Identifier
Values
0 => 0 => [1] => [1,0] => 2
1 => 1 => [1] => [1,0] => 2
00 => 00 => [2] => [1,1,0,0] => 3
01 => 10 => [1,1] => [1,0,1,0] => 2
10 => 01 => [1,1] => [1,0,1,0] => 2
11 => 11 => [2] => [1,1,0,0] => 3
000 => 000 => [3] => [1,1,1,0,0,0] => 4
001 => 100 => [1,2] => [1,0,1,1,0,0] => 2
010 => 001 => [2,1] => [1,1,0,0,1,0] => 3
011 => 101 => [1,1,1] => [1,0,1,0,1,0] => 2
100 => 010 => [1,1,1] => [1,0,1,0,1,0] => 2
101 => 110 => [2,1] => [1,1,0,0,1,0] => 3
110 => 011 => [1,2] => [1,0,1,1,0,0] => 2
111 => 111 => [3] => [1,1,1,0,0,0] => 4
0000 => 0000 => [4] => [1,1,1,1,0,0,0,0] => 5
0001 => 1000 => [1,3] => [1,0,1,1,1,0,0,0] => 2
0010 => 0001 => [3,1] => [1,1,1,0,0,0,1,0] => 4
0011 => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
0100 => 0010 => [2,1,1] => [1,1,0,0,1,0,1,0] => 3
0101 => 1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
0110 => 0011 => [2,2] => [1,1,0,0,1,1,0,0] => 3
0111 => 1011 => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
1000 => 0100 => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
1001 => 1100 => [2,2] => [1,1,0,0,1,1,0,0] => 3
1010 => 0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 2
1011 => 1101 => [2,1,1] => [1,1,0,0,1,0,1,0] => 3
1100 => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
1101 => 1110 => [3,1] => [1,1,1,0,0,0,1,0] => 4
1110 => 0111 => [1,3] => [1,0,1,1,1,0,0,0] => 2
1111 => 1111 => [4] => [1,1,1,1,0,0,0,0] => 5
00000 => 00000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 6
00001 => 10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
00010 => 00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
00011 => 10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
00100 => 00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 4
00101 => 10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
00110 => 00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 4
00111 => 10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
01000 => 00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 3
01001 => 10100 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
01010 => 00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 3
01011 => 10101 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
01100 => 00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
01101 => 10110 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
01110 => 00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
01111 => 10111 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
10000 => 01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
10001 => 11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
10010 => 01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
10011 => 11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 3
10100 => 01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 2
10101 => 11010 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 3
10110 => 01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
10111 => 11011 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 3
11000 => 01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
11001 => 11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 4
11010 => 01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
11011 => 11101 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 4
11100 => 01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
11101 => 11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
11110 => 01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
11111 => 11111 => [5] => [1,1,1,1,1,0,0,0,0,0] => 6
000000 => 000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
000001 => 100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
000010 => 000001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
000011 => 100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
000100 => 000010 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
000101 => 100010 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
000110 => 000011 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 5
000111 => 100011 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
001000 => 000100 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
001001 => 100100 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
001010 => 000101 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
001011 => 100101 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
001100 => 000110 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 4
001101 => 100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
001110 => 000111 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
001111 => 100111 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
010000 => 001000 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
010001 => 101000 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
010010 => 001001 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
010011 => 101001 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
010100 => 001010 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 3
010101 => 101010 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 2
010110 => 001011 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
010111 => 101011 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
011000 => 001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
011001 => 101100 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
011010 => 001101 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
011011 => 101101 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
011100 => 001110 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
011101 => 101110 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
011110 => 001111 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
011111 => 101111 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
100000 => 010000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
100001 => 110000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
100010 => 010001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
100011 => 110001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
100100 => 010010 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
100101 => 110010 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
100110 => 010011 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
>>> Load all 533 entries. <<<
100111 => 110011 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
101000 => 010100 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
101001 => 110100 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
101010 => 010101 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 2
101011 => 110101 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 3
101100 => 010110 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
101101 => 110110 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
101110 => 010111 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
101111 => 110111 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
110000 => 011000 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
110001 => 111000 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
110010 => 011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
110011 => 111001 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 4
110100 => 011010 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
110101 => 111010 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
110110 => 011011 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
110111 => 111011 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
111000 => 011100 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
111001 => 111100 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 5
111010 => 011101 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
111011 => 111101 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
111100 => 011110 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
111101 => 111110 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
111110 => 011111 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
111111 => 111111 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
0000000 => 0000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
0000001 => 1000000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
0000010 => 0000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
0000011 => 1000001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
0000100 => 0000010 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
0000101 => 1000010 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
0000110 => 0000011 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
0000111 => 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
0001000 => 0000100 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
0001001 => 1000100 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
0001010 => 0000101 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
0001011 => 1000101 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
0001100 => 0000110 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 5
0001101 => 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
0001110 => 0000111 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
0001111 => 1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
0010000 => 0001000 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
0010001 => 1001000 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
0010010 => 0001001 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
0010011 => 1001001 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
0010100 => 0001010 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
0010101 => 1001010 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
