Identifier
Mp00178:
Binary words
—to composition⟶
Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Images
0 => [2] => [2]
1 => [1,1] => [1,1]
00 => [3] => [3]
01 => [2,1] => [1,2]
10 => [1,2] => [2,1]
11 => [1,1,1] => [1,1,1]
000 => [4] => [4]
001 => [3,1] => [1,3]
010 => [2,2] => [2,2]
011 => [2,1,1] => [1,1,2]
100 => [1,3] => [3,1]
101 => [1,2,1] => [1,2,1]
110 => [1,1,2] => [2,1,1]
111 => [1,1,1,1] => [1,1,1,1]
0000 => [5] => [5]
0001 => [4,1] => [1,4]
0010 => [3,2] => [2,3]
0011 => [3,1,1] => [1,1,3]
0100 => [2,3] => [3,2]
0101 => [2,2,1] => [1,2,2]
0110 => [2,1,2] => [2,1,2]
0111 => [2,1,1,1] => [1,1,1,2]
1000 => [1,4] => [4,1]
1001 => [1,3,1] => [1,3,1]
1010 => [1,2,2] => [2,2,1]
1011 => [1,2,1,1] => [1,1,2,1]
1100 => [1,1,3] => [3,1,1]
1101 => [1,1,2,1] => [1,2,1,1]
1110 => [1,1,1,2] => [2,1,1,1]
1111 => [1,1,1,1,1] => [1,1,1,1,1]
00000 => [6] => [6]
00001 => [5,1] => [1,5]
00010 => [4,2] => [2,4]
00011 => [4,1,1] => [1,1,4]
00100 => [3,3] => [3,3]
00101 => [3,2,1] => [1,2,3]
00110 => [3,1,2] => [2,1,3]
00111 => [3,1,1,1] => [1,1,1,3]
01000 => [2,4] => [4,2]
01001 => [2,3,1] => [1,3,2]
01010 => [2,2,2] => [2,2,2]
01011 => [2,2,1,1] => [1,1,2,2]
01100 => [2,1,3] => [3,1,2]
01101 => [2,1,2,1] => [1,2,1,2]
01110 => [2,1,1,2] => [2,1,1,2]
01111 => [2,1,1,1,1] => [1,1,1,1,2]
10000 => [1,5] => [5,1]
10001 => [1,4,1] => [1,4,1]
10010 => [1,3,2] => [2,3,1]
10011 => [1,3,1,1] => [1,1,3,1]
10100 => [1,2,3] => [3,2,1]
10101 => [1,2,2,1] => [1,2,2,1]
10110 => [1,2,1,2] => [2,1,2,1]
10111 => [1,2,1,1,1] => [1,1,1,2,1]
11000 => [1,1,4] => [4,1,1]
11001 => [1,1,3,1] => [1,3,1,1]
11010 => [1,1,2,2] => [2,2,1,1]
11011 => [1,1,2,1,1] => [1,1,2,1,1]
11100 => [1,1,1,3] => [3,1,1,1]
11101 => [1,1,1,2,1] => [1,2,1,1,1]
11110 => [1,1,1,1,2] => [2,1,1,1,1]
11111 => [1,1,1,1,1,1] => [1,1,1,1,1,1]
000000 => [7] => [7]
000001 => [6,1] => [1,6]
000010 => [5,2] => [2,5]
000011 => [5,1,1] => [1,1,5]
000100 => [4,3] => [3,4]
000101 => [4,2,1] => [1,2,4]
000110 => [4,1,2] => [2,1,4]
000111 => [4,1,1,1] => [1,1,1,4]
001000 => [3,4] => [4,3]
001001 => [3,3,1] => [1,3,3]
001010 => [3,2,2] => [2,2,3]
001011 => [3,2,1,1] => [1,1,2,3]
001100 => [3,1,3] => [3,1,3]
001101 => [3,1,2,1] => [1,2,1,3]
001110 => [3,1,1,2] => [2,1,1,3]
001111 => [3,1,1,1,1] => [1,1,1,1,3]
010000 => [2,5] => [5,2]
010001 => [2,4,1] => [1,4,2]
010010 => [2,3,2] => [2,3,2]
010011 => [2,3,1,1] => [1,1,3,2]
010100 => [2,2,3] => [3,2,2]
010101 => [2,2,2,1] => [1,2,2,2]
010110 => [2,2,1,2] => [2,1,2,2]
010111 => [2,2,1,1,1] => [1,1,1,2,2]
011000 => [2,1,4] => [4,1,2]
011001 => [2,1,3,1] => [1,3,1,2]
011010 => [2,1,2,2] => [2,2,1,2]
011011 => [2,1,2,1,1] => [1,1,2,1,2]
011100 => [2,1,1,3] => [3,1,1,2]
011101 => [2,1,1,2,1] => [1,2,1,1,2]
011110 => [2,1,1,1,2] => [2,1,1,1,2]
011111 => [2,1,1,1,1,1] => [1,1,1,1,1,2]
100000 => [1,6] => [6,1]
100001 => [1,5,1] => [1,5,1]
100010 => [1,4,2] => [2,4,1]
100011 => [1,4,1,1] => [1,1,4,1]
100100 => [1,3,3] => [3,3,1]
100101 => [1,3,2,1] => [1,2,3,1]
100110 => [1,3,1,2] => [2,1,3,1]
>>> Load all 1533 entries. <<<
100111 => [1,3,1,1,1] => [1,1,1,3,1]
101000 => [1,2,4] => [4,2,1]
101001 => [1,2,3,1] => [1,3,2,1]
101010 => [1,2,2,2] => [2,2,2,1]
101011 => [1,2,2,1,1] => [1,1,2,2,1]
101100 => [1,2,1,3] => [3,1,2,1]
101101 => [1,2,1,2,1] => [1,2,1,2,1]
101110 => [1,2,1,1,2] => [2,1,1,2,1]
101111 => [1,2,1,1,1,1] => [1,1,1,1,2,1]
110000 => [1,1,5] => [5,1,1]
110001 => [1,1,4,1] => [1,4,1,1]
110010 => [1,1,3,2] => [2,3,1,1]
110011 => [1,1,3,1,1] => [1,1,3,1,1]
110100 => [1,1,2,3] => [3,2,1,1]
110101 => [1,1,2,2,1] => [1,2,2,1,1]
110110 => [1,1,2,1,2] => [2,1,2,1,1]
110111 => [1,1,2,1,1,1] => [1,1,1,2,1,1]
111000 => [1,1,1,4] => [4,1,1,1]
111001 => [1,1,1,3,1] => [1,3,1,1,1]
111010 => [1,1,1,2,2] => [2,2,1,1,1]
111011 => [1,1,1,2,1,1] => [1,1,2,1,1,1]
111100 => [1,1,1,1,3] => [3,1,1,1,1]
111101 => [1,1,1,1,2,1] => [1,2,1,1,1,1]
111110 => [1,1,1,1,1,2] => [2,1,1,1,1,1]
111111 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1]
0000000 => [8] => [8]
0000001 => [7,1] => [1,7]
0000010 => [6,2] => [2,6]
0000011 => [6,1,1] => [1,1,6]
0000100 => [5,3] => [3,5]
0000101 => [5,2,1] => [1,2,5]
0000110 => [5,1,2] => [2,1,5]
0000111 => [5,1,1,1] => [1,1,1,5]
0001000 => [4,4] => [4,4]
0001001 => [4,3,1] => [1,3,4]
0001010 => [4,2,2] => [2,2,4]
0001011 => [4,2,1,1] => [1,1,2,4]
0001100 => [4,1,3] => [3,1,4]
0001101 => [4,1,2,1] => [1,2,1,4]
0001110 => [4,1,1,2] => [2,1,1,4]
0001111 => [4,1,1,1,1] => [1,1,1,1,4]
0010000 => [3,5] => [5,3]
0010001 => [3,4,1] => [1,4,3]
0010010 => [3,3,2] => [2,3,3]
0010011 => [3,3,1,1] => [1,1,3,3]
0010100 => [3,2,3] => [3,2,3]
0010101 => [3,2,2,1] => [1,2,2,3]
0010110 => [3,2,1,2] => [2,1,2,3]
0010111 => [3,2,1,1,1] => [1,1,1,2,3]
0011000 => [3,1,4] => [4,1,3]
0011001 => [3,1,3,1] => [1,3,1,3]
0011010 => [3,1,2,2] => [2,2,1,3]
0011011 => [3,1,2,1,1] => [1,1,2,1,3]
0011100 => [3,1,1,3] => [3,1,1,3]
0011101 => [3,1,1,2,1] => [1,2,1,1,3]
0011110 => [3,1,1,1,2] => [2,1,1,1,3]
0011111 => [3,1,1,1,1,1] => [1,1,1,1,1,3]
0100000 => [2,6] => [6,2]
0100001 => [2,5,1] => [1,5,2]
0100010 => [2,4,2] => [2,4,2]
0100011 => [2,4,1,1] => [1,1,4,2]
0100100 => [2,3,3] => [3,3,2]
0100101 => [2,3,2,1] => [1,2,3,2]
0100110 => [2,3,1,2] => [2,1,3,2]
0100111 => [2,3,1,1,1] => [1,1,1,3,2]
0101000 => [2,2,4] => [4,2,2]
0101001 => [2,2,3,1] => [1,3,2,2]
0101010 => [2,2,2,2] => [2,2,2,2]
0101011 => [2,2,2,1,1] => [1,1,2,2,2]
0101100 => [2,2,1,3] => [3,1,2,2]
0101101 => [2,2,1,2,1] => [1,2,1,2,2]
0101110 => [2,2,1,1,2] => [2,1,1,2,2]
0101111 => [2,2,1,1,1,1] => [1,1,1,1,2,2]
0110000 => [2,1,5] => [5,1,2]
0110001 => [2,1,4,1] => [1,4,1,2]
0110010 => [2,1,3,2] => [2,3,1,2]
0110011 => [2,1,3,1,1] => [1,1,3,1,2]
0110100 => [2,1,2,3] => [3,2,1,2]
0110101 => [2,1,2,2,1] => [1,2,2,1,2]
0110110 => [2,1,2,1,2] => [2,1,2,1,2]
0110111 => [2,1,2,1,1,1] => [1,1,1,2,1,2]
0111000 => [2,1,1,4] => [4,1,1,2]
0111001 => [2,1,1,3,1] => [1,3,1,1,2]
0111010 => [2,1,1,2,2] => [2,2,1,1,2]
0111011 => [2,1,1,2,1,1] => [1,1,2,1,1,2]
0111100 => [2,1,1,1,3] => [3,1,1,1,2]
0111101 => [2,1,1,1,2,1] => [1,2,1,1,1,2]
0111110 => [2,1,1,1,1,2] => [2,1,1,1,1,2]
0111111 => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2]
1000000 => [1,7] => [7,1]
1000001 => [1,6,1] => [1,6,1]
1000010 => [1,5,2] => [2,5,1]
1000011 => [1,5,1,1] => [1,1,5,1]
1000100 => [1,4,3] => [3,4,1]
1000101 => [1,4,2,1] => [1,2,4,1]
1000110 => [1,4,1,2] => [2,1,4,1]
1000111 => [1,4,1,1,1] => [1,1,1,4,1]
1001000 => [1,3,4] => [4,3,1]
1001001 => [1,3,3,1] => [1,3,3,1]
1001010 => [1,3,2,2] => [2,2,3,1]
1001011 => [1,3,2,1,1] => [1,1,2,3,1]
1001100 => [1,3,1,3] => [3,1,3,1]
1001101 => [1,3,1,2,1] => [1,2,1,3,1]
1001110 => [1,3,1,1,2] => [2,1,1,3,1]
1001111 => [1,3,1,1,1,1] => [1,1,1,1,3,1]
1010000 => [1,2,5] => [5,2,1]
1010001 => [1,2,4,1] => [1,4,2,1]
1010010 => [1,2,3,2] => [2,3,2,1]
1010011 => [1,2,3,1,1] => [1,1,3,2,1]
1010100 => [1,2,2,3] => [3,2,2,1]
1010101 => [1,2,2,2,1] => [1,2,2,2,1]
1010110 => [1,2,2,1,2] => [2,1,2,2,1]
1010111 => [1,2,2,1,1,1] => [1,1,1,2,2,1]
1011000 => [1,2,1,4] => [4,1,2,1]
1011001 => [1,2,1,3,1] => [1,3,1,2,1]
1011010 => [1,2,1,2,2] => [2,2,1,2,1]
1011011 => [1,2,1,2,1,1] => [1,1,2,1,2,1]
1011100 => [1,2,1,1,3] => [3,1,1,2,1]
1011101 => [1,2,1,1,2,1] => [1,2,1,1,2,1]
1011110 => [1,2,1,1,1,2] => [2,1,1,1,2,1]
1011111 => [1,2,1,1,1,1,1] => [1,1,1,1,1,2,1]
1100000 => [1,1,6] => [6,1,1]
1100001 => [1,1,5,1] => [1,5,1,1]
1100010 => [1,1,4,2] => [2,4,1,1]
1100011 => [1,1,4,1,1] => [1,1,4,1,1]
1100100 => [1,1,3,3] => [3,3,1,1]
1100101 => [1,1,3,2,1] => [1,2,3,1,1]
1100110 => [1,1,3,1,2] => [2,1,3,1,1]
1100111 => [1,1,3,1,1,1] => [1,1,1,3,1,1]
1101000 => [1,1,2,4] => [4,2,1,1]
1101001 => [1,1,2,3,1] => [1,3,2,1,1]
1101010 => [1,1,2,2,2] => [2,2,2,1,1]
1101011 => [1,1,2,2,1,1] => [1,1,2,2,1,1]
1101100 => [1,1,2,1,3] => [3,1,2,1,1]
1101101 => [1,1,2,1,2,1] => [1,2,1,2,1,1]
1101110 => [1,1,2,1,1,2] => [2,1,1,2,1,1]
1101111 => [1,1,2,1,1,1,1] => [1,1,1,1,2,1,1]
1110000 => [1,1,1,5] => [5,1,1,1]
1110001 => [1,1,1,4,1] => [1,4,1,1,1]
1110010 => [1,1,1,3,2] => [2,3,1,1,1]
1110011 => [1,1,1,3,1,1] => [1,1,3,1,1,1]
1110100 => [1,1,1,2,3] => [3,2,1,1,1]
1110101 => [1,1,1,2,2,1] => [1,2,2,1,1,1]
1110110 => [1,1,1,2,1,2] => [2,1,2,1,1,1]
1110111 => [1,1,1,2,1,1,1] => [1,1,1,2,1,1,1]
