Identifier
Values
0 => 1 => [1,1] => 2
1 => 1 => [1,1] => 2
00 => 01 => [2,1] => 3
01 => 10 => [1,2] => 3
10 => 11 => [1,1,1] => 2
11 => 11 => [1,1,1] => 2
000 => 001 => [3,1] => 3
001 => 010 => [2,2] => 4
010 => 101 => [1,2,1] => 4
011 => 101 => [1,2,1] => 4
100 => 101 => [1,2,1] => 4
101 => 110 => [1,1,2] => 3
110 => 111 => [1,1,1,1] => 2
111 => 111 => [1,1,1,1] => 2
0000 => 0001 => [4,1] => 3
0001 => 0010 => [3,2] => 4
0010 => 0101 => [2,2,1] => 5
0011 => 0101 => [2,2,1] => 5
0100 => 1001 => [1,3,1] => 4
0101 => 1010 => [1,2,2] => 5
0110 => 1011 => [1,2,1,1] => 4
0111 => 1011 => [1,2,1,1] => 4
1000 => 1001 => [1,3,1] => 4
1001 => 1010 => [1,2,2] => 5
1010 => 1101 => [1,1,2,1] => 4
1011 => 1101 => [1,1,2,1] => 4
1100 => 1101 => [1,1,2,1] => 4
1101 => 1110 => [1,1,1,2] => 3
1110 => 1111 => [1,1,1,1,1] => 2
1111 => 1111 => [1,1,1,1,1] => 2
00000 => 00001 => [5,1] => 3
00001 => 00010 => [4,2] => 4
00010 => 00101 => [3,2,1] => 5
00011 => 00101 => [3,2,1] => 5
00100 => 01001 => [2,3,1] => 5
00101 => 01010 => [2,2,2] => 6
00110 => 01011 => [2,2,1,1] => 5
00111 => 01011 => [2,2,1,1] => 5
01000 => 10001 => [1,4,1] => 4
01001 => 10010 => [1,3,2] => 5
01010 => 10101 => [1,2,2,1] => 6
01011 => 10101 => [1,2,2,1] => 6
01100 => 10101 => [1,2,2,1] => 6
01101 => 10110 => [1,2,1,2] => 5
01110 => 10111 => [1,2,1,1,1] => 4
01111 => 10111 => [1,2,1,1,1] => 4
10000 => 10001 => [1,4,1] => 4
10001 => 10010 => [1,3,2] => 5
10010 => 10101 => [1,2,2,1] => 6
10011 => 10101 => [1,2,2,1] => 6
10100 => 11001 => [1,1,3,1] => 4
10101 => 11010 => [1,1,2,2] => 5
10110 => 11011 => [1,1,2,1,1] => 4
10111 => 11011 => [1,1,2,1,1] => 4
11000 => 11001 => [1,1,3,1] => 4
11001 => 11010 => [1,1,2,2] => 5
11010 => 11101 => [1,1,1,2,1] => 4
11011 => 11101 => [1,1,1,2,1] => 4
11100 => 11101 => [1,1,1,2,1] => 4
11101 => 11110 => [1,1,1,1,2] => 3
11110 => 11111 => [1,1,1,1,1,1] => 2
11111 => 11111 => [1,1,1,1,1,1] => 2
000000 => 000001 => [6,1] => 3
000001 => 000010 => [5,2] => 4
000010 => 000101 => [4,2,1] => 5
000011 => 000101 => [4,2,1] => 5
000100 => 001001 => [3,3,1] => 5
000101 => 001010 => [3,2,2] => 6
000110 => 001011 => [3,2,1,1] => 5
000111 => 001011 => [3,2,1,1] => 5
001000 => 010001 => [2,4,1] => 5
001001 => 010010 => [2,3,2] => 6
001010 => 010101 => [2,2,2,1] => 7
001011 => 010101 => [2,2,2,1] => 7
001100 => 010101 => [2,2,2,1] => 7
001101 => 010110 => [2,2,1,2] => 6
001110 => 010111 => [2,2,1,1,1] => 5
