 => 00011101 => [4,1,1,2,1] => [1,4,1,1,2]
01001000 => 00000101 => [6,2,1] => [1,6,2]
01001001 => 00100101 => [3,3,2,1] => [1,3,3,2]
01001010 => 00010101 => [4,2,2,1] => [1,4,2,2]
01001011 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
01001100 => 00001101 => [5,1,2,1] => [1,5,1,2]
01001101 => 00110101 => [3,1,2,2,1] => [1,3,1,2,2]
01001110 => 00011101 => [4,1,1,2,1] => [1,4,1,1,2]
01001111 => 00111101 => [3,1,1,1,2,1] => [1,3,1,1,1,2]
01010000 => 00000101 => [6,2,1] => [1,6,2]
01010001 => 00010101 => [4,2,2,1] => [1,4,2,2]
01010010 => 00010101 => [4,2,2,1] => [1,4,2,2]
01010011 => 00110101 => [3,1,2,2,1] => [1,3,1,2,2]
01010100 => 00010101 => [4,2,2,1] => [1,4,2,2]
01010101 => 01010101 => [2,2,2,2,1] => [1,2,2,2,2]
01010110 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
01010111 => 01010111 => [2,2,2,1,1,1] => [1,2,2,2,1,1]
01011000 => 00001011 => [5,2,1,1] => [1,5,2,1]
01011001 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
01011010 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
01011011 => 01011011 => [2,2,1,2,1,1] => [1,2,2,1,2,1]
01011100 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
01011101 => 01010111 => [2,2,2,1,1,1] => [1,2,2,2,1,1]
01011110 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
01011111 => 01011111 => [2,2,1,1,1,1,1] => [1,2,2,1,1,1,1]
01100000 => 00000011 => [7,1,1] => [1,7,1]
01100001 => 00001011 => [5,2,1,1] => [1,5,2,1]
01100010 => 00001011 => [5,2,1,1] => [1,5,2,1]
01100011 => 00011011 => [4,1,2,1,1] => [1,4,1,2,1]
01100100 => 00001011 => [5,2,1,1] => [1,5,2,1]
01100101 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
01100110 => 00011011 => [4,1,2,1,1] => [1,4,1,2,1]
01100111 => 00111011 => [3,1,1,2,1,1] => [1,3,1,1,2,1]
01101000 => 00001011 => [5,2,1,1] => [1,5,2,1]
01101001 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
01101010 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
01101011 => 01011011 => [2,2,1,2,1,1] => [1,2,2,1,2,1]
01101100 => 00011011 => [4,1,2,1,1] => [1,4,1,2,1]
01101101 => 01011011 => [2,2,1,2,1,1] => [1,2,2,1,2,1]
01101110 => 00110111 => [3,1,2,1,1,1] => [1,3,1,2,1,1]
01101111 => 01101111 => [2,1,2,1,1,1,1] => [1,2,1,2,1,1,1]
01110000 => 00000111 => [6,1,1,1] => [1,6,1,1]
01110001 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
01110010 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
01110011 => 00110111 => [3,1,2,1,1,1] => [1,3,1,2,1,1]
01110100 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
01110101 => 01010111 => [2,2,2,1,1,1] => [1,2,2,2,1,1]
01110110 => 00110111 => [3,1,2,1,1,1] => [1,3,1,2,1,1]
01110111 => 01110111 => [2,1,1,2,1,1,1] => [1,2,1,1,2,1,1]
01111000 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
01111001 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
01111010 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
01111011 => 01101111 => [2,1,2,1,1,1,1] => [1,2,1,2,1,1,1]
01111100 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
01111101 => 01011111 => [2,2,1,1,1,1,1] => [1,2,2,1,1,1,1]
01111110 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
01111111 => 01111111 => [2,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1]
10000000 => 00000001 => [8,1] => [1,8]
10000001 => 00000011 => [7,1,1] => [1,7,1]
10000010 => 00000011 => [7,1,1] => [1,7,1]
10000011 => 00000111 => [6,1,1,1] => [1,6,1,1]
10000100 => 00000011 => [7,1,1] => [1,7,1]
10000101 => 00001011 => [5,2,1,1] => [1,5,2,1]
10000110 => 00000111 => [6,1,1,1] => [1,6,1,1]
10000111 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
10001000 => 00000011 => [7,1,1] => [1,7,1]
10001001 => 00010011 => [4,3,1,1] => [1,4,3,1]
10001010 => 00001011 => [5,2,1,1] => [1,5,2,1]
10001011 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
10001100 => 00000111 => [6,1,1,1] => [1,6,1,1]
10001101 => 00011011 => [4,1,2,1,1] => [1,4,1,2,1]
10001110 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
10001111 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
10010000 => 00000011 => [7,1,1] => [1,7,1]
10010001 => 00010011 => [4,3,1,1] => [1,4,3,1]
10010010 => 00010011 => [4,3,1,1] => [1,4,3,1]
10010011 => 00100111 => [3,3,1,1,1] => [1,3,3,1,1]
10010100 => 00001011 => [5,2,1,1] => [1,5,2,1]
10010101 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
10010110 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
10010111 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
10011000 => 00000111 => [6,1,1,1] => [1,6,1,1]
10011001 => 00100111 => [3,3,1,1,1] => [1,3,3,1,1]
10011010 => 00011011 => [4,1,2,1,1] => [1,4,1,2,1]
10011011 => 00110111 => [3,1,2,1,1,1] => [1,3,1,2,1,1]
10011100 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
10011101 => 00111011 => [3,1,1,2,1,1] => [1,3,1,1,2,1]
10011110 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
10011111 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
10100000 => 00000011 => [7,1,1] => [1,7,1]
10100001 => 00001011 => [5,2,1,1] => [1,5,2,1]
10100010 => 00001011 => [5,2,1,1] => [1,5,2,1]
10100011 => 00011011 => [4,1,2,1,1] => [1,4,1,2,1]
10100100 => 00001011 => [5,2,1,1] => [1,5,2,1]
10100101 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
10100110 => 00011011 => [4,1,2,1,1] => [1,4,1,2,1]
10100111 => 00111011 => [3,1,1,2,1,1] => [1,3,1,1,2,1]
10101000 => 00001011 => [5,2,1,1] => [1,5,2,1]
10101001 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
10101010 => 00101011 => [3,2,2,1,1] => [1,3,2,2,1]
10101011 => 01010111 => [2,2,2,1,1,1] => [1,2,2,2,1,1]
10101100 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
10101101 => 01010111 => [2,2,2,1,1,1] => [1,2,2,2,1,1]
10101110 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
10101111 => 01011111 => [2,2,1,1,1,1,1] => [1,2,2,1,1,1,1]
10110000 => 00000111 => [6,1,1,1] => [1,6,1,1]
10110001 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
10110010 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
10110011 => 00110111 => [3,1,2,1,1,1] => [1,3,1,2,1,1]
10110100 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
10110101 => 01010111 => [2,2,2,1,1,1] => [1,2,2,2,1,1]
10110110 => 00110111 => [3,1,2,1,1,1] => [1,3,1,2,1,1]
10110111 => 01101111 => [2,1,2,1,1,1,1] => [1,2,1,2,1,1,1]
10111000 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
10111001 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
10111010 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
10111011 => 01101111 => [2,1,2,1,1,1,1] => [1,2,1,2,1,1,1]
10111100 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
10111101 => 01011111 => [2,2,1,1,1,1,1] => [1,2,2,1,1,1,1]
10111110 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
10111111 => 01111111 => [2,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1]
11000000 => 00000011 => [7,1,1] => [1,7,1]
11000001 => 00000111 => [6,1,1,1] => [1,6,1,1]
11000010 => 00000111 => [6,1,1,1] => [1,6,1,1]
11000011 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
11000100 => 00000111 => [6,1,1,1] => [1,6,1,1]
11000101 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
11000110 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
11000111 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11001000 => 00000111 => [6,1,1,1] => [1,6,1,1]
11001001 => 00100111 => [3,3,1,1,1] => [1,3,3,1,1]
11001010 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
11001011 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
11001100 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
11001101 => 00110111 => [3,1,2,1,1,1] => [1,3,1,2,1,1]
11001110 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11001111 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
11010000 => 00000111 => [6,1,1,1] => [1,6,1,1]
11010001 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
11010010 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
11010011 => 00110111 => [3,1,2,1,1,1] => [1,3,1,2,1,1]
11010100 => 00010111 => [4,2,1,1,1] => [1,4,2,1,1]
11010101 => 01010111 => [2,2,2,1,1,1] => [1,2,2,2,1,1]
11010110 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
11010111 => 01011111 => [2,2,1,1,1,1,1] => [1,2,2,1,1,1,1]
11011000 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
11011001 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
11011010 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
11011011 => 01101111 => [2,1,2,1,1,1,1] => [1,2,1,2,1,1,1]
11011100 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11011101 => 01011111 => [2,2,1,1,1,1,1] => [1,2,2,1,1,1,1]
11011110 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
11011111 => 01111111 => [2,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1]
11100000 => 00000111 => [6,1,1,1] => [1,6,1,1]
11100001 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
11100010 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
11100011 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11100100 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
11100101 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
11100110 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11100111 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
11101000 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
11101001 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
11101010 => 00101111 => [3,2,1,1,1,1] => [1,3,2,1,1,1]
11101011 => 01011111 => [2,2,1,1,1,1,1] => [1,2,2,1,1,1,1]
11101100 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11101101 => 01011111 => [2,2,1,1,1,1,1] => [1,2,2,1,1,1,1]
11101110 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
11101111 => 01111111 => [2,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1]
11110000 => 00001111 => [5,1,1,1,1] => [1,5,1,1,1]
11110001 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11110010 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11110011 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
11110100 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11110101 => 01011111 => [2,2,1,1,1,1,1] => [1,2,2,1,1,1,1]
11110110 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
11110111 => 01111111 => [2,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1]
11111000 => 00011111 => [4,1,1,1,1,1] => [1,4,1,1,1,1]
11111001 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
11111010 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
11111011 => 01111111 => [2,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1]
11111100 => 00111111 => [3,1,1,1,1,1,1] => [1,3,1,1,1,1,1]
11111101 => 01111111 => [2,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1]
11111110 => 01111111 => [2,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1]
11111111 => 11111111 => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1]
000000000 => 000000000 => [10] => [10]
000000001 => 000000001 => [9,1] => [1,9]
000000010 => 000000001 => [9,1] => [1,9]
000000011 => 000000011 => [8,1,1] => [1,8,1]
000000100 => 000000001 => [9,1] => [1,9]
000000101 => 000000101 => [7,2,1] => [1,7,2]
000000110 => 000000011 => [8,1,1] => [1,8,1]
000000111 => 000000111 => [7,1,1,1] => [1,7,1,1]
000001000 => 000000001 => [9,1] => [1,9]
000001001 => 000001001 => [6,3,1] => [1,6,3]
000001010 => 000000101 => [7,2,1] => [1,7,2]
000001011 => 000001011 => [6,2,1,1] => [1,6,2,1]
000001100 => 000000011 => [8,1,1] => [1,8,1]
000001101 => 000001101 => [6,1,2,1] => [1,6,1,2]
000001110 => 000000111 => [7,1,1,1] => [1,7,1,1]
000001111 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
000010000 => 000000001 => [9,1] => [1,9]
000010001 => 000010001 => [5,4,1] => [1,5,4]
000010010 => 000001001 => [6,3,1] => [1,6,3]
000010011 => 000010011 => [5,3,1,1] => [1,5,3,1]
000010100 => 000000101 => [7,2,1] => [1,7,2]
000010101 => 000010101 => [5,2,2,1] => [1,5,2,2]
000010110 => 000001011 => [6,2,1,1] => [1,6,2,1]
000010111 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
000011000 => 000000011 => [8,1,1] => [1,8,1]
000011001 => 000011001 => [5,1,3,1] => [1,5,1,3]
000011010 => 000001101 => [6,1,2,1] => [1,6,1,2]
000011011 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
000011100 => 000000111 => [7,1,1,1] => [1,7,1,1]
000011101 => 000011101 => [5,1,1,2,1] => [1,5,1,1,2]
000011110 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
000011111 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