1111000 => [1,1,1,1,4] => [4,1,1,1,1]
1111001 => [1,1,1,1,3,1] => [1,3,1,1,1,1]
1111010 => [1,1,1,1,2,2] => [2,2,1,1,1,1]
1111011 => [1,1,1,1,2,1,1] => [1,1,2,1,1,1,1]
1111100 => [1,1,1,1,1,3] => [3,1,1,1,1,1]
1111101 => [1,1,1,1,1,2,1] => [1,2,1,1,1,1,1]
1111110 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1]
1111111 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1]
00000000 => [9] => [9]
00000001 => [8,1] => [1,8]
00000010 => [7,2] => [2,7]
00000011 => [7,1,1] => [1,1,7]
00000100 => [6,3] => [3,6]
00000101 => [6,2,1] => [1,2,6]
00000110 => [6,1,2] => [2,1,6]
00000111 => [6,1,1,1] => [1,1,1,6]
00001000 => [5,4] => [4,5]
00001001 => [5,3,1] => [1,3,5]
00001010 => [5,2,2] => [2,2,5]
00001011 => [5,2,1,1] => [1,1,2,5]
00001100 => [5,1,3] => [3,1,5]
00001101 => [5,1,2,1] => [1,2,1,5]
00001110 => [5,1,1,2] => [2,1,1,5]
00001111 => [5,1,1,1,1] => [1,1,1,1,5]
00010000 => [4,5] => [5,4]
00010001 => [4,4,1] => [1,4,4]
00010010 => [4,3,2] => [2,3,4]
00010011 => [4,3,1,1] => [1,1,3,4]
00010100 => [4,2,3] => [3,2,4]
00010101 => [4,2,2,1] => [1,2,2,4]
00010110 => [4,2,1,2] => [2,1,2,4]
00010111 => [4,2,1,1,1] => [1,1,1,2,4]
00011000 => [4,1,4] => [4,1,4]
00011001 => [4,1,3,1] => [1,3,1,4]
00011010 => [4,1,2,2] => [2,2,1,4]
00011011 => [4,1,2,1,1] => [1,1,2,1,4]
00011100 => [4,1,1,3] => [3,1,1,4]
00011101 => [4,1,1,2,1] => [1,2,1,1,4]
00011110 => [4,1,1,1,2] => [2,1,1,1,4]
00011111 => [4,1,1,1,1,1] => [1,1,1,1,1,4]
00100000 => [3,6] => [6,3]
00100001 => [3,5,1] => [1,5,3]
00100010 => [3,4,2] => [2,4,3]
00100011 => [3,4,1,1] => [1,1,4,3]
00100100 => [3,3,3] => [3,3,3]
00100101 => [3,3,2,1] => [1,2,3,3]
00100110 => [3,3,1,2] => [2,1,3,3]
00100111 => [3,3,1,1,1] => [1,1,1,3,3]
00101000 => [3,2,4] => [4,2,3]
00101001 => [3,2,3,1] => [1,3,2,3]
00101010 => [3,2,2,2] => [2,2,2,3]
00101011 => [3,2,2,1,1] => [1,1,2,2,3]
00101100 => [3,2,1,3] => [3,1,2,3]
00101101 => [3,2,1,2,1] => [1,2,1,2,3]
00101110 => [3,2,1,1,2] => [2,1,1,2,3]
00101111 => [3,2,1,1,1,1] => [1,1,1,1,2,3]
00110000 => [3,1,5] => [5,1,3]
00110001 => [3,1,4,1] => [1,4,1,3]
00110010 => [3,1,3,2] => [2,3,1,3]
00110011 => [3,1,3,1,1] => [1,1,3,1,3]
00110100 => [3,1,2,3] => [3,2,1,3]
00110101 => [3,1,2,2,1] => [1,2,2,1,3]
00110110 => [3,1,2,1,2] => [2,1,2,1,3]
00110111 => [3,1,2,1,1,1] => [1,1,1,2,1,3]
00111000 => [3,1,1,4] => [4,1,1,3]
00111001 => [3,1,1,3,1] => [1,3,1,1,3]
00111010 => [3,1,1,2,2] => [2,2,1,1,3]
00111011 => [3,1,1,2,1,1] => [1,1,2,1,1,3]
00111100 => [3,1,1,1,3] => [3,1,1,1,3]
00111101 => [3,1,1,1,2,1] => [1,2,1,1,1,3]
00111110 => [3,1,1,1,1,2] => [2,1,1,1,1,3]
00111111 => [3,1,1,1,1,1,1] => [1,1,1,1,1,1,3]
01000000 => [2,7] => [7,2]
01000001 => [2,6,1] => [1,6,2]
01000010 => [2,5,2] => [2,5,2]
01000011 => [2,5,1,1] => [1,1,5,2]
01000100 => [2,4,3] => [3,4,2]
01000101 => [2,4,2,1] => [1,2,4,2]
01000110 => [2,4,1,2] => [2,1,4,2]
01000111 => [2,4,1,1,1] => [1,1,1,4,2]
01001000 => [2,3,4] => [4,3,2]
01001001 => [2,3,3,1] => [1,3,3,2]
01001010 => [2,3,2,2] => [2,2,3,2]
01001011 => [2,3,2,1,1] => [1,1,2,3,2]
01001100 => [2,3,1,3] => [3,1,3,2]
01001101 => [2,3,1,2,1] => [1,2,1,3,2]
01001110 => [2,3,1,1,2] => [2,1,1,3,2]
01001111 => [2,3,1,1,1,1] => [1,1,1,1,3,2]
01010000 => [2,2,5] => [5,2,2]
01010001 => [2,2,4,1] => [1,4,2,2]
01010010 => [2,2,3,2] => [2,3,2,2]
01010011 => [2,2,3,1,1] => [1,1,3,2,2]
01010100 => [2,2,2,3] => [3,2,2,2]
01010101 => [2,2,2,2,1] => [1,2,2,2,2]
01010110 => [2,2,2,1,2] => [2,1,2,2,2]
01010111 => [2,2,2,1,1,1] => [1,1,1,2,2,2]
01011000 => [2,2,1,4] => [4,1,2,2]
01011001 => [2,2,1,3,1] => [1,3,1,2,2]
01011010 => [2,2,1,2,2] => [2,2,1,2,2]
01011011 => [2,2,1,2,1,1] => [1,1,2,1,2,2]
01011100 => [2,2,1,1,3] => [3,1,1,2,2]
01011101 => [2,2,1,1,2,1] => [1,2,1,1,2,2]
01011110 => [2,2,1,1,1,2] => [2,1,1,1,2,2]
01011111 => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2]
01100000 => [2,1,6] => [6,1,2]
01100001 => [2,1,5,1] => [1,5,1,2]
01100010 => [2,1,4,2] => [2,4,1,2]
01100011 => [2,1,4,1,1] => [1,1,4,1,2]
01100100 => [2,1,3,3] => [3,3,1,2]
01100101 => [2,1,3,2,1] => [1,2,3,1,2]
01100110 => [2,1,3,1,2] => [2,1,3,1,2]
01100111 => [2,1,3,1,1,1] => [1,1,1,3,1,2]
01101000 => [2,1,2,4] => [4,2,1,2]
01101001 => [2,1,2,3,1] => [1,3,2,1,2]
01101010 => [2,1,2,2,2] => [2,2,2,1,2]
01101011 => [2,1,2,2,1,1] => [1,1,2,2,1,2]
01101100 => [2,1,2,1,3] => [3,1,2,1,2]
01101101 => [2,1,2,1,2,1] => [1,2,1,2,1,2]
01101110 => [2,1,2,1,1,2] => [2,1,1,2,1,2]
01101111 => [2,1,2,1,1,1,1] => [1,1,1,1,2,1,2]
01110000 => [2,1,1,5] => [5,1,1,2]
01110001 => [2,1,1,4,1] => [1,4,1,1,2]
01110010 => [2,1,1,3,2] => [2,3,1,1,2]
01110011 => [2,1,1,3,1,1] => [1,1,3,1,1,2]
01110100 => [2,1,1,2,3] => [3,2,1,1,2]
01110101 => [2,1,1,2,2,1] => [1,2,2,1,1,2]
01110110 => [2,1,1,2,1,2] => [2,1,2,1,1,2]
01110111 => [2,1,1,2,1,1,1] => [1,1,1,2,1,1,2]
01111000 => [2,1,1,1,4] => [4,1,1,1,2]
01111001 => [2,1,1,1,3,1] => [1,3,1,1,1,2]
01111010 => [2,1,1,1,2,2] => [2,2,1,1,1,2]
01111011 => [2,1,1,1,2,1,1] => [1,1,2,1,1,1,2]
01111100 => [2,1,1,1,1,3] => [3,1,1,1,1,2]
01111101 => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2]
01111110 => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2]
01111111 => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2]
10000000 => [1,8] => [8,1]
10000001 => [1,7,1] => [1,7,1]
10000010 => [1,6,2] => [2,6,1]
10000011 => [1,6,1,1] => [1,1,6,1]
10000100 => [1,5,3] => [3,5,1]
10000101 => [1,5,2,1] => [1,2,5,1]
10000110 => [1,5,1,2] => [2,1,5,1]
10000111 => [1,5,1,1,1] => [1,1,1,5,1]
10001000 => [1,4,4] => [4,4,1]
10001001 => [1,4,3,1] => [1,3,4,1]
10001010 => [1,4,2,2] => [2,2,4,1]
10001011 => [1,4,2,1,1] => [1,1,2,4,1]
10001100 => [1,4,1,3] => [3,1,4,1]
10001101 => [1,4,1,2,1] => [1,2,1,4,1]
10001110 => [1,4,1,1,2] => [2,1,1,4,1]
10001111 => [1,4,1,1,1,1] => [1,1,1,1,4,1]
10010000 => [1,3,5] => [5,3,1]
10010001 => [1,3,4,1] => [1,4,3,1]
10010010 => [1,3,3,2] => [2,3,3,1]
10010011 => [1,3,3,1,1] => [1,1,3,3,1]
10010100 => [1,3,2,3] => [3,2,3,1]
10010101 => [1,3,2,2,1] => [1,2,2,3,1]
10010110 => [1,3,2,1,2] => [2,1,2,3,1]
10010111 => [1,3,2,1,1,1] => [1,1,1,2,3,1]
10011000 => [1,3,1,4] => [4,1,3,1]
10011001 => [1,3,1,3,1] => [1,3,1,3,1]
10011010 => [1,3,1,2,2] => [2,2,1,3,1]
10011011 => [1,3,1,2,1,1] => [1,1,2,1,3,1]
10011100 => [1,3,1,1,3] => [3,1,1,3,1]
10011101 => [1,3,1,1,2,1] => [1,2,1,1,3,1]
10011110 => [1,3,1,1,1,2] => [2,1,1,1,3,1]
10011111 => [1,3,1,1,1,1,1] => [1,1,1,1,1,3,1]
10100000 => [1,2,6] => [6,2,1]
10100001 => [1,2,5,1] => [1,5,2,1]
10100010 => [1,2,4,2] => [2,4,2,1]
10100011 => [1,2,4,1,1] => [1,1,4,2,1]
10100100 => [1,2,3,3] => [3,3,2,1]
10100101 => [1,2,3,2,1] => [1,2,3,2,1]
10100110 => [1,2,3,1,2] => [2,1,3,2,1]
10100111 => [1,2,3,1,1,1] => [1,1,1,3,2,1]
10101000 => [1,2,2,4] => [4,2,2,1]
10101001 => [1,2,2,3,1] => [1,3,2,2,1]
10101010 => [1,2,2,2,2] => [2,2,2,2,1]
10101011 => [1,2,2,2,1,1] => [1,1,2,2,2,1]
10101100 => [1,2,2,1,3] => [3,1,2,2,1]
10101101 => [1,2,2,1,2,1] => [1,2,1,2,2,1]
10101110 => [1,2,2,1,1,2] => [2,1,1,2,2,1]
10101111 => [1,2,2,1,1,1,1] => [1,1,1,1,2,2,1]
10110000 => [1,2,1,5] => [5,1,2,1]
10110001 => [1,2,1,4,1] => [1,4,1,2,1]
10110010 => [1,2,1,3,2] => [2,3,1,2,1]
10110011 => [1,2,1,3,1,1] => [1,1,3,1,2,1]
10110100 => [1,2,1,2,3] => [3,2,1,2,1]
10110101 => [1,2,1,2,2,1] => [1,2,2,1,2,1]
10110110 => [1,2,1,2,1,2] => [2,1,2,1,2,1]
10110111 => [1,2,1,2,1,1,1] => [1,1,1,2,1,2,1]
10111000 => [1,2,1,1,4] => [4,1,1,2,1]
10111001 => [1,2,1,1,3,1] => [1,3,1,1,2,1]
10111010 => [1,2,1,1,2,2] => [2,2,1,1,2,1]
10111011 => [1,2,1,1,2,1,1] => [1,1,2,1,1,2,1]
10111100 => [1,2,1,1,1,3] => [3,1,1,1,2,1]
10111101 => [1,2,1,1,1,2,1] => [1,2,1,1,1,2,1]
10111110 => [1,2,1,1,1,1,2] => [2,1,1,1,1,2,1]
10111111 => [1,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1]
11000000 => [1,1,7] => [7,1,1]
11000001 => [1,1,6,1] => [1,6,1,1]
11000010 => [1,1,5,2] => [2,5,1,1]
11000011 => [1,1,5,1,1] => [1,1,5,1,1]
11000100 => [1,1,4,3] => [3,4,1,1]
11000101 => [1,1,4,2,1] => [1,2,4,1,1]
11000110 => [1,1,4,1,2] => [2,1,4,1,1]
11000111 => [1,1,4,1,1,1] => [1,1,1,4,1,1]
11001000 => [1,1,3,4] => [4,3,1,1]
11001001 => [1,1,3,3,1] => [1,3,3,1,1]
11001010 => [1,1,3,2,2] => [2,2,3,1,1]
11001011 => [1,1,3,2,1,1] => [1,1,2,3,1,1]
11001100 => [1,1,3,1,3] => [3,1,3,1,1]
11001101 => [1,1,3,1,2,1] => [1,2,1,3,1,1]