001111 => 010111 => [2,2,1,1,1] => 5
010000 => 100001 => [1,5,1] => 4
010001 => 100010 => [1,4,2] => 5
010010 => 100101 => [1,3,2,1] => 6
010011 => 100101 => [1,3,2,1] => 6
010100 => 101001 => [1,2,3,1] => 6
010101 => 101010 => [1,2,2,2] => 7
010110 => 101011 => [1,2,2,1,1] => 6
010111 => 101011 => [1,2,2,1,1] => 6
011000 => 101001 => [1,2,3,1] => 6
011001 => 101010 => [1,2,2,2] => 7
011010 => 101101 => [1,2,1,2,1] => 6
011011 => 101101 => [1,2,1,2,1] => 6
011100 => 101101 => [1,2,1,2,1] => 6
011101 => 101110 => [1,2,1,1,2] => 5
011110 => 101111 => [1,2,1,1,1,1] => 4
011111 => 101111 => [1,2,1,1,1,1] => 4
100000 => 100001 => [1,5,1] => 4
100001 => 100010 => [1,4,2] => 5
100010 => 100101 => [1,3,2,1] => 6
100011 => 100101 => [1,3,2,1] => 6
100100 => 101001 => [1,2,3,1] => 6
100101 => 101010 => [1,2,2,2] => 7
100110 => 101011 => [1,2,2,1,1] => 6
>>> Load all 1022 entries. <<<
100111 => 101011 => [1,2,2,1,1] => 6
101000 => 110001 => [1,1,4,1] => 4
101001 => 110010 => [1,1,3,2] => 5
101010 => 110101 => [1,1,2,2,1] => 6
101011 => 110101 => [1,1,2,2,1] => 6
101100 => 110101 => [1,1,2,2,1] => 6
101101 => 110110 => [1,1,2,1,2] => 5
101110 => 110111 => [1,1,2,1,1,1] => 4
101111 => 110111 => [1,1,2,1,1,1] => 4
110000 => 110001 => [1,1,4,1] => 4
110001 => 110010 => [1,1,3,2] => 5
110010 => 110101 => [1,1,2,2,1] => 6
110011 => 110101 => [1,1,2,2,1] => 6
110100 => 111001 => [1,1,1,3,1] => 4
110101 => 111010 => [1,1,1,2,2] => 5
110110 => 111011 => [1,1,1,2,1,1] => 4
110111 => 111011 => [1,1,1,2,1,1] => 4
111000 => 111001 => [1,1,1,3,1] => 4
111001 => 111010 => [1,1,1,2,2] => 5
111010 => 111101 => [1,1,1,1,2,1] => 4
111011 => 111101 => [1,1,1,1,2,1] => 4
111100 => 111101 => [1,1,1,1,2,1] => 4
111101 => 111110 => [1,1,1,1,1,2] => 3
111110 => 111111 => [1,1,1,1,1,1,1] => 2
111111 => 111111 => [1,1,1,1,1,1,1] => 2
0000000 => 0000001 => [7,1] => 3
0000001 => 0000010 => [6,2] => 4
0000010 => 0000101 => [5,2,1] => 5
0000011 => 0000101 => [5,2,1] => 5
0000100 => 0001001 => [4,3,1] => 5
0000101 => 0001010 => [4,2,2] => 6
0000110 => 0001011 => [4,2,1,1] => 5
0000111 => 0001011 => [4,2,1,1] => 5
0001000 => 0010001 => [3,4,1] => 5
0001001 => 0010010 => [3,3,2] => 6
0001010 => 0010101 => [3,2,2,1] => 7
0001011 => 0010101 => [3,2,2,1] => 7
0001100 => 0010101 => [3,2,2,1] => 7
0001101 => 0010110 => [3,2,1,2] => 6
0001110 => 0010111 => [3,2,1,1,1] => 5
0001111 => 0010111 => [3,2,1,1,1] => 5