000100000 => 000000001 => [9,1] => [1,9]
000100001 => 000010001 => [5,4,1] => [1,5,4]
000100010 => 000010001 => [5,4,1] => [1,5,4]
000100011 => 000100011 => [4,4,1,1] => [1,4,4,1]
000100100 => 000001001 => [6,3,1] => [1,6,3]
000100101 => 000100101 => [4,3,2,1] => [1,4,3,2]
000100110 => 000010011 => [5,3,1,1] => [1,5,3,1]
000100111 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
000101000 => 000000101 => [7,2,1] => [1,7,2]
000101001 => 000100101 => [4,3,2,1] => [1,4,3,2]
000101010 => 000010101 => [5,2,2,1] => [1,5,2,2]
000101011 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
000101100 => 000001011 => [6,2,1,1] => [1,6,2,1]
000101101 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
000101110 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
000101111 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
000110000 => 000000011 => [8,1,1] => [1,8,1]
000110001 => 000100011 => [4,4,1,1] => [1,4,4,1]
000110010 => 000011001 => [5,1,3,1] => [1,5,1,3]
000110011 => 000110011 => [4,1,3,1,1] => [1,4,1,3,1]
000110100 => 000001101 => [6,1,2,1] => [1,6,1,2]
000110101 => 000110101 => [4,1,2,2,1] => [1,4,1,2,2]
000110110 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
000110111 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
000111000 => 000000111 => [7,1,1,1] => [1,7,1,1]
000111001 => 000111001 => [4,1,1,3,1] => [1,4,1,1,3]
000111010 => 000011101 => [5,1,1,2,1] => [1,5,1,1,2]
000111011 => 000111011 => [4,1,1,2,1,1] => [1,4,1,1,2,1]
000111100 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
000111101 => 000111101 => [4,1,1,1,2,1] => [1,4,1,1,1,2]
000111110 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
000111111 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
001000000 => 000000001 => [9,1] => [1,9]
001000001 => 000001001 => [6,3,1] => [1,6,3]
001000010 => 000001001 => [6,3,1] => [1,6,3]
001000011 => 000011001 => [5,1,3,1] => [1,5,1,3]
001000100 => 000001001 => [6,3,1] => [1,6,3]
001000101 => 000100101 => [4,3,2,1] => [1,4,3,2]
001000110 => 000011001 => [5,1,3,1] => [1,5,1,3]
001000111 => 000111001 => [4,1,1,3,1] => [1,4,1,1,3]
001001000 => 000001001 => [6,3,1] => [1,6,3]
001001001 => 001001001 => [3,3,3,1] => [1,3,3,3]
001001010 => 000100101 => [4,3,2,1] => [1,4,3,2]
001001011 => 001001011 => [3,3,2,1,1] => [1,3,3,2,1]
001001100 => 000010011 => [5,3,1,1] => [1,5,3,1]
001001101 => 001001101 => [3,3,1,2,1] => [1,3,3,1,2]
001001110 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
001001111 => 001001111 => [3,3,1,1,1,1] => [1,3,3,1,1,1]
001010000 => 000000101 => [7,2,1] => [1,7,2]
001010001 => 000100101 => [4,3,2,1] => [1,4,3,2]
001010010 => 000100101 => [4,3,2,1] => [1,4,3,2]
001010011 => 001001101 => [3,3,1,2,1] => [1,3,3,1,2]
001010100 => 000010101 => [5,2,2,1] => [1,5,2,2]
001010101 => 001010101 => [3,2,2,2,1] => [1,3,2,2,2]
001010110 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
001010111 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
001011000 => 000001011 => [6,2,1,1] => [1,6,2,1]
001011001 => 001001011 => [3,3,2,1,1] => [1,3,3,2,1]
001011010 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
001011011 => 001011011 => [3,2,1,2,1,1] => [1,3,2,1,2,1]
001011100 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
001011101 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
001011110 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
001011111 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
001100000 => 000000011 => [8,1,1] => [1,8,1]
001100001 => 000010011 => [5,3,1,1] => [1,5,3,1]
001100010 => 000010011 => [5,3,1,1] => [1,5,3,1]
001100011 => 000110011 => [4,1,3,1,1] => [1,4,1,3,1]
001100100 => 000010011 => [5,3,1,1] => [1,5,3,1]
001100101 => 001001101 => [3,3,1,2,1] => [1,3,3,1,2]
001100110 => 000110011 => [4,1,3,1,1] => [1,4,1,3,1]
001100111 => 001100111 => [3,1,3,1,1,1] => [1,3,1,3,1,1]
001101000 => 000001101 => [6,1,2,1] => [1,6,1,2]
001101001 => 001001101 => [3,3,1,2,1] => [1,3,3,1,2]
001101010 => 000110101 => [4,1,2,2,1] => [1,4,1,2,2]
001101011 => 001101011 => [3,1,2,2,1,1] => [1,3,1,2,2,1]
001101100 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
001101101 => 001101011 => [3,1,2,2,1,1] => [1,3,1,2,2,1]
001101110 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
001101111 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
001110000 => 000000111 => [7,1,1,1] => [1,7,1,1]
001110001 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
001110010 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
001110011 => 001100111 => [3,1,3,1,1,1] => [1,3,1,3,1,1]
001110100 => 000011101 => [5,1,1,2,1] => [1,5,1,1,2]
001110101 => 001110101 => [3,1,1,2,2,1] => [1,3,1,1,2,2]
001110110 => 000111011 => [4,1,1,2,1,1] => [1,4,1,1,2,1]
001110111 => 001110111 => [3,1,1,2,1,1,1] => [1,3,1,1,2,1,1]
001111000 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
001111001 => 001001111 => [3,3,1,1,1,1] => [1,3,3,1,1,1]
001111010 => 000111101 => [4,1,1,1,2,1] => [1,4,1,1,1,2]
001111011 => 001111011 => [3,1,1,1,2,1,1] => [1,3,1,1,1,2,1]
001111100 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
001111101 => 001111101 => [3,1,1,1,1,2,1] => [1,3,1,1,1,1,2]
001111110 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
001111111 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
010000000 => 000000001 => [9,1] => [1,9]
010000001 => 000000101 => [7,2,1] => [1,7,2]
010000010 => 000000101 => [7,2,1] => [1,7,2]
010000011 => 000001101 => [6,1,2,1] => [1,6,1,2]
010000100 => 000000101 => [7,2,1] => [1,7,2]
010000101 => 000010101 => [5,2,2,1] => [1,5,2,2]
010000110 => 000001101 => [6,1,2,1] => [1,6,1,2]
010000111 => 000011101 => [5,1,1,2,1] => [1,5,1,1,2]
010001000 => 000000101 => [7,2,1] => [1,7,2]
010001001 => 000100101 => [4,3,2,1] => [1,4,3,2]
010001010 => 000010101 => [5,2,2,1] => [1,5,2,2]
010001011 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
010001100 => 000001101 => [6,1,2,1] => [1,6,1,2]
010001101 => 000110101 => [4,1,2,2,1] => [1,4,1,2,2]
010001110 => 000011101 => [5,1,1,2,1] => [1,5,1,1,2]
010001111 => 000111101 => [4,1,1,1,2,1] => [1,4,1,1,1,2]
010010000 => 000000101 => [7,2,1] => [1,7,2]
010010001 => 000100101 => [4,3,2,1] => [1,4,3,2]
010010010 => 000100101 => [4,3,2,1] => [1,4,3,2]
010010011 => 001001101 => [3,3,1,2,1] => [1,3,3,1,2]
010010100 => 000010101 => [5,2,2,1] => [1,5,2,2]
010010101 => 001010101 => [3,2,2,2,1] => [1,3,2,2,2]
010010110 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
010010111 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
010011000 => 000001101 => [6,1,2,1] => [1,6,1,2]
010011001 => 001001101 => [3,3,1,2,1] => [1,3,3,1,2]
010011010 => 000110101 => [4,1,2,2,1] => [1,4,1,2,2]
010011011 => 001101011 => [3,1,2,2,1,1] => [1,3,1,2,2,1]
010011100 => 000011101 => [5,1,1,2,1] => [1,5,1,1,2]
010011101 => 001110101 => [3,1,1,2,2,1] => [1,3,1,1,2,2]
010011110 => 000111101 => [4,1,1,1,2,1] => [1,4,1,1,1,2]
010011111 => 001111101 => [3,1,1,1,1,2,1] => [1,3,1,1,1,1,2]
010100000 => 000000101 => [7,2,1] => [1,7,2]
010100001 => 000010101 => [5,2,2,1] => [1,5,2,2]
010100010 => 000010101 => [5,2,2,1] => [1,5,2,2]
010100011 => 000110101 => [4,1,2,2,1] => [1,4,1,2,2]
010100100 => 000010101 => [5,2,2,1] => [1,5,2,2]
010100101 => 001010101 => [3,2,2,2,1] => [1,3,2,2,2]
010100110 => 000110101 => [4,1,2,2,1] => [1,4,1,2,2]
010100111 => 001110101 => [3,1,1,2,2,1] => [1,3,1,1,2,2]
010101000 => 000010101 => [5,2,2,1] => [1,5,2,2]
010101001 => 001010101 => [3,2,2,2,1] => [1,3,2,2,2]
010101010 => 001010101 => [3,2,2,2,1] => [1,3,2,2,2]
010101011 => 010101011 => [2,2,2,2,1,1] => [1,2,2,2,2,1]
010101100 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
010101101 => 010101011 => [2,2,2,2,1,1] => [1,2,2,2,2,1]
010101110 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
010101111 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
010110000 => 000001011 => [6,2,1,1] => [1,6,2,1]
010110001 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
010110010 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
010110011 => 001101011 => [3,1,2,2,1,1] => [1,3,1,2,2,1]
010110100 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
010110101 => 010101011 => [2,2,2,2,1,1] => [1,2,2,2,2,1]
010110110 => 001011011 => [3,2,1,2,1,1] => [1,3,2,1,2,1]
010110111 => 010110111 => [2,2,1,2,1,1,1] => [1,2,2,1,2,1,1]
010111000 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
010111001 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
010111010 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
010111011 => 010110111 => [2,2,1,2,1,1,1] => [1,2,2,1,2,1,1]
010111100 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
010111101 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
010111110 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
010111111 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
011000000 => 000000011 => [8,1,1] => [1,8,1]
011000001 => 000001011 => [6,2,1,1] => [1,6,2,1]
011000010 => 000001011 => [6,2,1,1] => [1,6,2,1]
011000011 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
011000100 => 000001011 => [6,2,1,1] => [1,6,2,1]
011000101 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
011000110 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
011000111 => 000111011 => [4,1,1,2,1,1] => [1,4,1,1,2,1]
011001000 => 000001011 => [6,2,1,1] => [1,6,2,1]
011001001 => 001001011 => [3,3,2,1,1] => [1,3,3,2,1]
011001010 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
011001011 => 001011011 => [3,2,1,2,1,1] => [1,3,2,1,2,1]
011001100 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
011001101 => 001101011 => [3,1,2,2,1,1] => [1,3,1,2,2,1]
011001110 => 000111011 => [4,1,1,2,1,1] => [1,4,1,1,2,1]
011001111 => 001111011 => [3,1,1,1,2,1,1] => [1,3,1,1,1,2,1]
011010000 => 000001011 => [6,2,1,1] => [1,6,2,1]
011010001 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
011010010 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
011010011 => 001101011 => [3,1,2,2,1,1] => [1,3,1,2,2,1]
011010100 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
011010101 => 010101011 => [2,2,2,2,1,1] => [1,2,2,2,2,1]
011010110 => 001011011 => [3,2,1,2,1,1] => [1,3,2,1,2,1]
011010111 => 010110111 => [2,2,1,2,1,1,1] => [1,2,2,1,2,1,1]
011011000 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
011011001 => 001011011 => [3,2,1,2,1,1] => [1,3,2,1,2,1]
011011010 => 001011011 => [3,2,1,2,1,1] => [1,3,2,1,2,1]
011011011 => 011011011 => [2,1,2,1,2,1,1] => [1,2,1,2,1,2,1]
011011100 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
011011101 => 010110111 => [2,2,1,2,1,1,1] => [1,2,2,1,2,1,1]
011011110 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
011011111 => 011011111 => [2,1,2,1,1,1,1,1] => [1,2,1,2,1,1,1,1]
011100000 => 000000111 => [7,1,1,1] => [1,7,1,1]
011100001 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
011100010 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
011100011 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
011100100 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
011100101 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
011100110 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
011100111 => 001110111 => [3,1,1,2,1,1,1] => [1,3,1,1,2,1,1]
011101000 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
011101001 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
011101010 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
011101011 => 010110111 => [2,2,1,2,1,1,1] => [1,2,2,1,2,1,1]
011101100 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
011101101 => 010110111 => [2,2,1,2,1,1,1] => [1,2,2,1,2,1,1]
011101110 => 001110111 => [3,1,1,2,1,1,1] => [1,3,1,1,2,1,1]
011101111 => 011101111 => [2,1,1,2,1,1,1,1] => [1,2,1,1,2,1,1,1]
011110000 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
011110001 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
011110010 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
011110011 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
011110100 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
011110101 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
011110110 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