11001110 => [1,1,3,1,1,2] => [2,1,1,3,1,1]
11001111 => [1,1,3,1,1,1,1] => [1,1,1,1,3,1,1]
11010000 => [1,1,2,5] => [5,2,1,1]
11010001 => [1,1,2,4,1] => [1,4,2,1,1]
11010010 => [1,1,2,3,2] => [2,3,2,1,1]
11010011 => [1,1,2,3,1,1] => [1,1,3,2,1,1]
11010100 => [1,1,2,2,3] => [3,2,2,1,1]
11010101 => [1,1,2,2,2,1] => [1,2,2,2,1,1]
11010110 => [1,1,2,2,1,2] => [2,1,2,2,1,1]
11010111 => [1,1,2,2,1,1,1] => [1,1,1,2,2,1,1]
11011000 => [1,1,2,1,4] => [4,1,2,1,1]
11011001 => [1,1,2,1,3,1] => [1,3,1,2,1,1]
11011010 => [1,1,2,1,2,2] => [2,2,1,2,1,1]
11011011 => [1,1,2,1,2,1,1] => [1,1,2,1,2,1,1]
11011100 => [1,1,2,1,1,3] => [3,1,1,2,1,1]
11011101 => [1,1,2,1,1,2,1] => [1,2,1,1,2,1,1]
11011110 => [1,1,2,1,1,1,2] => [2,1,1,1,2,1,1]
11011111 => [1,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,1]
11100000 => [1,1,1,6] => [6,1,1,1]
11100001 => [1,1,1,5,1] => [1,5,1,1,1]
11100010 => [1,1,1,4,2] => [2,4,1,1,1]
11100011 => [1,1,1,4,1,1] => [1,1,4,1,1,1]
11100100 => [1,1,1,3,3] => [3,3,1,1,1]
11100101 => [1,1,1,3,2,1] => [1,2,3,1,1,1]
11100110 => [1,1,1,3,1,2] => [2,1,3,1,1,1]
11100111 => [1,1,1,3,1,1,1] => [1,1,1,3,1,1,1]
11101000 => [1,1,1,2,4] => [4,2,1,1,1]
11101001 => [1,1,1,2,3,1] => [1,3,2,1,1,1]
11101010 => [1,1,1,2,2,2] => [2,2,2,1,1,1]
11101011 => [1,1,1,2,2,1,1] => [1,1,2,2,1,1,1]
11101100 => [1,1,1,2,1,3] => [3,1,2,1,1,1]
11101101 => [1,1,1,2,1,2,1] => [1,2,1,2,1,1,1]
11101110 => [1,1,1,2,1,1,2] => [2,1,1,2,1,1,1]
11101111 => [1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1]
11110000 => [1,1,1,1,5] => [5,1,1,1,1]
11110001 => [1,1,1,1,4,1] => [1,4,1,1,1,1]
11110010 => [1,1,1,1,3,2] => [2,3,1,1,1,1]
11110011 => [1,1,1,1,3,1,1] => [1,1,3,1,1,1,1]
11110100 => [1,1,1,1,2,3] => [3,2,1,1,1,1]
11110101 => [1,1,1,1,2,2,1] => [1,2,2,1,1,1,1]
11110110 => [1,1,1,1,2,1,2] => [2,1,2,1,1,1,1]
11110111 => [1,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,1]
11111000 => [1,1,1,1,1,4] => [4,1,1,1,1,1]
11111001 => [1,1,1,1,1,3,1] => [1,3,1,1,1,1,1]
11111010 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1]
11111011 => [1,1,1,1,1,2,1,1] => [1,1,2,1,1,1,1,1]
11111100 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1]
11111101 => [1,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,1]
11111110 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1]
11111111 => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1]
000000000 => [10] => [10]
000000001 => [9,1] => [1,9]
000000010 => [8,2] => [2,8]
000000011 => [8,1,1] => [1,1,8]
000000100 => [7,3] => [3,7]
000000101 => [7,2,1] => [1,2,7]
000000110 => [7,1,2] => [2,1,7]
000000111 => [7,1,1,1] => [1,1,1,7]
000001000 => [6,4] => [4,6]
000001001 => [6,3,1] => [1,3,6]
000001010 => [6,2,2] => [2,2,6]
000001011 => [6,2,1,1] => [1,1,2,6]
000001100 => [6,1,3] => [3,1,6]
000001101 => [6,1,2,1] => [1,2,1,6]
000001110 => [6,1,1,2] => [2,1,1,6]
000001111 => [6,1,1,1,1] => [1,1,1,1,6]
000010000 => [5,5] => [5,5]
000010001 => [5,4,1] => [1,4,5]
000010010 => [5,3,2] => [2,3,5]
000010011 => [5,3,1,1] => [1,1,3,5]
000010100 => [5,2,3] => [3,2,5]
000010101 => [5,2,2,1] => [1,2,2,5]
000010110 => [5,2,1,2] => [2,1,2,5]
000010111 => [5,2,1,1,1] => [1,1,1,2,5]
000011000 => [5,1,4] => [4,1,5]
000011001 => [5,1,3,1] => [1,3,1,5]
000011010 => [5,1,2,2] => [2,2,1,5]
000011011 => [5,1,2,1,1] => [1,1,2,1,5]
000011100 => [5,1,1,3] => [3,1,1,5]
000011101 => [5,1,1,2,1] => [1,2,1,1,5]
000011110 => [5,1,1,1,2] => [2,1,1,1,5]
000011111 => [5,1,1,1,1,1] => [1,1,1,1,1,5]
000100000 => [4,6] => [6,4]
000100001 => [4,5,1] => [1,5,4]
000100010 => [4,4,2] => [2,4,4]
000100011 => [4,4,1,1] => [1,1,4,4]
000100100 => [4,3,3] => [3,3,4]
000100101 => [4,3,2,1] => [1,2,3,4]
000100110 => [4,3,1,2] => [2,1,3,4]
000100111 => [4,3,1,1,1] => [1,1,1,3,4]
000101000 => [4,2,4] => [4,2,4]
000101001 => [4,2,3,1] => [1,3,2,4]
000101010 => [4,2,2,2] => [2,2,2,4]
000101011 => [4,2,2,1,1] => [1,1,2,2,4]
000101100 => [4,2,1,3] => [3,1,2,4]
000101101 => [4,2,1,2,1] => [1,2,1,2,4]
000101110 => [4,2,1,1,2] => [2,1,1,2,4]
000101111 => [4,2,1,1,1,1] => [1,1,1,1,2,4]
000110000 => [4,1,5] => [5,1,4]
000110001 => [4,1,4,1] => [1,4,1,4]
000110010 => [4,1,3,2] => [2,3,1,4]
000110011 => [4,1,3,1,1] => [1,1,3,1,4]
000110100 => [4,1,2,3] => [3,2,1,4]
000110101 => [4,1,2,2,1] => [1,2,2,1,4]
000110110 => [4,1,2,1,2] => [2,1,2,1,4]
000110111 => [4,1,2,1,1,1] => [1,1,1,2,1,4]
000111000 => [4,1,1,4] => [4,1,1,4]
000111001 => [4,1,1,3,1] => [1,3,1,1,4]
000111010 => [4,1,1,2,2] => [2,2,1,1,4]
000111011 => [4,1,1,2,1,1] => [1,1,2,1,1,4]
000111100 => [4,1,1,1,3] => [3,1,1,1,4]
000111101 => [4,1,1,1,2,1] => [1,2,1,1,1,4]
000111110 => [4,1,1,1,1,2] => [2,1,1,1,1,4]
000111111 => [4,1,1,1,1,1,1] => [1,1,1,1,1,1,4]
001000000 => [3,7] => [7,3]
001000001 => [3,6,1] => [1,6,3]
001000010 => [3,5,2] => [2,5,3]
001000011 => [3,5,1,1] => [1,1,5,3]
001000100 => [3,4,3] => [3,4,3]
001000101 => [3,4,2,1] => [1,2,4,3]
001000110 => [3,4,1,2] => [2,1,4,3]
001000111 => [3,4,1,1,1] => [1,1,1,4,3]
001001000 => [3,3,4] => [4,3,3]
001001001 => [3,3,3,1] => [1,3,3,3]
001001010 => [3,3,2,2] => [2,2,3,3]
001001011 => [3,3,2,1,1] => [1,1,2,3,3]
001001100 => [3,3,1,3] => [3,1,3,3]
001001101 => [3,3,1,2,1] => [1,2,1,3,3]
001001110 => [3,3,1,1,2] => [2,1,1,3,3]
001001111 => [3,3,1,1,1,1] => [1,1,1,1,3,3]
001010000 => [3,2,5] => [5,2,3]
001010001 => [3,2,4,1] => [1,4,2,3]
001010010 => [3,2,3,2] => [2,3,2,3]
001010011 => [3,2,3,1,1] => [1,1,3,2,3]
001010100 => [3,2,2,3] => [3,2,2,3]
001010101 => [3,2,2,2,1] => [1,2,2,2,3]
001010110 => [3,2,2,1,2] => [2,1,2,2,3]
001010111 => [3,2,2,1,1,1] => [1,1,1,2,2,3]
001011000 => [3,2,1,4] => [4,1,2,3]
001011001 => [3,2,1,3,1] => [1,3,1,2,3]
001011010 => [3,2,1,2,2] => [2,2,1,2,3]
001011011 => [3,2,1,2,1,1] => [1,1,2,1,2,3]
001011100 => [3,2,1,1,3] => [3,1,1,2,3]
001011101 => [3,2,1,1,2,1] => [1,2,1,1,2,3]
001011110 => [3,2,1,1,1,2] => [2,1,1,1,2,3]
001011111 => [3,2,1,1,1,1,1] => [1,1,1,1,1,2,3]
001100000 => [3,1,6] => [6,1,3]
001100001 => [3,1,5,1] => [1,5,1,3]
001100010 => [3,1,4,2] => [2,4,1,3]
001100011 => [3,1,4,1,1] => [1,1,4,1,3]
001100100 => [3,1,3,3] => [3,3,1,3]
001100101 => [3,1,3,2,1] => [1,2,3,1,3]
001100110 => [3,1,3,1,2] => [2,1,3,1,3]
001100111 => [3,1,3,1,1,1] => [1,1,1,3,1,3]
001101000 => [3,1,2,4] => [4,2,1,3]
001101001 => [3,1,2,3,1] => [1,3,2,1,3]
001101010 => [3,1,2,2,2] => [2,2,2,1,3]
001101011 => [3,1,2,2,1,1] => [1,1,2,2,1,3]
001101100 => [3,1,2,1,3] => [3,1,2,1,3]
001101101 => [3,1,2,1,2,1] => [1,2,1,2,1,3]
001101110 => [3,1,2,1,1,2] => [2,1,1,2,1,3]
001101111 => [3,1,2,1,1,1,1] => [1,1,1,1,2,1,3]
001110000 => [3,1,1,5] => [5,1,1,3]
001110001 => [3,1,1,4,1] => [1,4,1,1,3]
001110010 => [3,1,1,3,2] => [2,3,1,1,3]
001110011 => [3,1,1,3,1,1] => [1,1,3,1,1,3]
001110100 => [3,1,1,2,3] => [3,2,1,1,3]
001110101 => [3,1,1,2,2,1] => [1,2,2,1,1,3]
001110110 => [3,1,1,2,1,2] => [2,1,2,1,1,3]
001110111 => [3,1,1,2,1,1,1] => [1,1,1,2,1,1,3]
001111000 => [3,1,1,1,4] => [4,1,1,1,3]
001111001 => [3,1,1,1,3,1] => [1,3,1,1,1,3]
001111010 => [3,1,1,1,2,2] => [2,2,1,1,1,3]
001111011 => [3,1,1,1,2,1,1] => [1,1,2,1,1,1,3]
001111100 => [3,1,1,1,1,3] => [3,1,1,1,1,3]
001111101 => [3,1,1,1,1,2,1] => [1,2,1,1,1,1,3]
001111110 => [3,1,1,1,1,1,2] => [2,1,1,1,1,1,3]
001111111 => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,3]
010000000 => [2,8] => [8,2]
010000001 => [2,7,1] => [1,7,2]
010000010 => [2,6,2] => [2,6,2]
010000011 => [2,6,1,1] => [1,1,6,2]
010000100 => [2,5,3] => [3,5,2]
010000101 => [2,5,2,1] => [1,2,5,2]
010000110 => [2,5,1,2] => [2,1,5,2]
010000111 => [2,5,1,1,1] => [1,1,1,5,2]
010001000 => [2,4,4] => [4,4,2]
010001001 => [2,4,3,1] => [1,3,4,2]
010001010 => [2,4,2,2] => [2,2,4,2]
010001011 => [2,4,2,1,1] => [1,1,2,4,2]
010001100 => [2,4,1,3] => [3,1,4,2]
010001101 => [2,4,1,2,1] => [1,2,1,4,2]
010001110 => [2,4,1,1,2] => [2,1,1,4,2]
010001111 => [2,4,1,1,1,1] => [1,1,1,1,4,2]
010010000 => [2,3,5] => [5,3,2]
010010001 => [2,3,4,1] => [1,4,3,2]
010010010 => [2,3,3,2] => [2,3,3,2]
010010011 => [2,3,3,1,1] => [1,1,3,3,2]
010010100 => [2,3,2,3] => [3,2,3,2]
010010101 => [2,3,2,2,1] => [1,2,2,3,2]
010010110 => [2,3,2,1,2] => [2,1,2,3,2]
010010111 => [2,3,2,1,1,1] => [1,1,1,2,3,2]
010011000 => [2,3,1,4] => [4,1,3,2]
010011001 => [2,3,1,3,1] => [1,3,1,3,2]
010011010 => [2,3,1,2,2] => [2,2,1,3,2]