0010000 => 0100001 => [2,5,1] => 5
0010001 => 0100010 => [2,4,2] => 6
0010010 => 0100101 => [2,3,2,1] => 7
0010011 => 0100101 => [2,3,2,1] => 7
0010100 => 0101001 => [2,2,3,1] => 7
0010101 => 0101010 => [2,2,2,2] => 8
0010110 => 0101011 => [2,2,2,1,1] => 7
0010111 => 0101011 => [2,2,2,1,1] => 7
0011000 => 0101001 => [2,2,3,1] => 7
0011001 => 0101010 => [2,2,2,2] => 8
0011010 => 0101101 => [2,2,1,2,1] => 7
0011011 => 0101101 => [2,2,1,2,1] => 7
0011100 => 0101101 => [2,2,1,2,1] => 7
0011101 => 0101110 => [2,2,1,1,2] => 6
0011110 => 0101111 => [2,2,1,1,1,1] => 5
0011111 => 0101111 => [2,2,1,1,1,1] => 5
0100000 => 1000001 => [1,6,1] => 4
0100001 => 1000010 => [1,5,2] => 5
0100010 => 1000101 => [1,4,2,1] => 6
0100011 => 1000101 => [1,4,2,1] => 6
0100100 => 1001001 => [1,3,3,1] => 6
0100101 => 1001010 => [1,3,2,2] => 7
0100110 => 1001011 => [1,3,2,1,1] => 6
0100111 => 1001011 => [1,3,2,1,1] => 6
0101000 => 1010001 => [1,2,4,1] => 6
0101001 => 1010010 => [1,2,3,2] => 7
0101010 => 1010101 => [1,2,2,2,1] => 8
0101011 => 1010101 => [1,2,2,2,1] => 8
0101100 => 1010101 => [1,2,2,2,1] => 8
0101101 => 1010110 => [1,2,2,1,2] => 7
0101110 => 1010111 => [1,2,2,1,1,1] => 6
0101111 => 1010111 => [1,2,2,1,1,1] => 6
0110000 => 1010001 => [1,2,4,1] => 6
0110001 => 1010010 => [1,2,3,2] => 7
0110010 => 1010101 => [1,2,2,2,1] => 8
0110011 => 1010101 => [1,2,2,2,1] => 8
0110100 => 1011001 => [1,2,1,3,1] => 6
0110101 => 1011010 => [1,2,1,2,2] => 7
0110110 => 1011011 => [1,2,1,2,1,1] => 6
0110111 => 1011011 => [1,2,1,2,1,1] => 6
0111000 => 1011001 => [1,2,1,3,1] => 6
0111001 => 1011010 => [1,2,1,2,2] => 7
0111010 => 1011101 => [1,2,1,1,2,1] => 6
0111011 => 1011101 => [1,2,1,1,2,1] => 6
0111100 => 1011101 => [1,2,1,1,2,1] => 6
0111101 => 1011110 => [1,2,1,1,1,2] => 5
0111110 => 1011111 => [1,2,1,1,1,1,1] => 4
0111111 => 1011111 => [1,2,1,1,1,1,1] => 4
1000000 => 1000001 => [1,6,1] => 4
1000001 => 1000010 => [1,5,2] => 5
1000010 => 1000101 => [1,4,2,1] => 6
1000011 => 1000101 => [1,4,2,1] => 6
1000100 => 1001001 => [1,3,3,1] => 6
1000101 => 1001010 => [1,3,2,2] => 7
1000110 => 1001011 => [1,3,2,1,1] => 6
1000111 => 1001011 => [1,3,2,1,1] => 6
1001000 => 1010001 => [1,2,4,1] => 6
1001001 => 1010010 => [1,2,3,2] => 7
1001010 => 1010101 => [1,2,2,2,1] => 8
1001011 => 1010101 => [1,2,2,2,1] => 8
1001100 => 1010101 => [1,2,2,2,1] => 8
1001101 => 1010110 => [1,2,2,1,2] => 7
1001110 => 1010111 => [1,2,2,1,1,1] => 6