011110111 => 011101111 => [2,1,1,2,1,1,1,1] => [1,2,1,1,2,1,1,1]
011111000 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
011111001 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
011111010 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
011111011 => 011011111 => [2,1,2,1,1,1,1,1] => [1,2,1,2,1,1,1,1]
011111100 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
011111101 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
011111110 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
011111111 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1]
100000000 => 000000001 => [9,1] => [1,9]
100000001 => 000000011 => [8,1,1] => [1,8,1]
100000010 => 000000011 => [8,1,1] => [1,8,1]
100000011 => 000000111 => [7,1,1,1] => [1,7,1,1]
100000100 => 000000011 => [8,1,1] => [1,8,1]
100000101 => 000001011 => [6,2,1,1] => [1,6,2,1]
100000110 => 000000111 => [7,1,1,1] => [1,7,1,1]
100000111 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
100001000 => 000000011 => [8,1,1] => [1,8,1]
100001001 => 000010011 => [5,3,1,1] => [1,5,3,1]
100001010 => 000001011 => [6,2,1,1] => [1,6,2,1]
100001011 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
100001100 => 000000111 => [7,1,1,1] => [1,7,1,1]
100001101 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
100001110 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
100001111 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
100010000 => 000000011 => [8,1,1] => [1,8,1]
100010001 => 000100011 => [4,4,1,1] => [1,4,4,1]
100010010 => 000010011 => [5,3,1,1] => [1,5,3,1]
100010011 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
100010100 => 000001011 => [6,2,1,1] => [1,6,2,1]
100010101 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
100010110 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
100010111 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
100011000 => 000000111 => [7,1,1,1] => [1,7,1,1]
100011001 => 000110011 => [4,1,3,1,1] => [1,4,1,3,1]
100011010 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
100011011 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
100011100 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
100011101 => 000111011 => [4,1,1,2,1,1] => [1,4,1,1,2,1]
100011110 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
100011111 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
100100000 => 000000011 => [8,1,1] => [1,8,1]
100100001 => 000010011 => [5,3,1,1] => [1,5,3,1]
100100010 => 000010011 => [5,3,1,1] => [1,5,3,1]
100100011 => 000110011 => [4,1,3,1,1] => [1,4,1,3,1]
100100100 => 000010011 => [5,3,1,1] => [1,5,3,1]
100100101 => 001001011 => [3,3,2,1,1] => [1,3,3,2,1]
100100110 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
100100111 => 001001111 => [3,3,1,1,1,1] => [1,3,3,1,1,1]
100101000 => 000001011 => [6,2,1,1] => [1,6,2,1]
100101001 => 001001011 => [3,3,2,1,1] => [1,3,3,2,1]
100101010 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
100101011 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
100101100 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
100101101 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
100101110 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
100101111 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
100110000 => 000000111 => [7,1,1,1] => [1,7,1,1]
100110001 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
100110010 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
100110011 => 001100111 => [3,1,3,1,1,1] => [1,3,1,3,1,1]
100110100 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
100110101 => 001101011 => [3,1,2,2,1,1] => [1,3,1,2,2,1]
100110110 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
100110111 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
100111000 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
100111001 => 001001111 => [3,3,1,1,1,1] => [1,3,3,1,1,1]
100111010 => 000111011 => [4,1,1,2,1,1] => [1,4,1,1,2,1]
100111011 => 001110111 => [3,1,1,2,1,1,1] => [1,3,1,1,2,1,1]
100111100 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
100111101 => 001111011 => [3,1,1,1,2,1,1] => [1,3,1,1,1,2,1]
100111110 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
100111111 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
101000000 => 000000011 => [8,1,1] => [1,8,1]
101000001 => 000001011 => [6,2,1,1] => [1,6,2,1]
101000010 => 000001011 => [6,2,1,1] => [1,6,2,1]
101000011 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
101000100 => 000001011 => [6,2,1,1] => [1,6,2,1]
101000101 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
101000110 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
101000111 => 000111011 => [4,1,1,2,1,1] => [1,4,1,1,2,1]
101001000 => 000001011 => [6,2,1,1] => [1,6,2,1]
101001001 => 001001011 => [3,3,2,1,1] => [1,3,3,2,1]
101001010 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
101001011 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
101001100 => 000011011 => [5,1,2,1,1] => [1,5,1,2,1]
101001101 => 001101011 => [3,1,2,2,1,1] => [1,3,1,2,2,1]
101001110 => 000111011 => [4,1,1,2,1,1] => [1,4,1,1,2,1]
101001111 => 001111011 => [3,1,1,1,2,1,1] => [1,3,1,1,1,2,1]
101010000 => 000001011 => [6,2,1,1] => [1,6,2,1]
101010001 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
101010010 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
101010011 => 001101011 => [3,1,2,2,1,1] => [1,3,1,2,2,1]
101010100 => 000101011 => [4,2,2,1,1] => [1,4,2,2,1]
101010101 => 010101011 => [2,2,2,2,1,1] => [1,2,2,2,2,1]
101010110 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
101010111 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
101011000 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
101011001 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
101011010 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
101011011 => 010110111 => [2,2,1,2,1,1,1] => [1,2,2,1,2,1,1]
101011100 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
101011101 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
101011110 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
101011111 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
101100000 => 000000111 => [7,1,1,1] => [1,7,1,1]
101100001 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
101100010 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
101100011 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
101100100 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
101100101 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
101100110 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
101100111 => 001110111 => [3,1,1,2,1,1,1] => [1,3,1,1,2,1,1]
101101000 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
101101001 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
101101010 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
101101011 => 010110111 => [2,2,1,2,1,1,1] => [1,2,2,1,2,1,1]
101101100 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
101101101 => 010110111 => [2,2,1,2,1,1,1] => [1,2,2,1,2,1,1]
101101110 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
101101111 => 011011111 => [2,1,2,1,1,1,1,1] => [1,2,1,2,1,1,1,1]
101110000 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
101110001 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
101110010 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
101110011 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
101110100 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
101110101 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
101110110 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
101110111 => 011101111 => [2,1,1,2,1,1,1,1] => [1,2,1,1,2,1,1,1]
101111000 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
101111001 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
101111010 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
101111011 => 011011111 => [2,1,2,1,1,1,1,1] => [1,2,1,2,1,1,1,1]
101111100 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
101111101 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
101111110 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
101111111 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1]
110000000 => 000000011 => [8,1,1] => [1,8,1]
110000001 => 000000111 => [7,1,1,1] => [1,7,1,1]
110000010 => 000000111 => [7,1,1,1] => [1,7,1,1]
110000011 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
110000100 => 000000111 => [7,1,1,1] => [1,7,1,1]
110000101 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
110000110 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
110000111 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
110001000 => 000000111 => [7,1,1,1] => [1,7,1,1]
110001001 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
110001010 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
110001011 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
110001100 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
110001101 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
110001110 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
110001111 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
110010000 => 000000111 => [7,1,1,1] => [1,7,1,1]
110010001 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
110010010 => 000100111 => [4,3,1,1,1] => [1,4,3,1,1]
110010011 => 001001111 => [3,3,1,1,1,1] => [1,3,3,1,1,1]
110010100 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
110010101 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
110010110 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
110010111 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
110011000 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
110011001 => 001001111 => [3,3,1,1,1,1] => [1,3,3,1,1,1]
110011010 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
110011011 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
110011100 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
110011101 => 001110111 => [3,1,1,2,1,1,1] => [1,3,1,1,2,1,1]
110011110 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
110011111 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
110100000 => 000000111 => [7,1,1,1] => [1,7,1,1]
110100001 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
110100010 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
110100011 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
110100100 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
110100101 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
110100110 => 000110111 => [4,1,2,1,1,1] => [1,4,1,2,1,1]
110100111 => 001110111 => [3,1,1,2,1,1,1] => [1,3,1,1,2,1,1]
110101000 => 000010111 => [5,2,1,1,1] => [1,5,2,1,1]
110101001 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
110101010 => 001010111 => [3,2,2,1,1,1] => [1,3,2,2,1,1]
110101011 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
110101100 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
110101101 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
110101110 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
110101111 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
110110000 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
110110001 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
110110010 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
110110011 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
110110100 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
110110101 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
110110110 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
110110111 => 011011111 => [2,1,2,1,1,1,1,1] => [1,2,1,2,1,1,1,1]
110111000 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
110111001 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
110111010 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
110111011 => 011011111 => [2,1,2,1,1,1,1,1] => [1,2,1,2,1,1,1,1]
110111100 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
110111101 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
110111110 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
110111111 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1]
111000000 => 000000111 => [7,1,1,1] => [1,7,1,1]
111000001 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