010011011 => [2,3,1,2,1,1] => [1,1,2,1,3,2]
010011100 => [2,3,1,1,3] => [3,1,1,3,2]
010011101 => [2,3,1,1,2,1] => [1,2,1,1,3,2]
010011110 => [2,3,1,1,1,2] => [2,1,1,1,3,2]
010011111 => [2,3,1,1,1,1,1] => [1,1,1,1,1,3,2]
010100000 => [2,2,6] => [6,2,2]
010100001 => [2,2,5,1] => [1,5,2,2]
010100010 => [2,2,4,2] => [2,4,2,2]
010100011 => [2,2,4,1,1] => [1,1,4,2,2]
010100100 => [2,2,3,3] => [3,3,2,2]
010100101 => [2,2,3,2,1] => [1,2,3,2,2]
010100110 => [2,2,3,1,2] => [2,1,3,2,2]
010100111 => [2,2,3,1,1,1] => [1,1,1,3,2,2]
010101000 => [2,2,2,4] => [4,2,2,2]
010101001 => [2,2,2,3,1] => [1,3,2,2,2]
010101010 => [2,2,2,2,2] => [2,2,2,2,2]
010101011 => [2,2,2,2,1,1] => [1,1,2,2,2,2]
010101100 => [2,2,2,1,3] => [3,1,2,2,2]
010101101 => [2,2,2,1,2,1] => [1,2,1,2,2,2]
010101110 => [2,2,2,1,1,2] => [2,1,1,2,2,2]
010101111 => [2,2,2,1,1,1,1] => [1,1,1,1,2,2,2]
010110000 => [2,2,1,5] => [5,1,2,2]
010110001 => [2,2,1,4,1] => [1,4,1,2,2]
010110010 => [2,2,1,3,2] => [2,3,1,2,2]
010110011 => [2,2,1,3,1,1] => [1,1,3,1,2,2]
010110100 => [2,2,1,2,3] => [3,2,1,2,2]
010110101 => [2,2,1,2,2,1] => [1,2,2,1,2,2]
010110110 => [2,2,1,2,1,2] => [2,1,2,1,2,2]
010110111 => [2,2,1,2,1,1,1] => [1,1,1,2,1,2,2]
010111000 => [2,2,1,1,4] => [4,1,1,2,2]
010111001 => [2,2,1,1,3,1] => [1,3,1,1,2,2]
010111010 => [2,2,1,1,2,2] => [2,2,1,1,2,2]
010111011 => [2,2,1,1,2,1,1] => [1,1,2,1,1,2,2]
010111100 => [2,2,1,1,1,3] => [3,1,1,1,2,2]
010111101 => [2,2,1,1,1,2,1] => [1,2,1,1,1,2,2]
010111110 => [2,2,1,1,1,1,2] => [2,1,1,1,1,2,2]
010111111 => [2,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,2]
011000000 => [2,1,7] => [7,1,2]
011000001 => [2,1,6,1] => [1,6,1,2]
011000010 => [2,1,5,2] => [2,5,1,2]
011000011 => [2,1,5,1,1] => [1,1,5,1,2]
011000100 => [2,1,4,3] => [3,4,1,2]
011000101 => [2,1,4,2,1] => [1,2,4,1,2]
011000110 => [2,1,4,1,2] => [2,1,4,1,2]
011000111 => [2,1,4,1,1,1] => [1,1,1,4,1,2]
011001000 => [2,1,3,4] => [4,3,1,2]
011001001 => [2,1,3,3,1] => [1,3,3,1,2]
011001010 => [2,1,3,2,2] => [2,2,3,1,2]
011001011 => [2,1,3,2,1,1] => [1,1,2,3,1,2]
011001100 => [2,1,3,1,3] => [3,1,3,1,2]
011001101 => [2,1,3,1,2,1] => [1,2,1,3,1,2]
011001110 => [2,1,3,1,1,2] => [2,1,1,3,1,2]
011001111 => [2,1,3,1,1,1,1] => [1,1,1,1,3,1,2]
011010000 => [2,1,2,5] => [5,2,1,2]
011010001 => [2,1,2,4,1] => [1,4,2,1,2]
011010010 => [2,1,2,3,2] => [2,3,2,1,2]
011010011 => [2,1,2,3,1,1] => [1,1,3,2,1,2]
011010100 => [2,1,2,2,3] => [3,2,2,1,2]
011010101 => [2,1,2,2,2,1] => [1,2,2,2,1,2]
011010110 => [2,1,2,2,1,2] => [2,1,2,2,1,2]
011010111 => [2,1,2,2,1,1,1] => [1,1,1,2,2,1,2]
011011000 => [2,1,2,1,4] => [4,1,2,1,2]
011011001 => [2,1,2,1,3,1] => [1,3,1,2,1,2]
011011010 => [2,1,2,1,2,2] => [2,2,1,2,1,2]
011011011 => [2,1,2,1,2,1,1] => [1,1,2,1,2,1,2]
011011100 => [2,1,2,1,1,3] => [3,1,1,2,1,2]
011011101 => [2,1,2,1,1,2,1] => [1,2,1,1,2,1,2]
011011110 => [2,1,2,1,1,1,2] => [2,1,1,1,2,1,2]
011011111 => [2,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,2]
011100000 => [2,1,1,6] => [6,1,1,2]
011100001 => [2,1,1,5,1] => [1,5,1,1,2]
011100010 => [2,1,1,4,2] => [2,4,1,1,2]
011100011 => [2,1,1,4,1,1] => [1,1,4,1,1,2]
011100100 => [2,1,1,3,3] => [3,3,1,1,2]
011100101 => [2,1,1,3,2,1] => [1,2,3,1,1,2]
011100110 => [2,1,1,3,1,2] => [2,1,3,1,1,2]
011100111 => [2,1,1,3,1,1,1] => [1,1,1,3,1,1,2]
011101000 => [2,1,1,2,4] => [4,2,1,1,2]
011101001 => [2,1,1,2,3,1] => [1,3,2,1,1,2]
011101010 => [2,1,1,2,2,2] => [2,2,2,1,1,2]
011101011 => [2,1,1,2,2,1,1] => [1,1,2,2,1,1,2]
011101100 => [2,1,1,2,1,3] => [3,1,2,1,1,2]
011101101 => [2,1,1,2,1,2,1] => [1,2,1,2,1,1,2]
011101110 => [2,1,1,2,1,1,2] => [2,1,1,2,1,1,2]
011101111 => [2,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,2]
011110000 => [2,1,1,1,5] => [5,1,1,1,2]
011110001 => [2,1,1,1,4,1] => [1,4,1,1,1,2]
011110010 => [2,1,1,1,3,2] => [2,3,1,1,1,2]
011110011 => [2,1,1,1,3,1,1] => [1,1,3,1,1,1,2]
011110100 => [2,1,1,1,2,3] => [3,2,1,1,1,2]
011110101 => [2,1,1,1,2,2,1] => [1,2,2,1,1,1,2]
011110110 => [2,1,1,1,2,1,2] => [2,1,2,1,1,1,2]
011110111 => [2,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,2]
011111000 => [2,1,1,1,1,4] => [4,1,1,1,1,2]
011111001 => [2,1,1,1,1,3,1] => [1,3,1,1,1,1,2]
011111010 => [2,1,1,1,1,2,2] => [2,2,1,1,1,1,2]
011111011 => [2,1,1,1,1,2,1,1] => [1,1,2,1,1,1,1,2]
011111100 => [2,1,1,1,1,1,3] => [3,1,1,1,1,1,2]
011111101 => [2,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,2]
011111110 => [2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2]
011111111 => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2]
100000000 => [1,9] => [9,1]
100000001 => [1,8,1] => [1,8,1]
100000010 => [1,7,2] => [2,7,1]
100000011 => [1,7,1,1] => [1,1,7,1]
100000100 => [1,6,3] => [3,6,1]
100000101 => [1,6,2,1] => [1,2,6,1]
100000110 => [1,6,1,2] => [2,1,6,1]
100000111 => [1,6,1,1,1] => [1,1,1,6,1]
100001000 => [1,5,4] => [4,5,1]
100001001 => [1,5,3,1] => [1,3,5,1]
100001010 => [1,5,2,2] => [2,2,5,1]
100001011 => [1,5,2,1,1] => [1,1,2,5,1]
100001100 => [1,5,1,3] => [3,1,5,1]
100001101 => [1,5,1,2,1] => [1,2,1,5,1]
100001110 => [1,5,1,1,2] => [2,1,1,5,1]
100001111 => [1,5,1,1,1,1] => [1,1,1,1,5,1]
100010000 => [1,4,5] => [5,4,1]
100010001 => [1,4,4,1] => [1,4,4,1]
100010010 => [1,4,3,2] => [2,3,4,1]
100010011 => [1,4,3,1,1] => [1,1,3,4,1]
100010100 => [1,4,2,3] => [3,2,4,1]
100010101 => [1,4,2,2,1] => [1,2,2,4,1]
100010110 => [1,4,2,1,2] => [2,1,2,4,1]
100010111 => [1,4,2,1,1,1] => [1,1,1,2,4,1]
100011000 => [1,4,1,4] => [4,1,4,1]
100011001 => [1,4,1,3,1] => [1,3,1,4,1]
100011010 => [1,4,1,2,2] => [2,2,1,4,1]
100011011 => [1,4,1,2,1,1] => [1,1,2,1,4,1]
100011100 => [1,4,1,1,3] => [3,1,1,4,1]
100011101 => [1,4,1,1,2,1] => [1,2,1,1,4,1]
100011110 => [1,4,1,1,1,2] => [2,1,1,1,4,1]
100011111 => [1,4,1,1,1,1,1] => [1,1,1,1,1,4,1]
100100000 => [1,3,6] => [6,3,1]
100100001 => [1,3,5,1] => [1,5,3,1]
100100010 => [1,3,4,2] => [2,4,3,1]
100100011 => [1,3,4,1,1] => [1,1,4,3,1]
100100100 => [1,3,3,3] => [3,3,3,1]
100100101 => [1,3,3,2,1] => [1,2,3,3,1]
100100110 => [1,3,3,1,2] => [2,1,3,3,1]
100100111 => [1,3,3,1,1,1] => [1,1,1,3,3,1]
100101000 => [1,3,2,4] => [4,2,3,1]
100101001 => [1,3,2,3,1] => [1,3,2,3,1]
100101010 => [1,3,2,2,2] => [2,2,2,3,1]
100101011 => [1,3,2,2,1,1] => [1,1,2,2,3,1]
100101100 => [1,3,2,1,3] => [3,1,2,3,1]
100101101 => [1,3,2,1,2,1] => [1,2,1,2,3,1]
100101110 => [1,3,2,1,1,2] => [2,1,1,2,3,1]
100101111 => [1,3,2,1,1,1,1] => [1,1,1,1,2,3,1]
100110000 => [1,3,1,5] => [5,1,3,1]
100110001 => [1,3,1,4,1] => [1,4,1,3,1]
100110010 => [1,3,1,3,2] => [2,3,1,3,1]
100110011 => [1,3,1,3,1,1] => [1,1,3,1,3,1]
100110100 => [1,3,1,2,3] => [3,2,1,3,1]
100110101 => [1,3,1,2,2,1] => [1,2,2,1,3,1]
100110110 => [1,3,1,2,1,2] => [2,1,2,1,3,1]
100110111 => [1,3,1,2,1,1,1] => [1,1,1,2,1,3,1]
100111000 => [1,3,1,1,4] => [4,1,1,3,1]
100111001 => [1,3,1,1,3,1] => [1,3,1,1,3,1]
100111010 => [1,3,1,1,2,2] => [2,2,1,1,3,1]
100111011 => [1,3,1,1,2,1,1] => [1,1,2,1,1,3,1]
100111100 => [1,3,1,1,1,3] => [3,1,1,1,3,1]
100111101 => [1,3,1,1,1,2,1] => [1,2,1,1,1,3,1]
100111110 => [1,3,1,1,1,1,2] => [2,1,1,1,1,3,1]
100111111 => [1,3,1,1,1,1,1,1] => [1,1,1,1,1,1,3,1]
101000000 => [1,2,7] => [7,2,1]
101000001 => [1,2,6,1] => [1,6,2,1]
101000010 => [1,2,5,2] => [2,5,2,1]
101000011 => [1,2,5,1,1] => [1,1,5,2,1]
101000100 => [1,2,4,3] => [3,4,2,1]
101000101 => [1,2,4,2,1] => [1,2,4,2,1]
101000110 => [1,2,4,1,2] => [2,1,4,2,1]
101000111 => [1,2,4,1,1,1] => [1,1,1,4,2,1]
101001000 => [1,2,3,4] => [4,3,2,1]
101001001 => [1,2,3,3,1] => [1,3,3,2,1]
101001010 => [1,2,3,2,2] => [2,2,3,2,1]
101001011 => [1,2,3,2,1,1] => [1,1,2,3,2,1]
101001100 => [1,2,3,1,3] => [3,1,3,2,1]
101001101 => [1,2,3,1,2,1] => [1,2,1,3,2,1]
101001110 => [1,2,3,1,1,2] => [2,1,1,3,2,1]
101001111 => [1,2,3,1,1,1,1] => [1,1,1,1,3,2,1]
101010000 => [1,2,2,5] => [5,2,2,1]
101010001 => [1,2,2,4,1] => [1,4,2,2,1]
101010010 => [1,2,2,3,2] => [2,3,2,2,1]
101010011 => [1,2,2,3,1,1] => [1,1,3,2,2,1]
101010100 => [1,2,2,2,3] => [3,2,2,2,1]
101010101 => [1,2,2,2,2,1] => [1,2,2,2,2,1]
101010110 => [1,2,2,2,1,2] => [2,1,2,2,2,1]
101010111 => [1,2,2,2,1,1,1] => [1,1,1,2,2,2,1]
101011000 => [1,2,2,1,4] => [4,1,2,2,1]
101011001 => [1,2,2,1,3,1] => [1,3,1,2,2,1]
101011010 => [1,2,2,1,2,2] => [2,2,1,2,2,1]
101011011 => [1,2,2,1,2,1,1] => [1,1,2,1,2,2,1]