0010110 => 0001011 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
0010111 => 1001011 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
0011000 => 0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
0011001 => 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
0011010 => 0001101 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
0011011 => 1001101 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
0011100 => 0001110 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
0011101 => 1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
0011110 => 0001111 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
0011111 => 1001111 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
0100000 => 0010000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
0100001 => 1010000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
0100010 => 0010001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
0100011 => 1010001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
0100100 => 0010010 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
0100101 => 1010010 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
0100110 => 0010011 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
0100111 => 1010011 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
0101000 => 0010100 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
0101001 => 1010100 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0101010 => 0010101 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
0101011 => 1010101 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
0101100 => 0010110 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
0101101 => 1010110 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
0101110 => 0010111 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
0101111 => 1010111 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
0110000 => 0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
0110001 => 1011000 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
0110010 => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
0110011 => 1011001 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
0110100 => 0011010 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
0110101 => 1011010 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
0110110 => 0011011 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
0110111 => 1011011 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
0111000 => 0011100 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
0111001 => 1011100 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
0111010 => 0011101 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
0111011 => 1011101 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
0111100 => 0011110 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
0111101 => 1011110 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
0111110 => 0011111 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
0111111 => 1011111 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
1000000 => 0100000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
1000001 => 1100000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
1000010 => 0100001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
1000011 => 1100001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
1000100 => 0100010 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
1000101 => 1100010 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
1000110 => 0100011 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
1000111 => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
1001000 => 0100100 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
1001001 => 1100100 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
1001010 => 0100101 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
1001011 => 1100101 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
1001100 => 0100110 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
1001101 => 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
1001110 => 0100111 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
1001111 => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
1010000 => 0101000 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
1010001 => 1101000 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
1010010 => 0101001 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
1010011 => 1101001 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
1010100 => 0101010 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
1010101 => 1101010 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
1010110 => 0101011 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1010111 => 1101011 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
1011000 => 0101100 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
1011001 => 1101100 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
1011010 => 0101101 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
1011011 => 1101101 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
1011100 => 0101110 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
1011101 => 1101110 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
1011110 => 0101111 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
1011111 => 1101111 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
1100000 => 0110000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
1100001 => 1110000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
1100010 => 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
1100011 => 1110001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
1100100 => 0110010 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
1100101 => 1110010 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
1100110 => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
1100111 => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
1101000 => 0110100 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
1101001 => 1110100 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
1101010 => 0110101 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
1101011 => 1110101 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
1101100 => 0110110 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
1101101 => 1110110 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
1101110 => 0110111 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
1101111 => 1110111 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
1110000 => 0111000 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
1110001 => 1111000 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
1110010 => 0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
1110011 => 1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 5
1110100 => 0111010 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
1110101 => 1111010 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
1110110 => 0111011 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
1110111 => 1111011 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
1111000 => 0111100 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
1111001 => 1111100 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
1111010 => 0111101 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
1111011 => 1111101 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
1111100 => 0111110 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
1111101 => 1111110 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
1111110 => 0111111 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
1111111 => 1111111 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
00000000 => 00000000 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
00000001 => 10000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
00000010 => 00000001 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
00000011 => 10000001 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
00000101 => 10000010 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
00000110 => 00000011 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 7
00000111 => 10000011 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
00001001 => 10000100 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
00001011 => 10000101 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
00001101 => 10000110 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
00001111 => 10000111 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
00010001 => 10001000 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
00010011 => 10001001 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
00010101 => 10001010 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
00010111 => 10001011 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
00011000 => 00001100 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5
00011001 => 10001100 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
00011011 => 10001101 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
00011101 => 10001110 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
00011110 => 00001111 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 5
00011111 => 10001111 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
00100001 => 10010000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
00100011 => 10010001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
00100101 => 10010010 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
00100111 => 10010011 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
00101000 => 00010100 => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 4
00101001 => 10010100 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
00101010 => 00010101 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