111000010 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
111000011 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
111000100 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
111000101 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
111000110 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
111000111 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111001000 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
111001001 => 001001111 => [3,3,1,1,1,1] => [1,3,3,1,1,1]
111001010 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
111001011 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
111001100 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
111001101 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
111001110 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111001111 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
111010000 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
111010001 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
111010010 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
111010011 => 001101111 => [3,1,2,1,1,1,1] => [1,3,1,2,1,1,1]
111010100 => 000101111 => [4,2,1,1,1,1] => [1,4,2,1,1,1]
111010101 => 010101111 => [2,2,2,1,1,1,1] => [1,2,2,2,1,1,1]
111010110 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
111010111 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
111011000 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
111011001 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
111011010 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
111011011 => 011011111 => [2,1,2,1,1,1,1,1] => [1,2,1,2,1,1,1,1]
111011100 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111011101 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
111011110 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
111011111 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1]
111100000 => 000001111 => [6,1,1,1,1] => [1,6,1,1,1]
111100001 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
111100010 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
111100011 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111100100 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
111100101 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
111100110 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111100111 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
111101000 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
111101001 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
111101010 => 001011111 => [3,2,1,1,1,1,1] => [1,3,2,1,1,1,1]
111101011 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
111101100 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111101101 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
111101110 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
111101111 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1]
111110000 => 000011111 => [5,1,1,1,1,1] => [1,5,1,1,1,1]
111110001 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111110010 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111110011 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
111110100 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111110101 => 010111111 => [2,2,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1]
111110110 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
111110111 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1]
111111000 => 000111111 => [4,1,1,1,1,1,1] => [1,4,1,1,1,1,1]
111111001 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
111111010 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
111111011 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1]
111111100 => 001111111 => [3,1,1,1,1,1,1,1] => [1,3,1,1,1,1,1,1]
111111101 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1]
111111110 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1]
111111111 => 111111111 => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1]
1010101010 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
1010101100 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1010110010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1010110100 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1010111000 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1011001010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1011001100 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
1011010010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1011010100 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1011011000 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
1011100010 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1011100100 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1011101000 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1011110000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1100101010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1100101100 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1100110010 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
1100110100 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
1100111000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1101001010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1101001100 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
1101010010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1101010100 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1101011000 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1101100010 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1101100100 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1101101000 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1101110000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1110001010 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1110001100 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1110010010 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
1110010100 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1110011000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1110100010 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1110100100 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1110101000 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1110110000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1111000010 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1111000100 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1111001000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1111010000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1111100000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
101010101010 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
101010101100 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101010110010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101010110100 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101010111000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101011001010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101011001100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
101011010010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101011010100 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101011011000 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
101011100010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101011100100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101011101000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101011110000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
101100101010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101100101100 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
101100110010 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
101100110100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
101100111000 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
101101001010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101101001100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
101101010010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101101010100 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101101011000 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
101101100010 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
101101100100 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
101101101000 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
101101110000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
101110001010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101110001100 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
101110010010 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
101110010100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101110011000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
101110100010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101110100100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101110101000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101110110000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
101111000010 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
101111000100 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
101111001000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
101111010000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
101111100000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
110010101010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
110010101100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110010110010 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
110010110100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110010111000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
110011001010 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
110011001100 => 000011001111 => [5,1,3,1,1,1,1] => [1,5,1,3,1,1,1]
110011010010 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
110011010100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
110011011000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
110011100010 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
110011100100 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
110011101000 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
110011110000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
110100101010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
110100101100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110100110010 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
110100110100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
110100111000 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
110101001010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
110101001100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
110101010010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
110101010100 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
110101011000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110101100010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110101100100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110101101000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110101110000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
110110001010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110110001100 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
110110010010 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
110110010100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110110011000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
110110100010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110110100100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110110101000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110110110000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
110111000010 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
110111000100 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
110111001000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