1001111 => 1010111 => [1,2,2,1,1,1] => 6
1010000 => 1100001 => [1,1,5,1] => 4
1010001 => 1100010 => [1,1,4,2] => 5
1010010 => 1100101 => [1,1,3,2,1] => 6
1010011 => 1100101 => [1,1,3,2,1] => 6
1010100 => 1101001 => [1,1,2,3,1] => 6
1010101 => 1101010 => [1,1,2,2,2] => 7
1010110 => 1101011 => [1,1,2,2,1,1] => 6
1010111 => 1101011 => [1,1,2,2,1,1] => 6
1011000 => 1101001 => [1,1,2,3,1] => 6
1011001 => 1101010 => [1,1,2,2,2] => 7
1011010 => 1101101 => [1,1,2,1,2,1] => 6
1011011 => 1101101 => [1,1,2,1,2,1] => 6
1011100 => 1101101 => [1,1,2,1,2,1] => 6
1011101 => 1101110 => [1,1,2,1,1,2] => 5
1011110 => 1101111 => [1,1,2,1,1,1,1] => 4
1011111 => 1101111 => [1,1,2,1,1,1,1] => 4
1100000 => 1100001 => [1,1,5,1] => 4
1100001 => 1100010 => [1,1,4,2] => 5
1100010 => 1100101 => [1,1,3,2,1] => 6
1100011 => 1100101 => [1,1,3,2,1] => 6
1100100 => 1101001 => [1,1,2,3,1] => 6
1100101 => 1101010 => [1,1,2,2,2] => 7
1100110 => 1101011 => [1,1,2,2,1,1] => 6
1100111 => 1101011 => [1,1,2,2,1,1] => 6
1101000 => 1110001 => [1,1,1,4,1] => 4
1101001 => 1110010 => [1,1,1,3,2] => 5
1101010 => 1110101 => [1,1,1,2,2,1] => 6
1101011 => 1110101 => [1,1,1,2,2,1] => 6
1101100 => 1110101 => [1,1,1,2,2,1] => 6
1101101 => 1110110 => [1,1,1,2,1,2] => 5
1101110 => 1110111 => [1,1,1,2,1,1,1] => 4
1101111 => 1110111 => [1,1,1,2,1,1,1] => 4
1110000 => 1110001 => [1,1,1,4,1] => 4
1110001 => 1110010 => [1,1,1,3,2] => 5
1110010 => 1110101 => [1,1,1,2,2,1] => 6
1110011 => 1110101 => [1,1,1,2,2,1] => 6
1110100 => 1111001 => [1,1,1,1,3,1] => 4
1110101 => 1111010 => [1,1,1,1,2,2] => 5
1110110 => 1111011 => [1,1,1,1,2,1,1] => 4
1110111 => 1111011 => [1,1,1,1,2,1,1] => 4
1111000 => 1111001 => [1,1,1,1,3,1] => 4
1111001 => 1111010 => [1,1,1,1,2,2] => 5
1111010 => 1111101 => [1,1,1,1,1,2,1] => 4
1111011 => 1111101 => [1,1,1,1,1,2,1] => 4
1111100 => 1111101 => [1,1,1,1,1,2,1] => 4
1111101 => 1111110 => [1,1,1,1,1,1,2] => 3
1111110 => 1111111 => [1,1,1,1,1,1,1,1] => 2
1111111 => 1111111 => [1,1,1,1,1,1,1,1] => 2
00000000 => 00000001 => [8,1] => 3
00000001 => 00000010 => [7,2] => 4
00000010 => 00000101 => [6,2,1] => 5
00000011 => 00000101 => [6,2,1] => 5
00000100 => 00001001 => [5,3,1] => 5
00000101 => 00001010 => [5,2,2] => 6
00000110 => 00001011 => [5,2,1,1] => 5
00000111 => 00001011 => [5,2,1,1] => 5
00001000 => 00010001 => [4,4,1] => 5
00001001 => 00010010 => [4,3,2] => 6
00001010 => 00010101 => [4,2,2,1] => 7
00001011 => 00010101 => [4,2,2,1] => 7