00101011 => 10010101 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
00101101 => 10010110 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
00101111 => 10010111 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
00110001 => 10011000 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
00110011 => 10011001 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
00110101 => 10011010 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
00110111 => 10011011 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
00111001 => 10011100 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
00111011 => 10011101 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
00111100 => 00011110 => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
00111101 => 10011110 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
00111111 => 10011111 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
01000000 => 00100000 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
01000001 => 10100000 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
01000010 => 00100001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
01000011 => 10100001 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
01000100 => 00100010 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
01000101 => 10100010 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
01000110 => 00100011 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
01000111 => 10100011 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
01001000 => 00100100 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
01001001 => 10100100 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
01001010 => 00100101 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3
01001011 => 10100101 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
01001100 => 00100110 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
01001101 => 10100110 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
01001110 => 00100111 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
01001111 => 10100111 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
01010000 => 00101000 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
01010001 => 10101000 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
01010010 => 00101001 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
01010011 => 10101001 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
01010100 => 00101010 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
01010101 => 10101010 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
01010110 => 00101011 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
01010111 => 10101011 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
01011000 => 00101100 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
01011001 => 10101100 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
01011010 => 00101101 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
01011011 => 10101101 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
01011100 => 00101110 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
01011101 => 10101110 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
01011110 => 00101111 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
01011111 => 10101111 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
01100000 => 00110000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
01100001 => 10110000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
01100010 => 00110001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
01100011 => 10110001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
01100100 => 00110010 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
01100101 => 10110010 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
01100110 => 00110011 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
01100111 => 10110011 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
01101000 => 00110100 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
01101001 => 10110100 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
01101010 => 00110101 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3
01101011 => 10110101 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
01101100 => 00110110 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
01101101 => 10110110 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
01101110 => 00110111 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
01101111 => 10110111 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
01110000 => 00111000 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
01110001 => 10111000 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
01110010 => 00111001 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
01110011 => 10111001 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
01110100 => 00111010 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
01110101 => 10111010 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
01110110 => 00111011 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
01110111 => 10111011 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
01111000 => 00111100 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
01111001 => 10111100 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
01111010 => 00111101 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
01111011 => 10111101 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
01111100 => 00111110 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
01111101 => 10111110 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
01111110 => 00111111 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
01111111 => 10111111 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
10000000 => 01000000 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
10000001 => 11000000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
10000010 => 01000001 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
10000011 => 11000001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
10000100 => 01000010 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
10000101 => 11000010 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
10000110 => 01000011 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
10000111 => 11000011 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
10001000 => 01000100 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
10001001 => 11000100 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
10001010 => 01000101 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
10001011 => 11000101 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
10001100 => 01000110 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
10001101 => 11000110 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
10001110 => 01000111 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
10001111 => 11000111 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
10010000 => 01001000 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
10010001 => 11001000 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
10010010 => 01001001 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
10010011 => 11001001 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
10010100 => 01001010 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
10010101 => 11001010 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3
10010110 => 01001011 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
10010111 => 11001011 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
10011000 => 01001100 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
10011001 => 11001100 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
10011010 => 01001101 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
10011011 => 11001101 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
10011100 => 01001110 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
10011101 => 11001110 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
10011110 => 01001111 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
10011111 => 11001111 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
10100000 => 01010000 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
10100001 => 11010000 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
10100010 => 01010001 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
10100011 => 11010001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
10100100 => 01010010 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
10100101 => 11010010 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
10100110 => 01010011 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
10100111 => 11010011 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
10101000 => 01010100 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
10101001 => 11010100 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
10101010 => 01010101 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
10101011 => 11010101 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
10101100 => 01010110 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
10101101 => 11010110 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
10101110 => 01010111 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
10101111 => 11010111 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
10110000 => 01011000 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
10110001 => 11011000 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
10110010 => 01011001 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
10110011 => 11011001 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
10110100 => 01011010 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