110111010000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
110111100000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111000101010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
111000101100 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111000110010 => 000011001111 => [5,1,3,1,1,1,1] => [1,5,1,3,1,1,1]
111000110100 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
111000111000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111001001010 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
111001001100 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
111001010010 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
111001010100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
111001011000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111001100010 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
111001100100 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
111001101000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
111001110000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111010001010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
111010001100 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
111010010010 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
111010010100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
111010011000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
111010100010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
111010100100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
111010101000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
111010110000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111011000010 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111011000100 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111011001000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111011010000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111011100000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111100001010 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111100001100 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111100010010 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
111100010100 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111100011000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111100100010 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
111100100100 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
111100101000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111100110000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111101000010 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111101000100 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111101001000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111101010000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111101100000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111110000010 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111110000100 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111110001000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111110010000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111110100000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111111000000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
1111111111 => 1111111111 => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1]
1111111110 => 0111111111 => [2,1,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1,1]
1111111101 => 0111111111 => [2,1,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1,1]
1111000001 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1110100001 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1110010001 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
1110001001 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
1110000101 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1101100001 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1101010001 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1101001001 => 0010010111 => [3,3,2,1,1,1] => [1,3,3,2,1,1]
1101000101 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1101000011 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
1100110001 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
1100101001 => 0010010111 => [3,3,2,1,1,1] => [1,3,3,2,1,1]
1100100110 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
1100100101 => 0010010111 => [3,3,2,1,1,1] => [1,3,3,2,1,1]
1100011001 => 0001100111 => [4,1,3,1,1,1] => [1,4,1,3,1,1]
1100010101 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1100001011 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1011100001 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1011010001 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1011001001 => 0010010111 => [3,3,2,1,1,1] => [1,3,3,2,1,1]
1011000101 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1010110001 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1010101001 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
1010100110 => 0001101011 => [4,1,2,2,1,1] => [1,4,1,2,2,1]
1010100101 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
1010011010 => 0001101011 => [4,1,2,2,1,1] => [1,4,1,2,2,1]
1010011001 => 0010011011 => [3,3,1,2,1,1] => [1,3,3,1,2,1]
1010010110 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1010010101 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
1010001110 => 0000111011 => [5,1,1,2,1,1] => [1,5,1,1,2,1]
1001111000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1001110100 => 0000111011 => [5,1,1,2,1,1] => [1,5,1,1,2,1]
1001110001 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
1001101100 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
1001101010 => 0001101011 => [4,1,2,2,1,1] => [1,4,1,2,2,1]
1001101001 => 0010011011 => [3,3,1,2,1,1] => [1,3,3,1,2,1]
1001100110 => 0001100111 => [4,1,3,1,1,1] => [1,4,1,3,1,1]
1001100101 => 0010011011 => [3,3,1,2,1,1] => [1,3,3,1,2,1]
1001011010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1001011001 => 0010010111 => [3,3,2,1,1,1] => [1,3,3,2,1,1]
1001010110 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1001010101 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
1001001110 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
1000111100 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1000111010 => 0000111011 => [5,1,1,2,1,1] => [1,5,1,1,2,1]
1000110110 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
1000101110 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
1000101011 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
1000011110 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
1000000000 => 0000000001 => [10,1] => [1,10]
10000000000 => 00000000001 => [11,1] => [1,11]
10000111110 => 00000111111 => [6,1,1,1,1,1,1] => [1,6,1,1,1,1,1]
11111111110 => 01111111111 => [2,1,1,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1,1,1]
100001111100 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
=> => [1] => [1]
0111111111 => 0111111111 => [2,1,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1,1]
0111100001 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
0000000001 => 0000000001 => [10,1] => [1,10]
01111111111 => 01111111111 => [2,1,1,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1,1,1]
01111111101 => 01011111111 => [2,2,1,1,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1,1,1]
0111010001 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
01000000001 => 00000000101 => [9,2,1] => [1,9,2]
00000000001 => 00000000001 => [11,1] => [1,11]
0101010101 => 0101010101 => [2,2,2,2,2,1] => [1,2,2,2,2,2]
0101010011 => 0011010101 => [3,1,2,2,2,1] => [1,3,1,2,2,2]
0101001101 => 0011010101 => [3,1,2,2,2,1] => [1,3,1,2,2,2]
0101001011 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0101000111 => 0001110101 => [4,1,1,2,2,1] => [1,4,1,1,2,2]
0100110101 => 0011010101 => [3,1,2,2,2,1] => [1,3,1,2,2,2]
0100110011 => 0011001101 => [3,1,3,1,2,1] => [1,3,1,3,1,2]
0100101101 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0100101011 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0100100111 => 0010011101 => [3,3,1,1,2,1] => [1,3,3,1,1,2]
0100011101 => 0001110101 => [4,1,1,2,2,1] => [1,4,1,1,2,2]
0100011011 => 0001101011 => [4,1,2,2,1,1] => [1,4,1,2,2,1]
0100010111 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0100001111 => 0000111101 => [5,1,1,1,2,1] => [1,5,1,1,1,2]
0011010101 => 0011010101 => [3,1,2,2,2,1] => [1,3,1,2,2,2]
0011010011 => 0011001101 => [3,1,3,1,2,1] => [1,3,1,3,1,2]
0011001101 => 0011001101 => [3,1,3,1,2,1] => [1,3,1,3,1,2]
0011001011 => 0010011011 => [3,3,1,2,1,1] => [1,3,3,1,2,1]
0011000111 => 0001110011 => [4,1,1,3,1,1] => [1,4,1,1,3,1]
0010110101 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0010110011 => 0010011011 => [3,3,1,2,1,1] => [1,3,3,1,2,1]
0010101101 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0010101011 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0010100111 => 0010011101 => [3,3,1,1,2,1] => [1,3,3,1,1,2]
0010011101 => 0010011101 => [3,3,1,1,2,1] => [1,3,3,1,1,2]
0010011011 => 0010011011 => [3,3,1,2,1,1] => [1,3,3,1,2,1]
0010010111 => 0010010111 => [3,3,2,1,1,1] => [1,3,3,2,1,1]
0001110101 => 0001110101 => [4,1,1,2,2,1] => [1,4,1,1,2,2]
0001110011 => 0001110011 => [4,1,1,3,1,1] => [1,4,1,1,3,1]
0001101101 => 0001101011 => [4,1,2,2,1,1] => [1,4,1,2,2,1]
0001101011 => 0001101011 => [4,1,2,2,1,1] => [1,4,1,2,2,1]
0001100111 => 0001100111 => [4,1,3,1,1,1] => [1,4,1,3,1,1]
0001011101 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0001011011 => 0001011011 => [4,2,1,2,1,1] => [1,4,2,1,2,1]
0001010111 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0001001111 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
0000111101 => 0000111101 => [5,1,1,1,2,1] => [1,5,1,1,1,2]
0000111011 => 0000111011 => [5,1,1,2,1,1] => [1,5,1,1,2,1]
0000110111 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
0000101111 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
0000011111 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
010101010101 => 010101010101 => [2,2,2,2,2,2,1] => [1,2,2,2,2,2,2]
010101010011 => 001101010101 => [3,1,2,2,2,2,1] => [1,3,1,2,2,2,2]
010101001101 => 001101010101 => [3,1,2,2,2,2,1] => [1,3,1,2,2,2,2]
010101001011 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010101000111 => 000111010101 => [4,1,1,2,2,2,1] => [1,4,1,1,2,2,2]
010100110101 => 001101010101 => [3,1,2,2,2,2,1] => [1,3,1,2,2,2,2]
010100110011 => 001100110101 => [3,1,3,1,2,2,1] => [1,3,1,3,1,2,2]
010100101101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010100101011 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010100100111 => 001001110101 => [3,3,1,1,2,2,1] => [1,3,3,1,1,2,2]
010100011101 => 000111010101 => [4,1,1,2,2,2,1] => [1,4,1,1,2,2,2]
010100011011 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
010100010111 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010100001111 => 000011110101 => [5,1,1,1,2,2,1] => [1,5,1,1,1,2,2]
010011010101 => 001101010101 => [3,1,2,2,2,2,1] => [1,3,1,2,2,2,2]
010011010011 => 001100110101 => [3,1,3,1,2,2,1] => [1,3,1,3,1,2,2]
010011001101 => 001100110101 => [3,1,3,1,2,2,1] => [1,3,1,3,1,2,2]
010011001011 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
010011000111 => 000111001101 => [4,1,1,3,1,2,1] => [1,4,1,1,3,1,2]
010010110101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010010110011 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
010010101101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010010101011 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010010100111 => 001001110101 => [3,3,1,1,2,2,1] => [1,3,3,1,1,2,2]
010010011101 => 001001110101 => [3,3,1,1,2,2,1] => [1,3,3,1,1,2,2]
010010011011 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
010010010111 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
010001110101 => 000111010101 => [4,1,1,2,2,2,1] => [1,4,1,1,2,2,2]
010001110011 => 000111001101 => [4,1,1,3,1,2,1] => [1,4,1,1,3,1,2]
010001101101 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
010001101011 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
010001100111 => 000110011101 => [4,1,3,1,1,2,1] => [1,4,1,3,1,1,2]