00001100 => 00010101 => [4,2,2,1] => 7
00001101 => 00010110 => [4,2,1,2] => 6
00001110 => 00010111 => [4,2,1,1,1] => 5
00001111 => 00010111 => [4,2,1,1,1] => 5
00010000 => 00100001 => [3,5,1] => 5
00010001 => 00100010 => [3,4,2] => 6
00010010 => 00100101 => [3,3,2,1] => 7
00010011 => 00100101 => [3,3,2,1] => 7
00010100 => 00101001 => [3,2,3,1] => 7
00010101 => 00101010 => [3,2,2,2] => 8
00010110 => 00101011 => [3,2,2,1,1] => 7
00010111 => 00101011 => [3,2,2,1,1] => 7
00011000 => 00101001 => [3,2,3,1] => 7
00011001 => 00101010 => [3,2,2,2] => 8
00011010 => 00101101 => [3,2,1,2,1] => 7
00011011 => 00101101 => [3,2,1,2,1] => 7
00011100 => 00101101 => [3,2,1,2,1] => 7
00011101 => 00101110 => [3,2,1,1,2] => 6
00011110 => 00101111 => [3,2,1,1,1,1] => 5
00011111 => 00101111 => [3,2,1,1,1,1] => 5
00100000 => 01000001 => [2,6,1] => 5
00100001 => 01000010 => [2,5,2] => 6
00100010 => 01000101 => [2,4,2,1] => 7
00100011 => 01000101 => [2,4,2,1] => 7
00100100 => 01001001 => [2,3,3,1] => 7
00100101 => 01001010 => [2,3,2,2] => 8
00100110 => 01001011 => [2,3,2,1,1] => 7
00100111 => 01001011 => [2,3,2,1,1] => 7
00101000 => 01010001 => [2,2,4,1] => 7
00101001 => 01010010 => [2,2,3,2] => 8
00101010 => 01010101 => [2,2,2,2,1] => 9
00101011 => 01010101 => [2,2,2,2,1] => 9
00101100 => 01010101 => [2,2,2,2,1] => 9
00101101 => 01010110 => [2,2,2,1,2] => 8
00101110 => 01010111 => [2,2,2,1,1,1] => 7
00101111 => 01010111 => [2,2,2,1,1,1] => 7
00110000 => 01010001 => [2,2,4,1] => 7
00110001 => 01010010 => [2,2,3,2] => 8
00110010 => 01010101 => [2,2,2,2,1] => 9
00110011 => 01010101 => [2,2,2,2,1] => 9
00110100 => 01011001 => [2,2,1,3,1] => 7
00110101 => 01011010 => [2,2,1,2,2] => 8
00110110 => 01011011 => [2,2,1,2,1,1] => 7
00110111 => 01011011 => [2,2,1,2,1,1] => 7
00111000 => 01011001 => [2,2,1,3,1] => 7
00111001 => 01011010 => [2,2,1,2,2] => 8
00111010 => 01011101 => [2,2,1,1,2,1] => 7
00111011 => 01011101 => [2,2,1,1,2,1] => 7
00111100 => 01011101 => [2,2,1,1,2,1] => 7
00111101 => 01011110 => [2,2,1,1,1,2] => 6
00111110 => 01011111 => [2,2,1,1,1,1,1] => 5
00111111 => 01011111 => [2,2,1,1,1,1,1] => 5
01000000 => 10000001 => [1,7,1] => 4
01000001 => 10000010 => [1,6,2] => 5
01000010 => 10000101 => [1,5,2,1] => 6
01000011 => 10000101 => [1,5,2,1] => 6
01000100 => 10001001 => [1,4,3,1] => 6
01000101 => 10001010 => [1,4,2,2] => 7
01000110 => 10001011 => [1,4,2,1,1] => 6