10110101 => 11011010 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3
10110110 => 01011011 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
10110111 => 11011011 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
10111000 => 01011100 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
10111001 => 11011100 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
10111010 => 01011101 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
10111011 => 11011101 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
10111100 => 01011110 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
10111101 => 11011110 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
10111110 => 01011111 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
10111111 => 11011111 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
11000000 => 01100000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
11000010 => 01100001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
11000011 => 11100001 => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
11000100 => 01100010 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
11000110 => 01100011 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
11001000 => 01100100 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
11001010 => 01100101 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
11001100 => 01100110 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
11001110 => 01100111 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
11010000 => 01101000 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
11010010 => 01101001 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
11010100 => 01101010 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
11010101 => 11101010 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
11010110 => 01101011 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
11010111 => 11101011 => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 4
11011000 => 01101100 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
11011010 => 01101101 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
11011100 => 01101110 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
11011110 => 01101111 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
11100000 => 01110000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
11100001 => 11110000 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 5
11100010 => 01110001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
11100100 => 01110010 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
11100110 => 01110011 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
11100111 => 11110011 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5
11101000 => 01110100 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
11101010 => 01110101 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
11101100 => 01110110 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
11101110 => 01110111 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
11110000 => 01111000 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
11110010 => 01111001 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
11110100 => 01111010 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
11110110 => 01111011 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
11111000 => 01111100 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
11111001 => 11111100 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 7
11111010 => 01111101 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
11111100 => 01111110 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
11111101 => 11111110 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 8
11111110 => 01111111 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
11111111 => 11111111 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
000000000 => 000000000 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
000000001 => 100000000 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
000000010 => 000000001 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9
000000011 => 100000001 => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
000000101 => 100000010 => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
000000110 => 000000011 => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 8
000000111 => 100000011 => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
000101011 => 100010101 => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
001010100 => 000101010 => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
001010111 => 100101011 => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
001111111 => 100111111 => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
010100111 => 101010011 => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
010101000 => 001010100 => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
010101001 => 101010100 => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
010101010 => 001010101 => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
010101100 => 001010110 => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
011111100 => 001111110 => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
011111101 => 101111110 => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
011111110 => 001111111 => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
011111111 => 101111111 => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
100000000 => 010000000 => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
100000001 => 110000000 => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 3
100000010 => 010000001 => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
100000011 => 110000001 => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
101010011 => 110101001 => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
101010101 => 110101010 => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
101010110 => 010101011 => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
101010111 => 110101011 => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
101011000 => 010101100 => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
110000000 => 011000000 => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
110101000 => 011010100 => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
110101011 => 111010101 => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
111010100 => 011101010 => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
111111000 => 011111100 => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
111111001 => 111111100 => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 8
111111010 => 011111101 => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
111111100 => 011111110 => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
111111101 => 111111110 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 9
111111110 => 011111111 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
111111111 => 111111111 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
1111111111 => 1111111111 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
1111111110 => 0111111111 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 2
1111111101 => 1111111110 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
1111111100 => 0111111110 => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
1111111001 => 1111111100 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 9
1101010101 => 1110101010 => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
1010101011 => 1101010101 => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
1010101001 => 1101010100 => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
1010101000 => 0101010100 => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1000000010 => 0100000001 => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
1000000001 => 1100000000 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
1000000000 => 0100000000 => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
10000000010 => 01000000001 => [1,1,8,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
11111111110 => 01111111111 => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 2
0111111111 => 1011111111 => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
0111111101 => 1011111110 => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
0000000001 => 1000000000 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 2
01111111101 => 10111111110 => [1,1,8,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
00000000001 => 10000000000 => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 2
0000000000 => 0000000000 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11
0000000110 => 0000000011 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 9
0111111110 => 0011111111 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 3
0010101010 => 0001010101 => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
0101010100 => 0010101010 => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
0000000010 => 0000000001 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 10
00000000010 => 00000000001 => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 11
0101010110 => 0010101011 => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
0000000101 => 1000000010 => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
11111111101 => 11111111110 => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 11
0000000011 => 1000000001 => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
0101010111 => 1010101011 => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
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Description
The position of the first down step of a Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.