010001011101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010001011011 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
010001010111 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010001001111 => 000100111101 => [4,3,1,1,1,2,1] => [1,4,3,1,1,1,2]
010000111101 => 000011110101 => [5,1,1,1,2,2,1] => [1,5,1,1,1,2,2]
010000111011 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
010000110111 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
010000101111 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
010000011111 => 000001111101 => [6,1,1,1,1,2,1] => [1,6,1,1,1,1,2]
001101010101 => 001101010101 => [3,1,2,2,2,2,1] => [1,3,1,2,2,2,2]
001101010011 => 001100110101 => [3,1,3,1,2,2,1] => [1,3,1,3,1,2,2]
001101001101 => 001100110101 => [3,1,3,1,2,2,1] => [1,3,1,3,1,2,2]
001101001011 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
001101000111 => 000111001101 => [4,1,1,3,1,2,1] => [1,4,1,1,3,1,2]
001100110101 => 001100110101 => [3,1,3,1,2,2,1] => [1,3,1,3,1,2,2]
001100110011 => 001100110011 => [3,1,3,1,3,1,1] => [1,3,1,3,1,3,1]
001100101101 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
001100101011 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
001100100111 => 001001100111 => [3,3,1,3,1,1,1] => [1,3,3,1,3,1,1]
001100011101 => 000111001101 => [4,1,1,3,1,2,1] => [1,4,1,1,3,1,2]
001100011011 => 000110011011 => [4,1,3,1,2,1,1] => [1,4,1,3,1,2,1]
001100010111 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
001100001111 => 000011110011 => [5,1,1,1,3,1,1] => [1,5,1,1,1,3,1]
001011010101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
001011010011 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
001011001101 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
001011001011 => 001001011011 => [3,3,2,1,2,1,1] => [1,3,3,2,1,2,1]
001011000111 => 000111001011 => [4,1,1,3,2,1,1] => [1,4,1,1,3,2,1]
001010110101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
001010110011 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
001010101101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
001010101011 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
001010100111 => 001001110101 => [3,3,1,1,2,2,1] => [1,3,3,1,1,2,2]
001010011101 => 001001110101 => [3,3,1,1,2,2,1] => [1,3,3,1,1,2,2]
001010011011 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
001010010111 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
001001110101 => 001001110101 => [3,3,1,1,2,2,1] => [1,3,3,1,1,2,2]
001001110011 => 001001100111 => [3,3,1,3,1,1,1] => [1,3,3,1,3,1,1]
001001101101 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
001001101011 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
001001100111 => 001001100111 => [3,3,1,3,1,1,1] => [1,3,3,1,3,1,1]
001001011101 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
001001011011 => 001001011011 => [3,3,2,1,2,1,1] => [1,3,3,2,1,2,1]
001001010111 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
001001001111 => 001001001111 => [3,3,3,1,1,1,1] => [1,3,3,3,1,1,1]
001000111011 => 000111001011 => [4,1,1,3,2,1,1] => [1,4,1,1,3,2,1]
001000110111 => 000110010111 => [4,1,3,2,1,1,1] => [1,4,1,3,2,1,1]
001000101111 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
000111010101 => 000111010101 => [4,1,1,2,2,2,1] => [1,4,1,1,2,2,2]
000111010011 => 000111001101 => [4,1,1,3,1,2,1] => [1,4,1,1,3,1,2]
000111001101 => 000111001101 => [4,1,1,3,1,2,1] => [1,4,1,1,3,1,2]
000111001011 => 000111001011 => [4,1,1,3,2,1,1] => [1,4,1,1,3,2,1]
000111000111 => 000111000111 => [4,1,1,4,1,1,1] => [1,4,1,1,4,1,1]
000110110101 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
000110110011 => 000110011011 => [4,1,3,1,2,1,1] => [1,4,1,3,1,2,1]
000110101101 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
000110101011 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
000110100111 => 000110011101 => [4,1,3,1,1,2,1] => [1,4,1,3,1,1,2]
000110011101 => 000110011101 => [4,1,3,1,1,2,1] => [1,4,1,3,1,1,2]
000110011011 => 000110011011 => [4,1,3,1,2,1,1] => [1,4,1,3,1,2,1]
000110010111 => 000110010111 => [4,1,3,2,1,1,1] => [1,4,1,3,2,1,1]
000110001111 => 000110001111 => [4,1,4,1,1,1,1] => [1,4,1,4,1,1,1]
000101110101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
000101110011 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
000101101101 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
000101101011 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
000101100111 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
000101011101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
000101011011 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
000101010111 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
000101001111 => 000100111101 => [4,3,1,1,1,2,1] => [1,4,3,1,1,1,2]
000100111101 => 000100111101 => [4,3,1,1,1,2,1] => [1,4,3,1,1,1,2]
000100111011 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
000100110111 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
000100101111 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
000100011111 => 000100011111 => [4,4,1,1,1,1,1] => [1,4,4,1,1,1,1]
000011110101 => 000011110101 => [5,1,1,1,2,2,1] => [1,5,1,1,1,2,2]
000011110011 => 000011110011 => [5,1,1,1,3,1,1] => [1,5,1,1,1,3,1]
000011101101 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
000011101011 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
000011100111 => 000011100111 => [5,1,1,3,1,1,1] => [1,5,1,1,3,1,1]
000011011101 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
000011011011 => 000011011011 => [5,1,2,1,2,1,1] => [1,5,1,2,1,2,1]
000011010111 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
000011001111 => 000011001111 => [5,1,3,1,1,1,1] => [1,5,1,3,1,1,1]
000010111101 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
000010111011 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
000010110111 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
000010101111 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
000010011111 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
000001111101 => 000001111101 => [6,1,1,1,1,2,1] => [1,6,1,1,1,1,2]
000001111011 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
000001110111 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
000001101111 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
000001011111 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
000000111111 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
11010101010 => 00101010111 => [3,2,2,2,1,1,1] => [1,3,2,2,2,1,1]
111111111111 => 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]
111110000001 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111001100001 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
111000011001 => 000011001111 => [5,1,3,1,1,1,1] => [1,5,1,3,1,1,1]
111000000111 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
111000001101 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
111000110001 => 000100011111 => [4,4,1,1,1,1,1] => [1,4,4,1,1,1,1]
111000100101 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
111011000001 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111010010001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
111010000101 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
100111100001 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
100110011001 => 001001100111 => [3,3,1,3,1,1,1] => [1,3,3,1,3,1,1]
100110000111 => 000011100111 => [5,1,1,3,1,1,1] => [1,5,1,1,3,1,1]
100110001101 => 000110011011 => [4,1,3,1,2,1,1] => [1,4,1,3,1,2,1]
100110110001 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
100110100101 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
100001111001 => 000011110011 => [5,1,1,1,3,1,1] => [1,5,1,1,1,3,1]
100001100111 => 000011001111 => [5,1,3,1,1,1,1] => [1,5,1,3,1,1,1]
100001101101 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
100000011111 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
100000110111 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
100000111101 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
100011011001 => 000110010111 => [4,1,3,2,1,1,1] => [1,4,1,3,2,1,1]
100011000111 => 000110001111 => [4,1,4,1,1,1,1] => [1,4,1,4,1,1,1]
100011001101 => 000110011011 => [4,1,3,1,2,1,1] => [1,4,1,3,1,2,1]
100011110001 => 000100011111 => [4,4,1,1,1,1,1] => [1,4,4,1,1,1,1]
100011100101 => 000111001011 => [4,1,1,3,2,1,1] => [1,4,1,1,3,2,1]
100010010111 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
100010011101 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
100010110101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101101100001 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
101100011001 => 000110010111 => [4,1,3,2,1,1,1] => [1,4,1,3,2,1,1]
101100000111 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
101100001101 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
101100110001 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
101100100101 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
101111000001 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
101110010001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
101110000101 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101001011001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
101001000111 => 000111001011 => [4,1,1,3,2,1,1] => [1,4,1,1,3,2,1]
101001001101 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
101001110001 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
101001100101 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
101000010111 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101000011101 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
101000110101 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
101011010001 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101011000101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101010010101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
0000000000 => 0000000000 => [11] => [11]
000001111110 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
000110011110 => 000011001111 => [5,1,3,1,1,1,1] => [1,5,1,3,1,1,1]
000111100110 => 000011110011 => [5,1,1,1,3,1,1] => [1,5,1,1,1,3,1]
000111111000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
000111001110 => 000011100111 => [5,1,1,3,1,1,1] => [1,5,1,1,3,1,1]
000111011010 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
000100111110 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
000101101110 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
000101111010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
011000011110 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
011001100110 => 000110011011 => [4,1,3,1,2,1,1] => [1,4,1,3,1,2,1]
011001111000 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
011001110010 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
011001001110 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
011001011010 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011110000110 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
011110011000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
011110010010 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
011111100000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
011111001000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
011111000010 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
011100100110 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
011100111000 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
011100110010 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
011100001110 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
011100011010 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
011101101000 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011101100010 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011101001010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010010011110 => 000100111101 => [4,3,1,1,1,2,1] => [1,4,3,1,1,1,2]
010011100110 => 000110011101 => [4,1,3,1,1,2,1] => [1,4,1,3,1,1,2]
010011111000 => 000001111101 => [6,1,1,1,1,2,1] => [1,6,1,1,1,1,2]
010011110010 => 000100111101 => [4,3,1,1,1,2,1] => [1,4,3,1,1,1,2]