01000111 => 10001011 => [1,4,2,1,1] => 6
01001000 => 10010001 => [1,3,4,1] => 6
01001001 => 10010010 => [1,3,3,2] => 7
01001010 => 10010101 => [1,3,2,2,1] => 8
01001011 => 10010101 => [1,3,2,2,1] => 8
01001100 => 10010101 => [1,3,2,2,1] => 8
01001101 => 10010110 => [1,3,2,1,2] => 7
01001110 => 10010111 => [1,3,2,1,1,1] => 6
01001111 => 10010111 => [1,3,2,1,1,1] => 6
01010000 => 10100001 => [1,2,5,1] => 6
01010001 => 10100010 => [1,2,4,2] => 7
01010010 => 10100101 => [1,2,3,2,1] => 8
01010011 => 10100101 => [1,2,3,2,1] => 8
01010100 => 10101001 => [1,2,2,3,1] => 8
01010101 => 10101010 => [1,2,2,2,2] => 9
01010110 => 10101011 => [1,2,2,2,1,1] => 8
01010111 => 10101011 => [1,2,2,2,1,1] => 8
01011000 => 10101001 => [1,2,2,3,1] => 8
01011001 => 10101010 => [1,2,2,2,2] => 9
01011010 => 10101101 => [1,2,2,1,2,1] => 8
01011011 => 10101101 => [1,2,2,1,2,1] => 8
01011100 => 10101101 => [1,2,2,1,2,1] => 8
01011101 => 10101110 => [1,2,2,1,1,2] => 7
01011110 => 10101111 => [1,2,2,1,1,1,1] => 6
01011111 => 10101111 => [1,2,2,1,1,1,1] => 6
01100000 => 10100001 => [1,2,5,1] => 6
01100001 => 10100010 => [1,2,4,2] => 7
01100010 => 10100101 => [1,2,3,2,1] => 8
01100011 => 10100101 => [1,2,3,2,1] => 8
01100100 => 10101001 => [1,2,2,3,1] => 8
01100101 => 10101010 => [1,2,2,2,2] => 9
01100110 => 10101011 => [1,2,2,2,1,1] => 8
01100111 => 10101011 => [1,2,2,2,1,1] => 8
01101000 => 10110001 => [1,2,1,4,1] => 6
01101001 => 10110010 => [1,2,1,3,2] => 7
01101010 => 10110101 => [1,2,1,2,2,1] => 8
01101011 => 10110101 => [1,2,1,2,2,1] => 8
01101100 => 10110101 => [1,2,1,2,2,1] => 8
01101101 => 10110110 => [1,2,1,2,1,2] => 7
01101110 => 10110111 => [1,2,1,2,1,1,1] => 6
01101111 => 10110111 => [1,2,1,2,1,1,1] => 6
01110000 => 10110001 => [1,2,1,4,1] => 6
01110001 => 10110010 => [1,2,1,3,2] => 7
01110010 => 10110101 => [1,2,1,2,2,1] => 8
01110011 => 10110101 => [1,2,1,2,2,1] => 8
01110100 => 10111001 => [1,2,1,1,3,1] => 6
01110101 => 10111010 => [1,2,1,1,2,2] => 7
01110110 => 10111011 => [1,2,1,1,2,1,1] => 6
01110111 => 10111011 => [1,2,1,1,2,1,1] => 6
01111000 => 10111001 => [1,2,1,1,3,1] => 6
01111001 => 10111010 => [1,2,1,1,2,2] => 7
01111010 => 10111101 => [1,2,1,1,1,2,1] => 6
01111011 => 10111101 => [1,2,1,1,1,2,1] => 6
01111100 => 10111101 => [1,2,1,1,1,2,1] => 6
01111101 => 10111110 => [1,2,1,1,1,1,2] => 5
01111110 => 10111111 => [1,2,1,1,1,1,1,1] => 4
01111111 => 10111111 => [1,2,1,1,1,1,1,1] => 4