101011100 => [1,2,2,1,1,3] => [3,1,1,2,2,1]
101011101 => [1,2,2,1,1,2,1] => [1,2,1,1,2,2,1]
101011110 => [1,2,2,1,1,1,2] => [2,1,1,1,2,2,1]
101011111 => [1,2,2,1,1,1,1,1] => [1,1,1,1,1,2,2,1]
101100000 => [1,2,1,6] => [6,1,2,1]
101100001 => [1,2,1,5,1] => [1,5,1,2,1]
101100010 => [1,2,1,4,2] => [2,4,1,2,1]
101100011 => [1,2,1,4,1,1] => [1,1,4,1,2,1]
101100100 => [1,2,1,3,3] => [3,3,1,2,1]
101100101 => [1,2,1,3,2,1] => [1,2,3,1,2,1]
101100110 => [1,2,1,3,1,2] => [2,1,3,1,2,1]
101100111 => [1,2,1,3,1,1,1] => [1,1,1,3,1,2,1]
101101000 => [1,2,1,2,4] => [4,2,1,2,1]
101101001 => [1,2,1,2,3,1] => [1,3,2,1,2,1]
101101010 => [1,2,1,2,2,2] => [2,2,2,1,2,1]
101101011 => [1,2,1,2,2,1,1] => [1,1,2,2,1,2,1]
101101100 => [1,2,1,2,1,3] => [3,1,2,1,2,1]
101101101 => [1,2,1,2,1,2,1] => [1,2,1,2,1,2,1]
101101110 => [1,2,1,2,1,1,2] => [2,1,1,2,1,2,1]
101101111 => [1,2,1,2,1,1,1,1] => [1,1,1,1,2,1,2,1]
101110000 => [1,2,1,1,5] => [5,1,1,2,1]
101110001 => [1,2,1,1,4,1] => [1,4,1,1,2,1]
101110010 => [1,2,1,1,3,2] => [2,3,1,1,2,1]
101110011 => [1,2,1,1,3,1,1] => [1,1,3,1,1,2,1]
101110100 => [1,2,1,1,2,3] => [3,2,1,1,2,1]
101110101 => [1,2,1,1,2,2,1] => [1,2,2,1,1,2,1]
101110110 => [1,2,1,1,2,1,2] => [2,1,2,1,1,2,1]
101110111 => [1,2,1,1,2,1,1,1] => [1,1,1,2,1,1,2,1]
101111000 => [1,2,1,1,1,4] => [4,1,1,1,2,1]
101111001 => [1,2,1,1,1,3,1] => [1,3,1,1,1,2,1]
101111010 => [1,2,1,1,1,2,2] => [2,2,1,1,1,2,1]
101111011 => [1,2,1,1,1,2,1,1] => [1,1,2,1,1,1,2,1]
101111100 => [1,2,1,1,1,1,3] => [3,1,1,1,1,2,1]
101111101 => [1,2,1,1,1,1,2,1] => [1,2,1,1,1,1,2,1]
101111110 => [1,2,1,1,1,1,1,2] => [2,1,1,1,1,1,2,1]
101111111 => [1,2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2,1]
110000000 => [1,1,8] => [8,1,1]
110000001 => [1,1,7,1] => [1,7,1,1]
110000010 => [1,1,6,2] => [2,6,1,1]
110000011 => [1,1,6,1,1] => [1,1,6,1,1]
110000100 => [1,1,5,3] => [3,5,1,1]
110000101 => [1,1,5,2,1] => [1,2,5,1,1]
110000110 => [1,1,5,1,2] => [2,1,5,1,1]
110000111 => [1,1,5,1,1,1] => [1,1,1,5,1,1]
110001000 => [1,1,4,4] => [4,4,1,1]
110001001 => [1,1,4,3,1] => [1,3,4,1,1]
110001010 => [1,1,4,2,2] => [2,2,4,1,1]
110001011 => [1,1,4,2,1,1] => [1,1,2,4,1,1]
110001100 => [1,1,4,1,3] => [3,1,4,1,1]
110001101 => [1,1,4,1,2,1] => [1,2,1,4,1,1]
110001110 => [1,1,4,1,1,2] => [2,1,1,4,1,1]
110001111 => [1,1,4,1,1,1,1] => [1,1,1,1,4,1,1]
110010000 => [1,1,3,5] => [5,3,1,1]
110010001 => [1,1,3,4,1] => [1,4,3,1,1]
110010010 => [1,1,3,3,2] => [2,3,3,1,1]
110010011 => [1,1,3,3,1,1] => [1,1,3,3,1,1]
110010100 => [1,1,3,2,3] => [3,2,3,1,1]
110010101 => [1,1,3,2,2,1] => [1,2,2,3,1,1]
110010110 => [1,1,3,2,1,2] => [2,1,2,3,1,1]
110010111 => [1,1,3,2,1,1,1] => [1,1,1,2,3,1,1]
110011000 => [1,1,3,1,4] => [4,1,3,1,1]
110011001 => [1,1,3,1,3,1] => [1,3,1,3,1,1]
110011010 => [1,1,3,1,2,2] => [2,2,1,3,1,1]
110011011 => [1,1,3,1,2,1,1] => [1,1,2,1,3,1,1]
110011100 => [1,1,3,1,1,3] => [3,1,1,3,1,1]
110011101 => [1,1,3,1,1,2,1] => [1,2,1,1,3,1,1]
110011110 => [1,1,3,1,1,1,2] => [2,1,1,1,3,1,1]
110011111 => [1,1,3,1,1,1,1,1] => [1,1,1,1,1,3,1,1]
110100000 => [1,1,2,6] => [6,2,1,1]
110100001 => [1,1,2,5,1] => [1,5,2,1,1]
110100010 => [1,1,2,4,2] => [2,4,2,1,1]
110100011 => [1,1,2,4,1,1] => [1,1,4,2,1,1]
110100100 => [1,1,2,3,3] => [3,3,2,1,1]
110100101 => [1,1,2,3,2,1] => [1,2,3,2,1,1]
110100110 => [1,1,2,3,1,2] => [2,1,3,2,1,1]
110100111 => [1,1,2,3,1,1,1] => [1,1,1,3,2,1,1]
110101000 => [1,1,2,2,4] => [4,2,2,1,1]
110101001 => [1,1,2,2,3,1] => [1,3,2,2,1,1]
110101010 => [1,1,2,2,2,2] => [2,2,2,2,1,1]
110101011 => [1,1,2,2,2,1,1] => [1,1,2,2,2,1,1]
110101100 => [1,1,2,2,1,3] => [3,1,2,2,1,1]
110101101 => [1,1,2,2,1,2,1] => [1,2,1,2,2,1,1]
110101110 => [1,1,2,2,1,1,2] => [2,1,1,2,2,1,1]
110101111 => [1,1,2,2,1,1,1,1] => [1,1,1,1,2,2,1,1]
110110000 => [1,1,2,1,5] => [5,1,2,1,1]
110110001 => [1,1,2,1,4,1] => [1,4,1,2,1,1]
110110010 => [1,1,2,1,3,2] => [2,3,1,2,1,1]
110110011 => [1,1,2,1,3,1,1] => [1,1,3,1,2,1,1]
110110100 => [1,1,2,1,2,3] => [3,2,1,2,1,1]
110110101 => [1,1,2,1,2,2,1] => [1,2,2,1,2,1,1]
110110110 => [1,1,2,1,2,1,2] => [2,1,2,1,2,1,1]
110110111 => [1,1,2,1,2,1,1,1] => [1,1,1,2,1,2,1,1]
110111000 => [1,1,2,1,1,4] => [4,1,1,2,1,1]
110111001 => [1,1,2,1,1,3,1] => [1,3,1,1,2,1,1]
110111010 => [1,1,2,1,1,2,2] => [2,2,1,1,2,1,1]
110111011 => [1,1,2,1,1,2,1,1] => [1,1,2,1,1,2,1,1]
110111100 => [1,1,2,1,1,1,3] => [3,1,1,1,2,1,1]
110111101 => [1,1,2,1,1,1,2,1] => [1,2,1,1,1,2,1,1]
110111110 => [1,1,2,1,1,1,1,2] => [2,1,1,1,1,2,1,1]
110111111 => [1,1,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1,1]
111000000 => [1,1,1,7] => [7,1,1,1]
111000001 => [1,1,1,6,1] => [1,6,1,1,1]
111000010 => [1,1,1,5,2] => [2,5,1,1,1]
111000011 => [1,1,1,5,1,1] => [1,1,5,1,1,1]
111000100 => [1,1,1,4,3] => [3,4,1,1,1]
111000101 => [1,1,1,4,2,1] => [1,2,4,1,1,1]
111000110 => [1,1,1,4,1,2] => [2,1,4,1,1,1]
111000111 => [1,1,1,4,1,1,1] => [1,1,1,4,1,1,1]
111001000 => [1,1,1,3,4] => [4,3,1,1,1]
111001001 => [1,1,1,3,3,1] => [1,3,3,1,1,1]
111001010 => [1,1,1,3,2,2] => [2,2,3,1,1,1]
111001011 => [1,1,1,3,2,1,1] => [1,1,2,3,1,1,1]
111001100 => [1,1,1,3,1,3] => [3,1,3,1,1,1]
111001101 => [1,1,1,3,1,2,1] => [1,2,1,3,1,1,1]
111001110 => [1,1,1,3,1,1,2] => [2,1,1,3,1,1,1]
111001111 => [1,1,1,3,1,1,1,1] => [1,1,1,1,3,1,1,1]
111010000 => [1,1,1,2,5] => [5,2,1,1,1]
111010001 => [1,1,1,2,4,1] => [1,4,2,1,1,1]
111010010 => [1,1,1,2,3,2] => [2,3,2,1,1,1]
111010011 => [1,1,1,2,3,1,1] => [1,1,3,2,1,1,1]
111010100 => [1,1,1,2,2,3] => [3,2,2,1,1,1]
111010101 => [1,1,1,2,2,2,1] => [1,2,2,2,1,1,1]
111010110 => [1,1,1,2,2,1,2] => [2,1,2,2,1,1,1]
111010111 => [1,1,1,2,2,1,1,1] => [1,1,1,2,2,1,1,1]
111011000 => [1,1,1,2,1,4] => [4,1,2,1,1,1]
111011001 => [1,1,1,2,1,3,1] => [1,3,1,2,1,1,1]
111011010 => [1,1,1,2,1,2,2] => [2,2,1,2,1,1,1]
111011011 => [1,1,1,2,1,2,1,1] => [1,1,2,1,2,1,1,1]
111011100 => [1,1,1,2,1,1,3] => [3,1,1,2,1,1,1]
111011101 => [1,1,1,2,1,1,2,1] => [1,2,1,1,2,1,1,1]
111011110 => [1,1,1,2,1,1,1,2] => [2,1,1,1,2,1,1,1]
111011111 => [1,1,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,1,1]
111100000 => [1,1,1,1,6] => [6,1,1,1,1]
111100001 => [1,1,1,1,5,1] => [1,5,1,1,1,1]
111100010 => [1,1,1,1,4,2] => [2,4,1,1,1,1]
111100011 => [1,1,1,1,4,1,1] => [1,1,4,1,1,1,1]
111100100 => [1,1,1,1,3,3] => [3,3,1,1,1,1]
111100101 => [1,1,1,1,3,2,1] => [1,2,3,1,1,1,1]
111100110 => [1,1,1,1,3,1,2] => [2,1,3,1,1,1,1]
111100111 => [1,1,1,1,3,1,1,1] => [1,1,1,3,1,1,1,1]
111101000 => [1,1,1,1,2,4] => [4,2,1,1,1,1]
111101001 => [1,1,1,1,2,3,1] => [1,3,2,1,1,1,1]
111101010 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1]
111101011 => [1,1,1,1,2,2,1,1] => [1,1,2,2,1,1,1,1]
111101100 => [1,1,1,1,2,1,3] => [3,1,2,1,1,1,1]
111101101 => [1,1,1,1,2,1,2,1] => [1,2,1,2,1,1,1,1]
111101110 => [1,1,1,1,2,1,1,2] => [2,1,1,2,1,1,1,1]
111101111 => [1,1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1,1]
111110000 => [1,1,1,1,1,5] => [5,1,1,1,1,1]
111110001 => [1,1,1,1,1,4,1] => [1,4,1,1,1,1,1]
111110010 => [1,1,1,1,1,3,2] => [2,3,1,1,1,1,1]
111110011 => [1,1,1,1,1,3,1,1] => [1,1,3,1,1,1,1,1]
111110100 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1]
111110101 => [1,1,1,1,1,2,2,1] => [1,2,2,1,1,1,1,1]
111110110 => [1,1,1,1,1,2,1,2] => [2,1,2,1,1,1,1,1]
111110111 => [1,1,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,1,1]
111111000 => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1]
111111001 => [1,1,1,1,1,1,3,1] => [1,3,1,1,1,1,1,1]
111111010 => [1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1]
111111011 => [1,1,1,1,1,1,2,1,1] => [1,1,2,1,1,1,1,1,1]
111111100 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1]
111111101 => [1,1,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,1,1]
111111110 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1]
111111111 => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1]
1011001100 => [1,2,1,3,1,3] => [3,1,3,1,2,1]
1011010010 => [1,2,1,2,3,2] => [2,3,2,1,2,1]
1101001010 => [1,1,2,3,2,2] => [2,2,3,2,1,1]
1110001100 => [1,1,1,4,1,3] => [3,1,4,1,1,1]
1110100100 => [1,1,1,2,3,3] => [3,3,2,1,1,1]
1110101000 => [1,1,1,2,2,4] => [4,2,2,1,1,1]
1111010000 => [1,1,1,1,2,5] => [5,2,1,1,1,1]
111010010010 => [1,1,1,2,3,3,2] => [2,3,3,2,1,1,1]
111010101000 => [1,1,1,2,2,2,4] => [4,2,2,2,1,1,1]
111101001000 => [1,1,1,1,2,3,4] => [4,3,2,1,1,1,1]