010011001110 => 000110011101 => [4,1,3,1,1,2,1] => [1,4,1,3,1,1,2]
010011011010 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
010000111110 => 000001111101 => [6,1,1,1,1,2,1] => [1,6,1,1,1,1,2]
010001101110 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
010001111010 => 000011110101 => [5,1,1,1,2,2,1] => [1,5,1,1,1,2,2]
010110100110 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
010110111000 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
010110110010 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
010110001110 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
010110011010 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
010111101000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
010111100010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
010111001010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010100101110 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010100111010 => 000111010101 => [4,1,1,2,2,2,1] => [1,4,1,1,2,2,2]
010101101010 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
00101010101 => 00101010101 => [3,2,2,2,2,1] => [1,3,2,2,2,2]
00101010111 => 00101010111 => [3,2,2,2,1,1,1] => [1,3,2,2,2,1,1]
0010101110 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
00101011011 => 00101011011 => [3,2,2,1,2,1,1] => [1,3,2,2,1,2,1]
0010111100 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
00101001011 => 00100101011 => [3,3,2,2,1,1] => [1,3,3,2,2,1]
00101101011 => 00101011011 => [3,2,2,1,2,1,1] => [1,3,2,2,1,2,1]
0011110100 => 0000111101 => [5,1,1,1,2,1] => [1,5,1,1,1,2]
00100101011 => 00100101011 => [3,3,2,2,1,1] => [1,3,3,2,2,1]
00110101011 => 00110101011 => [3,1,2,2,2,1,1] => [1,3,1,2,2,2,1]
0111010100 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
01010101011 => 01010101011 => [2,2,2,2,2,1,1] => [1,2,2,2,2,2,1]
0000000010 => 0000000001 => [10,1] => [1,10]
0000111110 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
00000000000 => 00000000000 => [12] => [12]
00000000010 => 00000000001 => [11,1] => [1,11]
0000000100 => 0000000001 => [10,1] => [1,10]
0001011110 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
00001111110 => 00000111111 => [6,1,1,1,1,1,1] => [1,6,1,1,1,1,1]
10101010101 => 01010101011 => [2,2,2,2,2,1,1] => [1,2,2,2,2,2,1]
10101001001 => 00100101011 => [3,3,2,2,1,1] => [1,3,3,2,2,1]
10100100101 => 00100101011 => [3,3,2,2,1,1] => [1,3,3,2,2,1]
10100101001 => 00100101011 => [3,3,2,2,1,1] => [1,3,3,2,2,1]
10010010101 => 00100101011 => [3,3,2,2,1,1] => [1,3,3,2,2,1]
10010100101 => 00100101011 => [3,3,2,2,1,1] => [1,3,3,2,2,1]
10010101001 => 00100101011 => [3,3,2,2,1,1] => [1,3,3,2,2,1]
01001010101 => 00101010101 => [3,2,2,2,2,1] => [1,3,2,2,2,2]
01001010010 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
01001001001 => 00100100101 => [3,3,3,2,1] => [1,3,3,3,2]
01001001010 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
01000100101 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
01000101001 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
01000101010 => 00001010101 => [5,2,2,2,1] => [1,5,2,2,2]
01000001000 => 00000000101 => [9,2,1] => [1,9,2]
01010010101 => 00101010101 => [3,2,2,2,2,1] => [1,3,2,2,2,2]
01010010010 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
01010001001 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
01010001010 => 00001010101 => [5,2,2,2,1] => [1,5,2,2,2]
01010100101 => 00101010101 => [3,2,2,2,2,1] => [1,3,2,2,2,2]
01010100010 => 00001010101 => [5,2,2,2,1] => [1,5,2,2,2]
01010101001 => 00101010101 => [3,2,2,2,2,1] => [1,3,2,2,2,2]
01010101010 => 00101010101 => [3,2,2,2,2,1] => [1,3,2,2,2,2]
01010100100 => 00001010101 => [5,2,2,2,1] => [1,5,2,2,2]
01010010001 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
01010010100 => 00001010101 => [5,2,2,2,1] => [1,5,2,2,2]
01001000101 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
01001010001 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
01001010100 => 00001010101 => [5,2,2,2,1] => [1,5,2,2,2]
01000010000 => 00000000101 => [9,2,1] => [1,9,2]
00100010101 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
00100100101 => 00100100101 => [3,3,3,2,1] => [1,3,3,3,2]
00100101001 => 00100100101 => [3,3,3,2,1] => [1,3,3,3,2]
00100101010 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
00100010001 => 00010001001 => [4,4,3,1] => [1,4,4,3]
00101000101 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
00101001001 => 00100100101 => [3,3,3,2,1] => [1,3,3,3,2]
00101001010 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
00101010001 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
00101010010 => 00010010101 => [4,3,2,2,1] => [1,4,3,2,2]
00101010100 => 00001010101 => [5,2,2,2,1] => [1,5,2,2,2]
00010001001 => 00010001001 => [4,4,3,1] => [1,4,4,3]
00010010001 => 00010001001 => [4,4,3,1] => [1,4,4,3]
00001010000 => 00000000101 => [9,2,1] => [1,9,2]
00000100000 => 00000000001 => [11,1] => [1,11]
0100000000 => 0000000001 => [10,1] => [1,10]
01000000000 => 00000000001 => [11,1] => [1,11]
01000011111 => 00001111101 => [5,1,1,1,1,2,1] => [1,5,1,1,1,1,2]
01011111111 => 01011111111 => [2,2,1,1,1,1,1,1,1,1] => [1,2,2,1,1,1,1,1,1,1]
0101010110 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0101011001 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0101011010 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0101011100 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0101100101 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0101100110 => 0001101011 => [4,1,2,2,1,1] => [1,4,1,2,2,1]
0101101001 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0101101010 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0101101100 => 0001011011 => [4,2,1,2,1,1] => [1,4,2,1,2,1]
0101110001 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0101110010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0101110100 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0101111000 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
0110010101 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0110010110 => 0001011011 => [4,2,1,2,1,1] => [1,4,2,1,2,1]
0110011001 => 0010011011 => [3,3,1,2,1,1] => [1,3,3,1,2,1]
0110011010 => 0001101011 => [4,1,2,2,1,1] => [1,4,1,2,2,1]
0110011100 => 0000111011 => [5,1,1,2,1,1] => [1,5,1,1,2,1]
0110100101 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0110100110 => 0001101011 => [4,1,2,2,1,1] => [1,4,1,2,2,1]
0110101001 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0110101010 => 0010101011 => [3,2,2,2,1,1] => [1,3,2,2,2,1]
0110101100 => 0001011011 => [4,2,1,2,1,1] => [1,4,2,1,2,1]
0110110001 => 0001011011 => [4,2,1,2,1,1] => [1,4,2,1,2,1]
0110110010 => 0001011011 => [4,2,1,2,1,1] => [1,4,2,1,2,1]
0110110100 => 0001011011 => [4,2,1,2,1,1] => [1,4,2,1,2,1]
0110111000 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
0111000101 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0111000110 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
0111001001 => 0010010111 => [3,3,2,1,1,1] => [1,3,3,2,1,1]
0111001010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0111001100 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
0111010010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0111011000 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
0111100010 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
0111100100 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
0111101000 => 0000101111 => [5,2,1,1,1,1] => [1,5,2,1,1,1]
0111110000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
010101010110 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010101011001 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010101011010 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010101011100 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010101100101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010101100110 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
010101101001 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010101101100 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
010101110001 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010101110010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010101110100 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010101111000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
010110010101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010110010110 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
010110011001 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
010110011100 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
010110100101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010110101001 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010110101010 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
010110101100 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
010110110001 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
010110110100 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
010111000101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010111000110 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
010111001001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
010111001100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
010111010001 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010111010010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010111010100 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
010111011000 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
010111100001 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
010111100100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
010111110000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
011001010101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
011001010110 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011001011001 => 001001011011 => [3,3,2,1,2,1,1] => [1,3,3,2,1,2,1]
011001011100 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011001100101 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
011001101001 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
011001101010 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
011001101100 => 000011011011 => [5,1,2,1,2,1,1] => [1,5,1,2,1,2,1]
011001110001 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
011001110100 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
011010010101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
011010010110 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011010011001 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
011010011010 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
011010011100 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
011010100101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
011010100110 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
011010101001 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
011010101010 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
011010101100 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011010110001 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011010110010 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011010110100 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011010111000 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011011000101 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011011000110 => 000011011011 => [5,1,2,1,2,1,1] => [1,5,1,2,1,2,1]
011011001001 => 001001011011 => [3,3,2,1,2,1,1] => [1,3,3,2,1,2,1]
011011001010 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011011001100 => 000011011011 => [5,1,2,1,2,1,1] => [1,5,1,2,1,2,1]
011011010001 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011011010010 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011011010100 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
011011011000 => 000011011011 => [5,1,2,1,2,1,1] => [1,5,1,2,1,2,1]
011011100001 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011011100010 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011011100100 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011011101000 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011011110000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