10000000 => 10000001 => [1,7,1] => 4
10000001 => 10000010 => [1,6,2] => 5
10000010 => 10000101 => [1,5,2,1] => 6
10000011 => 10000101 => [1,5,2,1] => 6
10000100 => 10001001 => [1,4,3,1] => 6
10000101 => 10001010 => [1,4,2,2] => 7
10000110 => 10001011 => [1,4,2,1,1] => 6
10000111 => 10001011 => [1,4,2,1,1] => 6
10001000 => 10010001 => [1,3,4,1] => 6
10001001 => 10010010 => [1,3,3,2] => 7
10001010 => 10010101 => [1,3,2,2,1] => 8
10001011 => 10010101 => [1,3,2,2,1] => 8
10001100 => 10010101 => [1,3,2,2,1] => 8
10001101 => 10010110 => [1,3,2,1,2] => 7
10001110 => 10010111 => [1,3,2,1,1,1] => 6
10001111 => 10010111 => [1,3,2,1,1,1] => 6
10010000 => 10100001 => [1,2,5,1] => 6
10010001 => 10100010 => [1,2,4,2] => 7
10010010 => 10100101 => [1,2,3,2,1] => 8
10010011 => 10100101 => [1,2,3,2,1] => 8
10010100 => 10101001 => [1,2,2,3,1] => 8
10010101 => 10101010 => [1,2,2,2,2] => 9
10010110 => 10101011 => [1,2,2,2,1,1] => 8
10010111 => 10101011 => [1,2,2,2,1,1] => 8
10011000 => 10101001 => [1,2,2,3,1] => 8
10011001 => 10101010 => [1,2,2,2,2] => 9
10011010 => 10101101 => [1,2,2,1,2,1] => 8
10011011 => 10101101 => [1,2,2,1,2,1] => 8
10011100 => 10101101 => [1,2,2,1,2,1] => 8
10011101 => 10101110 => [1,2,2,1,1,2] => 7
10011110 => 10101111 => [1,2,2,1,1,1,1] => 6
10011111 => 10101111 => [1,2,2,1,1,1,1] => 6
10100000 => 11000001 => [1,1,6,1] => 4
10100001 => 11000010 => [1,1,5,2] => 5
10100010 => 11000101 => [1,1,4,2,1] => 6
10100011 => 11000101 => [1,1,4,2,1] => 6
10100100 => 11001001 => [1,1,3,3,1] => 6
10100101 => 11001010 => [1,1,3,2,2] => 7
10100110 => 11001011 => [1,1,3,2,1,1] => 6
10100111 => 11001011 => [1,1,3,2,1,1] => 6
10101000 => 11010001 => [1,1,2,4,1] => 6
10101001 => 11010010 => [1,1,2,3,2] => 7
10101010 => 11010101 => [1,1,2,2,2,1] => 8
10101011 => 11010101 => [1,1,2,2,2,1] => 8
10101100 => 11010101 => [1,1,2,2,2,1] => 8
10101101 => 11010110 => [1,1,2,2,1,2] => 7
10101110 => 11010111 => [1,1,2,2,1,1,1] => 6
10101111 => 11010111 => [1,1,2,2,1,1,1] => 6
10110000 => 11010001 => [1,1,2,4,1] => 6
10110001 => 11010010 => [1,1,2,3,2] => 7
10110010 => 11010101 => [1,1,2,2,2,1] => 8
10110011 => 11010101 => [1,1,2,2,2,1] => 8
10110100 => 11011001 => [1,1,2,1,3,1] => 6
10110101 => 11011010 => [1,1,2,1,2,2] => 7
10110110 => 11011011 => [1,1,2,1,2,1,1] => 6
10110111 => 11011011 => [1,1,2,1,2,1,1] => 6
10111000 => 11011001 => [1,1,2,1,3,1] => 6
10111001 => 11011010 => [1,1,2,1,2,2] => 7