1111111111 => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1]
1111111110 => [1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1]
1111111101 => [1,1,1,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,1,1,1]
1111111011 => [1,1,1,1,1,1,1,2,1,1] => [1,1,2,1,1,1,1,1,1,1]
1111110110 => [1,1,1,1,1,1,2,1,2] => [2,1,2,1,1,1,1,1,1]
1111110011 => [1,1,1,1,1,1,3,1,1] => [1,1,3,1,1,1,1,1,1]
1111101101 => [1,1,1,1,1,2,1,2,1] => [1,2,1,2,1,1,1,1,1]
1111100111 => [1,1,1,1,1,3,1,1,1] => [1,1,1,3,1,1,1,1,1]
1111011110 => [1,1,1,1,2,1,1,1,2] => [2,1,1,1,2,1,1,1,1]
1111011011 => [1,1,1,1,2,1,2,1,1] => [1,1,2,1,2,1,1,1,1]
1111010101 => [1,1,1,1,2,2,2,1] => [1,2,2,2,1,1,1,1]
1111010100 => [1,1,1,1,2,2,3] => [3,2,2,1,1,1,1]
1111010010 => [1,1,1,1,2,3,2] => [2,3,2,1,1,1,1]
1111001111 => [1,1,1,1,3,1,1,1,1] => [1,1,1,1,3,1,1,1,1]
1111001100 => [1,1,1,1,3,1,3] => [3,1,3,1,1,1,1]
1111000110 => [1,1,1,1,4,1,2] => [2,1,4,1,1,1,1]
1111000001 => [1,1,1,1,6,1] => [1,6,1,1,1,1]
1110111111 => [1,1,1,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1,1,1]
1110111101 => [1,1,1,2,1,1,1,2,1] => [1,2,1,1,1,2,1,1,1]
1110110111 => [1,1,1,2,1,2,1,1,1] => [1,1,1,2,1,2,1,1,1]
1110101010 => [1,1,1,2,2,2,2] => [2,2,2,2,1,1,1]
1110100101 => [1,1,1,2,3,2,1] => [1,2,3,2,1,1,1]
1110011110 => [1,1,1,3,1,1,1,2] => [2,1,1,1,3,1,1,1]
1110011001 => [1,1,1,3,1,3,1] => [1,3,1,3,1,1,1]
1110000011 => [1,1,1,6,1,1] => [1,1,6,1,1,1]
1101111111 => [1,1,2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2,1,1]
1101111110 => [1,1,2,1,1,1,1,1,2] => [2,1,1,1,1,1,2,1,1]
1101111011 => [1,1,2,1,1,1,2,1,1] => [1,1,2,1,1,1,2,1,1]
1101111001 => [1,1,2,1,1,1,3,1] => [1,3,1,1,1,2,1,1]
1101101111 => [1,1,2,1,2,1,1,1,1] => [1,1,1,1,2,1,2,1,1]
1101101100 => [1,1,2,1,2,1,3] => [3,1,2,1,2,1,1]
1101100110 => [1,1,2,1,3,1,2] => [2,1,3,1,2,1,1]
1101100011 => [1,1,2,1,4,1,1] => [1,1,4,1,2,1,1]
1101010101 => [1,1,2,2,2,2,1] => [1,2,2,2,2,1,1]
1101001011 => [1,1,2,3,2,1,1] => [1,1,2,3,2,1,1]
1101001001 => [1,1,2,3,3,1] => [1,3,3,2,1,1]
1101001000 => [1,1,2,3,4] => [4,3,2,1,1]
1100111111 => [1,1,3,1,1,1,1,1,1] => [1,1,1,1,1,1,3,1,1]
1100111100 => [1,1,3,1,1,1,3] => [3,1,1,1,3,1,1]
1100110110 => [1,1,3,1,2,1,2] => [2,1,2,1,3,1,1]
1100110011 => [1,1,3,1,3,1,1] => [1,1,3,1,3,1,1]
1100110001 => [1,1,3,1,4,1] => [1,4,1,3,1,1]
1100011110 => [1,1,4,1,1,1,2] => [2,1,1,1,4,1,1]
1100011011 => [1,1,4,1,2,1,1] => [1,1,2,1,4,1,1]
1100011001 => [1,1,4,1,3,1] => [1,3,1,4,1,1]
1100011000 => [1,1,4,1,4] => [4,1,4,1,1]
1100001100 => [1,1,5,1,3] => [3,1,5,1,1]
1100000011 => [1,1,7,1,1] => [1,1,7,1,1]
1100000001 => [1,1,8,1] => [1,8,1,1]
1100000000 => [1,1,9] => [9,1,1]
1011111111 => [1,2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2,1]
1011111101 => [1,2,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,2,1]
1011110111 => [1,2,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,2,1]
1011101011 => [1,2,1,1,2,2,1,1] => [1,1,2,2,1,1,2,1]
1011100001 => [1,2,1,1,5,1] => [1,5,1,1,2,1]
1011011111 => [1,2,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,2,1]
1011011001 => [1,2,1,2,1,3,1] => [1,3,1,2,1,2,1]
1011001101 => [1,2,1,3,1,2,1] => [1,2,1,3,1,2,1]
1010110101 => [1,2,2,1,2,2,1] => [1,2,2,1,2,2,1]
1010101111 => [1,2,2,2,1,1,1,1] => [1,1,1,1,2,2,2,1]
1010000001 => [1,2,7,1] => [1,7,2,1]
1010000000 => [1,2,8] => [8,2,1]
1001111110 => [1,3,1,1,1,1,1,2] => [2,1,1,1,1,1,3,1]
1001111011 => [1,3,1,1,1,2,1,1] => [1,1,2,1,1,1,3,1]
1001111001 => [1,3,1,1,1,3,1] => [1,3,1,1,1,3,1]
1001110001 => [1,3,1,1,4,1] => [1,4,1,1,3,1]
1001101101 => [1,3,1,2,1,2,1] => [1,2,1,2,1,3,1]
1001101100 => [1,3,1,2,1,3] => [3,1,2,1,3,1]
1001100111 => [1,3,1,3,1,1,1] => [1,1,1,3,1,3,1]
1001100110 => [1,3,1,3,1,2] => [2,1,3,1,3,1]
1001100011 => [1,3,1,4,1,1] => [1,1,4,1,3,1]
1001000000 => [1,3,7] => [7,3,1]
1000111100 => [1,4,1,1,1,3] => [3,1,1,1,4,1]
1000111001 => [1,4,1,1,3,1] => [1,3,1,1,4,1]
1000110110 => [1,4,1,2,1,2] => [2,1,2,1,4,1]
1000110011 => [1,4,1,3,1,1] => [1,1,3,1,4,1]
1000110001 => [1,4,1,4,1] => [1,4,1,4,1]
1000100000 => [1,4,6] => [6,4,1]
1000011101 => [1,5,1,1,2,1] => [1,2,1,1,5,1]
1000010000 => [1,5,5] => [5,5,1]
1000001111 => [1,6,1,1,1,1] => [1,1,1,1,6,1]
1000001001 => [1,6,3,1] => [1,3,6,1]
1000000110 => [1,7,1,2] => [2,1,7,1]
1000000101 => [1,7,2,1] => [1,2,7,1]
1000000100 => [1,7,3] => [3,7,1]
1000000011 => [1,8,1,1] => [1,1,8,1]
1000000010 => [1,8,2] => [2,8,1]
1000000001 => [1,9,1] => [1,9,1]
1000000000 => [1,10] => [10,1]
11111111110 => [1,1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1,1]
10101111110 => [1,2,2,1,1,1,1,1,2] => [2,1,1,1,1,1,2,2,1]
11011111110 => [1,1,2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2,1,1]
10000010000 => [1,6,5] => [5,6,1]
10000100010 => [1,5,4,2] => [2,4,5,1]
10111011110 => [1,2,1,1,2,1,1,1,2] => [2,1,1,1,2,1,1,2,1]
11110111110 => [1,1,1,1,2,1,1,1,1,2] => [2,1,1,1,1,2,1,1,1,1]
10001000010 => [1,4,5,2] => [2,5,4,1]
10000100100 => [1,5,3,3] => [3,3,5,1]
10001001010 => [1,4,3,2,2] => [2,2,3,4,1]
10001000100 => [1,4,4,3] => [3,4,4,1]
10000101000 => [1,5,2,4] => [4,2,5,1]
10010001010 => [1,3,4,2,2] => [2,2,4,3,1]
10001010010 => [1,4,2,3,2] => [2,3,2,4,1]
10101110110 => [1,2,2,1,1,2,1,2] => [2,1,2,1,1,2,2,1]
11101011110 => [1,1,1,2,2,1,1,1,2] => [2,1,1,1,2,2,1,1,1]
11011101110 => [1,1,2,1,1,2,1,1,2] => [2,1,1,2,1,1,2,1,1]
11111101110 => [1,1,1,1,1,1,2,1,1,2] => [2,1,1,2,1,1,1,1,1,1]
10010000100 => [1,3,5,3] => [3,5,3,1]
10001001000 => [1,4,3,4] => [4,3,4,1]
10010010010 => [1,3,3,3,2] => [2,3,3,3,1]
10001010100 => [1,4,2,2,3] => [3,2,2,4,1]
10010101010 => [1,3,2,2,2,2] => [2,2,2,2,3,1]
10101010110 => [1,2,2,2,2,1,2] => [2,1,2,2,2,2,1]
11010101110 => [1,1,2,2,2,1,1,2] => [2,1,1,2,2,2,1,1]
10110110110 => [1,2,1,2,1,2,1,2] => [2,1,2,1,2,1,2,1]
10010001000 => [1,3,4,4] => [4,4,3,1]
10100010010 => [1,2,4,3,2] => [2,3,4,2,1]
10010100010 => [1,3,2,4,2] => [2,4,2,3,1]
10010010100 => [1,3,3,2,3] => [3,2,3,3,1]
10100101010 => [1,2,3,2,2,2] => [2,2,2,3,2,1]
11010001110 => [1,1,2,4,1,1,2] => [2,1,1,4,2,1,1]
10101011010 => [1,2,2,2,1,2,2] => [2,2,1,2,2,2,1]
11010110110 => [1,1,2,2,1,2,1,2] => [2,1,2,1,2,2,1,1]
10111010110 => [1,2,1,1,2,2,1,2] => [2,1,2,2,1,1,2,1]
10110111010 => [1,2,1,2,1,1,2,2] => [2,2,1,1,2,1,2,1]
11101110110 => [1,1,1,2,1,1,2,1,2] => [2,1,2,1,1,2,1,1,1]
10111111100 => [1,2,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,2,1]
11111111010 => [1,1,1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1,1,1]
=> [1] => [1]
0111111111 => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,2]
0111111101 => [2,1,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,1,2]
0111111001 => [2,1,1,1,1,1,3,1] => [1,3,1,1,1,1,1,2]
0110000001 => [2,1,7,1] => [1,7,1,2]
0100000001 => [2,8,1] => [1,8,2]
0000000001 => [10,1] => [1,10]
01111111111 => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,2]
0111111011 => [2,1,1,1,1,1,2,1,1] => [1,1,2,1,1,1,1,1,2]
0010000001 => [3,7,1] => [1,7,3]
00000000001 => [11,1] => [1,11]
0011001101 => [3,1,3,1,2,1] => [1,2,1,3,1,3]
0011000111 => [3,1,4,1,1,1] => [1,1,1,4,1,3]
0010110101 => [3,2,1,2,2,1] => [1,2,2,1,2,3]
0001110101 => [4,1,1,2,2,1] => [1,2,2,1,1,4]
0001110011 => [4,1,1,3,1,1] => [1,1,3,1,1,4]
0001101011 => [4,1,2,2,1,1] => [1,1,2,2,1,4]
0000111011 => [5,1,1,2,1,1] => [1,1,2,1,1,5]
0000011111 => [6,1,1,1,1,1] => [1,1,1,1,1,6]
001101010101 => [3,1,2,2,2,2,1] => [1,2,2,2,2,1,3]
001101001011 => [3,1,2,3,2,1,1] => [1,1,2,3,2,1,3]
11010101010 => [1,1,2,2,2,2,2] => [2,2,2,2,2,1,1]
11010100100 => [1,1,2,2,3,3] => [3,3,2,2,1,1]
11010110100 => [1,1,2,2,1,2,3] => [3,2,1,2,2,1,1]
11010010100 => [1,1,2,3,2,3] => [3,2,3,2,1,1]
11001010100 => [1,1,3,2,2,3] => [3,2,2,3,1,1]
11101010100 => [1,1,1,2,2,2,3] => [3,2,2,2,1,1,1]
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]
0000000000 => [11] => [11]
0001100110 => [4,1,3,1,2] => [2,1,3,1,4]
0001111000 => [4,1,1,1,4] => [4,1,1,1,4]
0110000110 => [2,1,5,1,2] => [2,1,5,1,2]
0110011000 => [2,1,3,1,4] => [4,1,3,1,2]
0110011110 => [2,1,3,1,1,1,2] => [2,1,1,1,3,1,2]
0111100110 => [2,1,1,1,3,1,2] => [2,1,3,1,1,1,2]
0111111110 => [2,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,2]
00101010101 => [3,2,2,2,2,1] => [1,2,2,2,2,3]
00101010111 => [3,2,2,2,1,1,1] => [1,1,1,2,2,2,3]
00101010011 => [3,2,2,3,1,1] => [1,1,3,2,2,3]
00101011011 => [3,2,2,1,2,1,1] => [1,1,2,1,2,2,3]