011100010101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
011100010110 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011100011001 => 000110010111 => [4,1,3,2,1,1,1] => [1,4,1,3,2,1,1]
011100011100 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
011100100101 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
011100101001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
011100101010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
011100101100 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011100110001 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
011100110100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
011101000101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
011101000110 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
011101001001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
011101001100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
011101010001 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
011101010010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
011101010100 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
011101011000 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011101100001 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011101100100 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
011101110000 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
011110000101 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
011110001001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
011110001010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
011110001100 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
011110010001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
011110010100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
011110100001 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
011110100010 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
011110100100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
011110101000 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
011110110000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
011111000001 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
011111000100 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
011111010000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
0011100110 => 0001100111 => [4,1,3,1,1,1] => [1,4,1,3,1,1]
0011101010 => 0001110101 => [4,1,1,2,2,1] => [1,4,1,1,2,2]
0011101100 => 0000111011 => [5,1,1,2,1,1] => [1,5,1,1,2,1]
0001101110 => 0000110111 => [5,1,2,1,1,1] => [1,5,1,2,1,1]
0010110110 => 0001011011 => [4,2,1,2,1,1] => [1,4,2,1,2,1]
0011110010 => 0001001111 => [4,3,1,1,1,1] => [1,4,3,1,1,1]
0001110110 => 0000111011 => [5,1,1,2,1,1] => [1,5,1,1,2,1]
0100111010 => 0001110101 => [4,1,1,2,2,1] => [1,4,1,1,2,2]
0010111010 => 0001010111 => [4,2,2,1,1,1] => [1,4,2,2,1,1]
0011111000 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
0001111010 => 0000111101 => [5,1,1,1,2,1] => [1,5,1,1,1,2]
0100111100 => 0000111101 => [5,1,1,1,2,1] => [1,5,1,1,1,2]
0001111100 => 0000011111 => [6,1,1,1,1,1] => [1,6,1,1,1,1]
001111000110 => 000011001111 => [5,1,3,1,1,1,1] => [1,5,1,3,1,1,1]
001111001010 => 000100111101 => [4,3,1,1,1,2,1] => [1,4,3,1,1,1,2]
100111001100 => 000011001111 => [5,1,3,1,1,1,1] => [1,5,1,3,1,1,1]
001111001100 => 000011001111 => [5,1,3,1,1,1,1] => [1,5,1,3,1,1,1]
001011010110 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
001111010010 => 000100111101 => [4,3,1,1,1,2,1] => [1,4,3,1,1,1,2]
100111010100 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
001111010100 => 000011110101 => [5,1,1,1,2,2,1] => [1,5,1,1,1,2,2]
000111010110 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
001011011010 => 000101011011 => [4,2,2,1,2,1,1] => [1,4,2,2,1,2,1]
100111011000 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
001111011000 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
100011011100 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
010011011100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
001011011100 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
000111011100 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
000011011110 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
001101100110 => 000110011011 => [4,1,3,1,2,1,1] => [1,4,1,3,1,2,1]
001101101010 => 000110101011 => [4,1,2,2,2,1,1] => [1,4,1,2,2,2,1]
100101101100 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
001101101100 => 000011011011 => [5,1,2,1,2,1,1] => [1,5,1,2,1,2,1]
001011100110 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
001111100010 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
100111100100 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
001111100100 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
010011101010 => 000111010101 => [4,1,1,2,2,2,1] => [1,4,1,1,2,2,2]
001011101010 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
100111101000 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
001111101000 => 000001111101 => [6,1,1,1,1,2,1] => [1,6,1,1,1,1,2]
000111101010 => 000011110101 => [5,1,1,1,2,2,1] => [1,5,1,1,1,2,2]
100011101100 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
010011101100 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
001011101100 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
000111101100 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
000011101110 => 000001110111 => [6,1,1,2,1,1,1] => [1,6,1,1,2,1,1]
101001110100 => 000011101011 => [5,1,1,2,2,1,1] => [1,5,1,1,2,2,1]
001001110110 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
001101110010 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
100101110100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
001101110100 => 000011010111 => [5,1,2,2,1,1,1] => [1,5,1,2,2,1,1]
000101110110 => 000010110111 => [5,2,1,2,1,1,1] => [1,5,2,1,2,1,1]
001011110010 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
100111110000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
001111110000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
100011110100 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
010011110100 => 000011110101 => [5,1,1,1,2,2,1] => [1,5,1,1,1,2,2]
001011110100 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
000111110100 => 000001111101 => [6,1,1,1,1,2,1] => [1,6,1,1,1,1,2]
000011110110 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
110001111000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
101001111000 => 000001111011 => [6,1,1,1,2,1,1] => [1,6,1,1,1,2,1]
001001111010 => 000100111101 => [4,3,1,1,1,2,1] => [1,4,3,1,1,1,2]
100101111000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
001101111000 => 000001101111 => [6,1,2,1,1,1,1] => [1,6,1,2,1,1,1]
100011111000 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
001011111000 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
000011111010 => 000001111101 => [6,1,1,1,1,2,1] => [1,6,1,1,1,1,2]
010001111100 => 000001111101 => [6,1,1,1,1,2,1] => [1,6,1,1,1,1,2]
001001111100 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
000101111100 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
000011111100 => 000000111111 => [7,1,1,1,1,1,1] => [1,7,1,1,1,1,1]
00000000101 => 00000000101 => [9,2,1] => [1,9,2]
00001111101 => 00001111101 => [5,1,1,1,1,2,1] => [1,5,1,1,1,1,2]
11111111101 => 01111111111 => [2,1,1,1,1,1,1,1,1,1,1] => [1,2,1,1,1,1,1,1,1,1,1]
100101010101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
100101011001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
100101100101 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
100101101001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
100101110001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
100110010101 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
100110101001 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
100111000101 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
100111001001 => 001001001111 => [3,3,3,1,1,1,1] => [1,3,3,3,1,1,1]
100111010001 => 000100111011 => [4,3,1,1,2,1,1] => [1,4,3,1,1,2,1]
101001010101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
101001101001 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
101010011001 => 001001101011 => [3,3,1,2,2,1,1] => [1,3,3,1,2,2,1]
101010100101 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
101010101001 => 001010101011 => [3,2,2,2,2,1,1] => [1,3,2,2,2,2,1]
101010110001 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101011001001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
101011100001 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
101100010101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101100101001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
101101000101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101101001001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
101101010001 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
101110001001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
101110100001 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110001010101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
110001011001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
110001100101 => 000110010111 => [4,1,3,2,1,1,1] => [1,4,1,3,2,1,1]
110001101001 => 000110010111 => [4,1,3,2,1,1,1] => [1,4,1,3,2,1,1]
110001110001 => 000100011111 => [4,4,1,1,1,1,1] => [1,4,4,1,1,1,1]
110010010101 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
110010011001 => 001001001111 => [3,3,3,1,1,1,1] => [1,3,3,3,1,1,1]
110010100101 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
110010101001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
110010110001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
110011000101 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
110011001001 => 001001001111 => [3,3,3,1,1,1,1] => [1,3,3,3,1,1,1]
110011010001 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
110011100001 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
110100010101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
110100011001 => 000110010111 => [4,1,3,2,1,1,1] => [1,4,1,3,2,1,1]
110100100101 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
110100101001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
110100110001 => 000100110111 => [4,3,1,2,1,1,1] => [1,4,3,1,2,1,1]
110101000101 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
110101001001 => 001001010111 => [3,3,2,2,1,1,1] => [1,3,3,2,2,1,1]
110101010001 => 000101010111 => [4,2,2,2,1,1,1] => [1,4,2,2,2,1,1]
110101100001 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110110000101 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110110001001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
110110010001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
110110100001 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
110111000001 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111000010101 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
111000101001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
111001000101 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
111001001001 => 001001001111 => [3,3,3,1,1,1,1] => [1,3,3,3,1,1,1]
111001010001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
111010001001 => 000100101111 => [4,3,2,1,1,1,1] => [1,4,3,2,1,1,1]
111010100001 => 000010101111 => [5,2,2,1,1,1,1] => [1,5,2,2,1,1,1]
111100000101 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
111100001001 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
111100010001 => 000100011111 => [4,4,1,1,1,1,1] => [1,4,4,1,1,1,1]
111100100001 => 000010011111 => [5,3,1,1,1,1,1] => [1,5,3,1,1,1,1]
111101000001 => 000001011111 => [6,2,1,1,1,1,1] => [1,6,2,1,1,1,1]
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.
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.
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
rotate back to front
Description
The back to front rotation of an integer composition.
searching the database
Sorry, this map was not found in the database.