00101101011 => [3,2,1,2,2,1,1] => [1,1,2,2,1,2,3]
00100101011 => [3,3,2,2,1,1] => [1,1,2,2,3,3]
00110101011 => [3,1,2,2,2,1,1] => [1,1,2,2,2,1,3]
01010101011 => [2,2,2,2,2,1,1] => [1,1,2,2,2,2,2]
0000000010 => [9,2] => [2,9]
0000111110 => [5,1,1,1,1,2] => [2,1,1,1,1,5]
00000000000 => [12] => [12]
00000000010 => [10,2] => [2,10]
01111111110 => [2,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,2]
0011001100 => [3,1,3,1,3] => [3,1,3,1,3]
0011010010 => [3,1,2,3,2] => [2,3,2,1,3]
0011011000 => [3,1,2,1,4] => [4,1,2,1,3]
0110001100 => [2,1,4,1,3] => [3,1,4,1,2]
10101010101 => [1,2,2,2,2,2,1] => [1,2,2,2,2,2,1]
10101010010 => [1,2,2,2,3,2] => [2,3,2,2,2,1]
10101001001 => [1,2,2,3,3,1] => [1,3,3,2,2,1]
10101001010 => [1,2,2,3,2,2] => [2,2,3,2,2,1]
10101000100 => [1,2,2,4,3] => [3,4,2,2,1]
10100100101 => [1,2,3,3,2,1] => [1,2,3,3,2,1]
10100100010 => [1,2,3,4,2] => [2,4,3,2,1]
10100101001 => [1,2,3,2,3,1] => [1,3,2,3,2,1]
10100100100 => [1,2,3,3,3] => [3,3,3,2,1]
10100010001 => [1,2,4,4,1] => [1,4,4,2,1]
10100010100 => [1,2,4,2,3] => [3,2,4,2,1]
10100001000 => [1,2,5,4] => [4,5,2,1]
10010010101 => [1,3,3,2,2,1] => [1,2,2,3,3,1]
10010001001 => [1,3,4,3,1] => [1,3,4,3,1]
10010100101 => [1,3,2,3,2,1] => [1,2,3,2,3,1]
10010101001 => [1,3,2,2,3,1] => [1,3,2,2,3,1]
10010100100 => [1,3,2,3,3] => [3,3,2,3,1]
10010010001 => [1,3,3,4,1] => [1,4,3,3,1]
10001000101 => [1,4,4,2,1] => [1,2,4,4,1]
10001001001 => [1,4,3,3,1] => [1,3,3,4,1]
10001010001 => [1,4,2,4,1] => [1,4,2,4,1]
10000100001 => [1,5,5,1] => [1,5,5,1]
01001010101 => [2,3,2,2,2,1] => [1,2,2,2,3,2]
01001010010 => [2,3,2,3,2] => [2,3,2,3,2]
01001001001 => [2,3,3,3,1] => [1,3,3,3,2]
01001001010 => [2,3,3,2,2] => [2,2,3,3,2]
01001000100 => [2,3,4,3] => [3,4,3,2]
01000100101 => [2,4,3,2,1] => [1,2,3,4,2]
01000100010 => [2,4,4,2] => [2,4,4,2]
01000101001 => [2,4,2,3,1] => [1,3,2,4,2]
01000101010 => [2,4,2,2,2] => [2,2,2,4,2]
01000100100 => [2,4,3,3] => [3,3,4,2]
01000010001 => [2,5,4,1] => [1,4,5,2]
01000010010 => [2,5,3,2] => [2,3,5,2]
01000010100 => [2,5,2,3] => [3,2,5,2]
01000001000 => [2,6,4] => [4,6,2]
01010010101 => [2,2,3,2,2,1] => [1,2,2,3,2,2]
01010010010 => [2,2,3,3,2] => [2,3,3,2,2]
01010001001 => [2,2,4,3,1] => [1,3,4,2,2]
01010001010 => [2,2,4,2,2] => [2,2,4,2,2]
01010000100 => [2,2,5,3] => [3,5,2,2]
01010100101 => [2,2,2,3,2,1] => [1,2,3,2,2,2]
01010100010 => [2,2,2,4,2] => [2,4,2,2,2]
01010101001 => [2,2,2,2,3,1] => [1,3,2,2,2,2]
01010101010 => [2,2,2,2,2,2] => [2,2,2,2,2,2]
01010100100 => [2,2,2,3,3] => [3,3,2,2,2]
01010010001 => [2,2,3,4,1] => [1,4,3,2,2]
01010010100 => [2,2,3,2,3] => [3,2,3,2,2]
01010001000 => [2,2,4,4] => [4,4,2,2]
01001000101 => [2,3,4,2,1] => [1,2,4,3,2]
01001000010 => [2,3,5,2] => [2,5,3,2]
01001010001 => [2,3,2,4,1] => [1,4,2,3,2]
01001010100 => [2,3,2,2,3] => [3,2,2,3,2]
01001001000 => [2,3,3,4] => [4,3,3,2]
01000100001 => [2,4,5,1] => [1,5,4,2]
01000101000 => [2,4,2,4] => [4,2,4,2]
01000010000 => [2,5,5] => [5,5,2]
00100010101 => [3,4,2,2,1] => [1,2,2,4,3]
00100010010 => [3,4,3,2] => [2,3,4,3]
00100001001 => [3,5,3,1] => [1,3,5,3]
00100001010 => [3,5,2,2] => [2,2,5,3]
00100000100 => [3,6,3] => [3,6,3]
00100100101 => [3,3,3,2,1] => [1,2,3,3,3]
00100100010 => [3,3,4,2] => [2,4,3,3]
00100101001 => [3,3,2,3,1] => [1,3,2,3,3]
00100101010 => [3,3,2,2,2] => [2,2,2,3,3]
00100100100 => [3,3,3,3] => [3,3,3,3]
00100010001 => [3,4,4,1] => [1,4,4,3]
00100010100 => [3,4,2,3] => [3,2,4,3]
00100001000 => [3,5,4] => [4,5,3]
00101000101 => [3,2,4,2,1] => [1,2,4,2,3]
00101000010 => [3,2,5,2] => [2,5,2,3]
00101001001 => [3,2,3,3,1] => [1,3,3,2,3]
00101001010 => [3,2,3,2,2] => [2,2,3,2,3]
00101000100 => [3,2,4,3] => [3,4,2,3]
00101010001 => [3,2,2,4,1] => [1,4,2,2,3]
00101010010 => [3,2,2,3,2] => [2,3,2,2,3]
00101010100 => [3,2,2,2,3] => [3,2,2,2,3]
00101001000 => [3,2,3,4] => [4,3,2,3]
00100100001 => [3,3,5,1] => [1,5,3,3]
00100101000 => [3,3,2,4] => [4,2,3,3]
00100010000 => [3,4,5] => [5,4,3]
00010000101 => [4,5,2,1] => [1,2,5,4]
00010000010 => [4,6,2] => [2,6,4]
00010001001 => [4,4,3,1] => [1,3,4,4]
00010001010 => [4,4,2,2] => [2,2,4,4]
00010000100 => [4,5,3] => [3,5,4]
00010010001 => [4,3,4,1] => [1,4,3,4]
00010010010 => [4,3,3,2] => [2,3,3,4]
00010010100 => [4,3,2,3] => [3,2,3,4]
00010001000 => [4,4,4] => [4,4,4]
00010100001 => [4,2,5,1] => [1,5,2,4]
00010100010 => [4,2,4,2] => [2,4,2,4]
00010100100 => [4,2,3,3] => [3,3,2,4]
00010101000 => [4,2,2,4] => [4,2,2,4]
00010010000 => [4,3,5] => [5,3,4]
00001000001 => [5,6,1] => [1,6,5]
00001000010 => [5,5,2] => [2,5,5]
00001000100 => [5,4,3] => [3,4,5]
00001001000 => [5,3,4] => [4,3,5]
00001010000 => [5,2,5] => [5,2,5]
00000100000 => [6,6] => [6,6]
0100000000 => [2,9] => [9,2]
0101111111 => [2,2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2,2]
01000000000 => [2,10] => [10,2]
01000011111 => [2,5,1,1,1,1,1] => [1,1,1,1,1,5,2]
0110111111 => [2,1,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1,2]
01011111111 => [2,2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2,2]
0101011010 => [2,2,2,1,2,2] => [2,2,1,2,2,2]
0110011001 => [2,1,3,1,3,1] => [1,3,1,3,1,2]
0110100101 => [2,1,2,3,2,1] => [1,2,3,2,1,2]
0110110001 => [2,1,2,1,4,1] => [1,4,1,2,1,2]
010110100101 => [2,2,1,2,3,2,1] => [1,2,3,2,1,2,2]
0000000101 => [8,2,1] => [1,2,8]
0000001101 => [7,1,2,1] => [1,2,1,7]
0000001001 => [7,3,1] => [1,3,7]
00001111101 => [5,1,1,1,1,2,1] => [1,2,1,1,1,1,5]
11111111101 => [1,1,1,1,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,1,1,1,1]
0111000011 => [2,1,1,5,1,1] => [1,1,5,1,1,2]
0011110001 => [3,1,1,1,4,1] => [1,4,1,1,1,3]
01111111011 => [2,1,1,1,1,1,1,2,1,1] => [1,1,2,1,1,1,1,1,1,2]
0011011001 => [3,1,2,1,3,1] => [1,3,1,2,1,3]
0001100001 => [4,1,5,1] => [1,5,1,4]
0001000001 => [4,6,1] => [1,6,4]
0011110011 => [3,1,1,1,3,1,1] => [1,1,3,1,1,1,3]
0111100011 => [2,1,1,1,4,1,1] => [1,1,4,1,1,1,2]
111010101001 => [1,1,1,2,2,2,3,1] => [1,3,2,2,2,1,1,1]
111101001001 => [1,1,1,1,2,3,3,1] => [1,3,3,2,1,1,1,1]
0001101100 => [4,1,2,1,3] => [3,1,2,1,4]
0011000110 => [3,1,4,1,2] => [2,1,4,1,3]
10111111101 => [1,2,1,1,1,1,1,1,2,1] => [1,2,1,1,1,1,1,1,2,1]
00010111101 => [4,2,1,1,1,2,1] => [1,2,1,1,1,2,4]
0000010001 => [6,4,1] => [1,4,6]
10000000001 => [1,10,1] => [1,10,1]
11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1]
0110011011 => [2,1,3,1,2,1,1] => [1,1,2,1,3,1,2]
0110110011 => [2,1,2,1,3,1,1] => [1,1,3,1,2,1,2]
0110110111 => [2,1,2,1,2,1,1,1] => [1,1,1,2,1,2,1,2]
01010101101 => [2,2,2,2,1,2,1] => [1,2,1,2,2,2,2]
01010110110 => [2,2,2,1,2,1,2] => [2,1,2,1,2,2,2]
01010110101 => [2,2,2,1,2,2,1] => [1,2,2,1,2,2,2]
01010111011 => [2,2,2,1,1,2,1,1] => [1,1,2,1,1,2,2,2]
01011011010 => [2,2,1,2,1,2,2] => [2,2,1,2,1,2,2]
01011011101 => [2,2,1,2,1,1,2,1] => [1,2,1,1,2,1,2,2]
01011010110 => [2,2,1,2,2,1,2] => [2,1,2,2,1,2,2]
01011010101 => [2,2,1,2,2,2,1] => [1,2,2,2,1,2,2]
01011101110 => [2,2,1,1,2,1,1,2] => [2,1,1,2,1,1,2,2]
01011101101 => [2,2,1,1,2,1,2,1] => [1,2,1,2,1,1,2,2]
01011101011 => [2,2,1,1,2,2,1,1] => [1,1,2,2,1,1,2,2]
01101101010 => [2,1,2,1,2,2,2] => [2,2,2,1,2,1,2]
01101101101 => [2,1,2,1,2,1,2,1] => [1,2,1,2,1,2,1,2]
01101110110 => [2,1,2,1,1,2,1,2] => [2,1,2,1,1,2,1,2]
01101110101 => [2,1,2,1,1,2,2,1] => [1,2,2,1,1,2,1,2]
01101011010 => [2,1,2,2,1,2,2] => [2,2,1,2,2,1,2]
01101011101 => [2,1,2,2,1,1,2,1] => [1,2,1,1,2,2,1,2]
01101010110 => [2,1,2,2,2,1,2] => [2,1,2,2,2,1,2]
01101010101 => [2,1,2,2,2,2,1] => [1,2,2,2,2,1,2]
01101011011 => [2,1,2,2,1,2,1,1] => [1,1,2,1,2,2,1,2]
01110111010 => [2,1,1,2,1,1,2,2] => [2,2,1,1,2,1,1,2]
01110111101 => [2,1,1,2,1,1,1,2,1] => [1,2,1,1,1,2,1,1,2]
01110110110 => [2,1,1,2,1,2,1,2] => [2,1,2,1,2,1,1,2]
01110110101 => [2,1,1,2,1,2,2,1] => [1,2,2,1,2,1,1,2]
01110111011 => [2,1,1,2,1,1,2,1,1] => [1,1,2,1,1,2,1,1,2]
01110101110 => [2,1,1,2,2,1,1,2] => [2,1,1,2,2,1,1,2]
01110101101 => [2,1,1,2,2,1,2,1] => [1,2,1,2,2,1,1,2]
01110101011 => [2,1,1,2,2,2,1,1] => [1,1,2,2,2,1,1,2]
01110110111 => [2,1,1,2,1,2,1,1,1] => [1,1,1,2,1,2,1,1,2]
01111101111 => [2,1,1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1,1,2]
10110101010 => [1,2,1,2,2,2,2] => [2,2,2,2,1,2,1]
10110101101 => [1,2,1,2,2,1,2,1] => [1,2,1,2,2,1,2,1]
10110110101 => [1,2,1,2,1,2,2,1] => [1,2,2,1,2,1,2,1]
10110111011 => [1,2,1,2,1,1,2,1,1] => [1,1,2,1,1,2,1,2,1]
10111011010 => [1,2,1,1,2,1,2,2] => [2,2,1,2,1,1,2,1]
10111011101 => [1,2,1,1,2,1,1,2,1] => [1,2,1,1,2,1,1,2,1]
10111010101 => [1,2,1,1,2,2,2,1] => [1,2,2,2,1,1,2,1]
10111011011 => [1,2,1,1,2,1,2,1,1] => [1,1,2,1,2,1,1,2,1]
10111101101 => [1,2,1,1,1,2,1,2,1] => [1,2,1,2,1,1,1,2,1]
10111101011 => [1,2,1,1,1,2,2,1,1] => [1,1,2,2,1,1,1,2,1]
10111110111 => [1,2,1,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,1,2,1]
10101101010 => [1,2,2,1,2,2,2] => [2,2,2,1,2,2,1]
10101101101 => [1,2,2,1,2,1,2,1] => [1,2,1,2,1,2,2,1]
10101110101 => [1,2,2,1,1,2,2,1] => [1,2,2,1,1,2,2,1]
10101111011 => [1,2,2,1,1,1,2,1,1] => [1,1,2,1,1,1,2,2,1]
10101011101 => [1,2,2,2,1,1,2,1] => [1,2,1,1,2,2,2,1]
10101011011 => [1,2,2,2,1,2,1,1] => [1,1,2,1,2,2,2,1]
10101101011 => [1,2,2,1,2,2,1,1] => [1,1,2,2,1,2,2,1]
10101110111 => [1,2,2,1,1,2,1,1,1] => [1,1,1,2,1,1,2,2,1]
10110111101 => [1,2,1,2,1,1,1,2,1] => [1,2,1,1,1,2,1,2,1]
10110101011 => [1,2,1,2,2,2,1,1] => [1,1,2,2,2,1,2,1]
10110110111 => [1,2,1,2,1,2,1,1,1] => [1,1,1,2,1,2,1,2,1]
10111010111 => [1,2,1,1,2,2,1,1,1] => [1,1,1,2,2,1,1,2,1]
10111101111 => [1,2,1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1,2,1]
11011101010 => [1,1,2,1,1,2,2,2] => [2,2,2,1,1,2,1,1]
11011101101 => [1,1,2,1,1,2,1,2,1] => [1,2,1,2,1,1,2,1,1]
11011110101 => [1,1,2,1,1,1,2,2,1] => [1,2,2,1,1,1,2,1,1]
11011111011 => [1,1,2,1,1,1,1,2,1,1] => [1,1,2,1,1,1,1,2,1,1]
11011011010 => [1,1,2,1,2,1,2,2] => [2,2,1,2,1,2,1,1]
11011011101 => [1,1,2,1,2,1,1,2,1] => [1,2,1,1,2,1,2,1,1]
11011010110 => [1,1,2,1,2,2,1,2] => [2,1,2,2,1,2,1,1]
11011010101 => [1,1,2,1,2,2,2,1] => [1,2,2,2,1,2,1,1]
11011011011 => [1,1,2,1,2,1,2,1,1] => [1,1,2,1,2,1,2,1,1]
11011101011 => [1,1,2,1,1,2,2,1,1] => [1,1,2,2,1,1,2,1,1]
11011110111 => [1,1,2,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,2,1,1]
11010111010 => [1,1,2,2,1,1,2,2] => [2,2,1,1,2,2,1,1]
11010111101 => [1,1,2,2,1,1,1,2,1] => [1,2,1,1,1,2,2,1,1]
11010110101 => [1,1,2,2,1,2,2,1] => [1,2,2,1,2,2,1,1]
11010111011 => [1,1,2,2,1,1,2,1,1] => [1,1,2,1,1,2,2,1,1]
11010101101 => [1,1,2,2,2,1,2,1] => [1,2,1,2,2,2,1,1]
11010101011 => [1,1,2,2,2,2,1,1] => [1,1,2,2,2,2,1,1]
11010110111 => [1,1,2,2,1,2,1,1,1] => [1,1,1,2,1,2,2,1,1]
11011010111 => [1,1,2,1,2,2,1,1,1] => [1,1,1,2,2,1,2,1,1]
11011101111 => [1,1,2,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,2,1,1]
11101111101 => [1,1,1,2,1,1,1,1,2,1] => [1,2,1,1,1,1,2,1,1,1]
11101110101 => [1,1,1,2,1,1,2,2,1] => [1,2,2,1,1,2,1,1,1]
11101111011 => [1,1,1,2,1,1,1,2,1,1] => [1,1,2,1,1,1,2,1,1,1]
11101101101 => [1,1,1,2,1,2,1,2,1] => [1,2,1,2,1,2,1,1,1]
11101101011 => [1,1,1,2,1,2,2,1,1] => [1,1,2,2,1,2,1,1,1]
11101110111 => [1,1,1,2,1,1,2,1,1,1] => [1,1,1,2,1,1,2,1,1,1]
11101011101 => [1,1,1,2,2,1,1,2,1] => [1,2,1,1,2,2,1,1,1]
11101011011 => [1,1,1,2,2,1,2,1,1] => [1,1,2,1,2,2,1,1,1]
11101010111 => [1,1,1,2,2,2,1,1,1] => [1,1,1,2,2,2,1,1,1]
11101101111 => [1,1,1,2,1,2,1,1,1,1] => [1,1,1,1,2,1,2,1,1,1]
11110111101 => [1,1,1,1,2,1,1,1,2,1] => [1,2,1,1,1,2,1,1,1,1]
11110111011 => [1,1,1,1,2,1,1,2,1,1] => [1,1,2,1,1,2,1,1,1,1]
11110110111 => [1,1,1,1,2,1,2,1,1,1] => [1,1,1,2,1,2,1,1,1,1]
11110101111 => [1,1,1,1,2,2,1,1,1,1] => [1,1,1,1,2,2,1,1,1,1]
11111011111 => [1,1,1,1,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,1,1,1,1]
0011001111 => [3,1,3,1,1,1,1] => [1,1,1,1,3,1,3]
0110011111 => [2,1,3,1,1,1,1,1] => [1,1,1,1,1,3,1,2]
00011001111 => [4,1,3,1,1,1,1] => [1,1,1,1,3,1,4]
0000000011 => [9,1,1] => [1,1,9]
00001101111 => [5,1,2,1,1,1,1] => [1,1,1,1,2,1,5]
11011111111 => [1,1,2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2,1,1]
01111010101 => [2,1,1,1,2,2,2,1] => [1,2,2,2,1,1,1,2]
0111100111 => [2,1,1,1,3,1,1,1] => [1,1,1,3,1,1,1,2]
0111110111 => [2,1,1,1,1,2,1,1,1] => [1,1,1,2,1,1,1,1,2]
0001000100 => [4,4,3] => [3,4,4]
0001100011 => [4,1,4,1,1] => [1,1,4,1,4]
0111101111 => [2,1,1,1,2,1,1,1,1] => [1,1,1,1,2,1,1,1,2]
101101010101 => [1,2,1,2,2,2,2,1] => [1,2,2,2,2,1,2,1]
101101001011 => [1,2,1,2,3,2,1,1] => [1,1,2,3,2,1,2,1]
0011111111 => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,3]
00000111111 => [6,1,1,1,1,1,1] => [1,1,1,1,1,1,6]
10111111111 => [1,2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,2,1]
10000101111 => [1,5,2,1,1,1,1] => [1,1,1,1,2,5,1]
10101111111 => [1,2,2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2,2,1]
0011011110 => [3,1,2,1,1,1,2] => [2,1,1,1,2,1,3]
0011110110 => [3,1,1,1,2,1,2] => [2,1,2,1,1,1,3]
0011111100 => [3,1,1,1,1,1,3] => [3,1,1,1,1,1,3]
00101111110 => [3,2,1,1,1,1,1,2] => [2,1,1,1,1,1,2,3]
00111011110 => [3,1,1,2,1,1,1,2] => [2,1,1,1,2,1,1,3]
00111110110 => [3,1,1,1,1,2,1,2] => [2,1,2,1,1,1,1,3]
00111111100 => [3,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,3]
0111101101 => [2,1,1,1,2,1,2,1] => [1,2,1,2,1,1,1,2]
0110001101 => [2,1,4,1,2,1] => [1,2,1,4,1,2]
0110111101 => [2,1,2,1,1,1,2,1] => [1,2,1,1,1,2,1,2]
11010001000 => [1,1,2,4,4] => [4,4,2,1,1]
00010010101 => [4,3,2,2,1] => [1,2,2,3,4]
00010100101 => [4,2,3,2,1] => [1,2,3,2,4]
00010101001 => [4,2,2,3,1] => [1,3,2,2,4]
00010101010 => [4,2,2,2,2] => [2,2,2,2,4]
00000100010 => [6,4,2] => [2,4,6]
01000100000 => [2,4,6] => [6,4,2]
0101010111 => [2,2,2,2,1,1,1] => [1,1,1,2,2,2,2]
01101010100 => [2,1,2,2,2,3] => [3,2,2,2,1,2]
01101001010 => [2,1,2,3,2,2] => [2,2,3,2,1,2]
01100101010 => [2,1,3,2,2,2] => [2,2,2,3,1,2]
01110101010 => [2,1,1,2,2,2,2] => [2,2,2,2,1,1,2]
0101110101 => [2,2,1,1,2,2,1] => [1,2,2,1,1,2,2]
01111100100 => [2,1,1,1,1,3,3] => [3,3,1,1,1,1,2]
01000101111 => [2,4,2,1,1,1,1] => [1,1,1,1,2,4,2]
10000011111 => [1,6,1,1,1,1,1] => [1,1,1,1,1,6,1]
01010101000 => [2,2,2,2,4] => [4,2,2,2,2]
01000000010 => [2,8,2] => [2,8,2]
00010000000 => [4,8] => [8,4]
00000001000 => [8,4] => [4,8]
01010100111 => [2,2,2,3,1,1,1] => [1,1,1,3,2,2,2]
01010010111 => [2,2,3,2,1,1,1] => [1,1,1,2,3,2,2]
01001010111 => [2,3,2,2,1,1,1] => [1,1,1,2,2,3,2]
01000111011 => [2,4,1,1,2,1,1] => [1,1,2,1,1,4,2]
00010111011 => [4,2,1,1,2,1,1] => [1,1,2,1,1,2,4]
00010101101 => [4,2,2,1,2,1] => [1,2,1,2,2,4]
00010110101 => [4,2,1,2,2,1] => [1,2,2,1,2,4]
00011010101 => [4,1,2,2,2,1] => [1,2,2,2,1,4]
01010101111 => [2,2,2,2,1,1,1,1] => [1,1,1,1,2,2,2,2]
10101010111 => [1,2,2,2,2,1,1,1] => [1,1,1,2,2,2,2,1]
11010000100 => [1,1,2,5,3] => [3,5,2,1,1]
11011110100 => [1,1,2,1,1,1,2,3] => [3,2,1,1,1,2,1,1]
0110001111 => [2,1,4,1,1,1,1] => [1,1,1,1,4,1,2]
0101101011 => [2,2,1,2,2,1,1] => [1,1,2,2,1,2,2]
0011000011 => [3,1,5,1,1] => [1,1,5,1,3]
0011011011 => [3,1,2,1,2,1,1] => [1,1,2,1,2,1,3]
111111001111 => [1,1,1,1,1,1,3,1,1,1,1] => [1,1,1,1,3,1,1,1,1,1,1]
01010110100 => [2,2,2,1,2,3] => [3,2,1,2,2,2]
0111011111 => [2,1,1,2,1,1,1,1,1] => [1,1,1,1,1,2,1,1,2]
111101010101 => [1,1,1,1,2,2,2,2,1] => [1,2,2,2,2,1,1,1,1]
10111101000 => [1,2,1,1,1,2,4] => [4,2,1,1,1,2,1]
11111101010 => [1,1,1,1,1,1,2,2,2] => [2,2,2,1,1,1,1,1,1]
11111111111111 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
11111111111111111111 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
01110111111 => [2,1,1,2,1,1,1,1,1,1] => [1,1,1,1,1,1,2,1,1,2]
0000110000 => [5,1,5] => [5,1,5]
11110001000 => [1,1,1,1,4,4] => [4,4,1,1,1,1]
11000111000 => [1,1,4,1,1,4] => [4,1,1,4,1,1]
11000100011 => [1,1,4,4,1,1] => [1,1,4,4,1,1]
11010001011 => [1,1,2,4,2,1,1] => [1,1,2,4,2,1,1]
00011111000 => [4,1,1,1,1,4] => [4,1,1,1,1,4]
00011100011 => [4,1,1,4,1,1] => [1,1,4,1,1,4]
00010001111 => [4,4,1,1,1,1] => [1,1,1,1,4,4]
00010111010 => [4,2,1,1,2,2] => [2,2,1,1,2,4]
01110001000 => [2,1,1,4,4] => [4,4,1,1,2]
01110001110 => [2,1,1,4,1,1,2] => [2,1,1,4,1,1,2]
01110111110 => [2,1,1,2,1,1,1,1,2] => [2,1,1,1,1,2,1,1,2]
01111101110 => [2,1,1,1,1,2,1,1,2] => [2,1,1,2,1,1,1,1,2]
01110001011 => [2,1,1,4,2,1,1] => [1,1,2,4,1,1,2]
01000100011 => [2,4,4,1,1] => [1,1,4,4,2]
01000111000 => [2,4,1,1,4] => [4,1,1,4,2]
01000111110 => [2,4,1,1,1,1,2] => [2,1,1,1,1,4,2]
01011111010 => [2,2,1,1,1,1,2,2] => [2,2,1,1,1,1,2,2]
0000100001 => [5,5,1] => [1,5,5]
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
reverse
Description
Return the reversal of a composition.
That is, the composition (i1,i2,…,ik) is sent to (ik,ik−1,…,i1).
That is, the composition (i1,i2,…,ik) is sent to (ik,ik−1,…,i1).
searching the database
Sorry, this map was not found in the database.