10111010 => 11011101 => [1,1,2,1,1,2,1] => 6
10111011 => 11011101 => [1,1,2,1,1,2,1] => 6
10111100 => 11011101 => [1,1,2,1,1,2,1] => 6
10111101 => 11011110 => [1,1,2,1,1,1,2] => 5
10111110 => 11011111 => [1,1,2,1,1,1,1,1] => 4
10111111 => 11011111 => [1,1,2,1,1,1,1,1] => 4
11000000 => 11000001 => [1,1,6,1] => 4
11000001 => 11000010 => [1,1,5,2] => 5
11000010 => 11000101 => [1,1,4,2,1] => 6
11000011 => 11000101 => [1,1,4,2,1] => 6
11000100 => 11001001 => [1,1,3,3,1] => 6
11000101 => 11001010 => [1,1,3,2,2] => 7
11000110 => 11001011 => [1,1,3,2,1,1] => 6
11000111 => 11001011 => [1,1,3,2,1,1] => 6
11001000 => 11010001 => [1,1,2,4,1] => 6
11001001 => 11010010 => [1,1,2,3,2] => 7
11001010 => 11010101 => [1,1,2,2,2,1] => 8
11001011 => 11010101 => [1,1,2,2,2,1] => 8
11001100 => 11010101 => [1,1,2,2,2,1] => 8
11001101 => 11010110 => [1,1,2,2,1,2] => 7
11001110 => 11010111 => [1,1,2,2,1,1,1] => 6
11001111 => 11010111 => [1,1,2,2,1,1,1] => 6
11010000 => 11100001 => [1,1,1,5,1] => 4
11010001 => 11100010 => [1,1,1,4,2] => 5
11010010 => 11100101 => [1,1,1,3,2,1] => 6
11010011 => 11100101 => [1,1,1,3,2,1] => 6
11010100 => 11101001 => [1,1,1,2,3,1] => 6
11010101 => 11101010 => [1,1,1,2,2,2] => 7
11010110 => 11101011 => [1,1,1,2,2,1,1] => 6
11010111 => 11101011 => [1,1,1,2,2,1,1] => 6
11011000 => 11101001 => [1,1,1,2,3,1] => 6
11011001 => 11101010 => [1,1,1,2,2,2] => 7
11011010 => 11101101 => [1,1,1,2,1,2,1] => 6
11011011 => 11101101 => [1,1,1,2,1,2,1] => 6
11011100 => 11101101 => [1,1,1,2,1,2,1] => 6
11011101 => 11101110 => [1,1,1,2,1,1,2] => 5
11011110 => 11101111 => [1,1,1,2,1,1,1,1] => 4
11011111 => 11101111 => [1,1,1,2,1,1,1,1] => 4
11100000 => 11100001 => [1,1,1,5,1] => 4
11100001 => 11100010 => [1,1,1,4,2] => 5
11100010 => 11100101 => [1,1,1,3,2,1] => 6
11100011 => 11100101 => [1,1,1,3,2,1] => 6
11100100 => 11101001 => [1,1,1,2,3,1] => 6
11100101 => 11101010 => [1,1,1,2,2,2] => 7
11100110 => 11101011 => [1,1,1,2,2,1,1] => 6
11100111 => 11101011 => [1,1,1,2,2,1,1] => 6
11101000 => 11110001 => [1,1,1,1,4,1] => 4
11101001 => 11110010 => [1,1,1,1,3,2] => 5
11101010 => 11110101 => [1,1,1,1,2,2,1] => 6
11101011 => 11110101 => [1,1,1,1,2,2,1] => 6
11101100 => 11110101 => [1,1,1,1,2,2,1] => 6
11101101 => 11110110 => [1,1,1,1,2,1,2] => 5
11101110 => 11110111 => [1,1,1,1,2,1,1,1] => 4
11101111 => 11110111 => [1,1,1,1,2,1,1,1] => 4
11110000 => 11110001 => [1,1,1,1,4,1] => 4
11110001 => 11110010 => [1,1,1,1,3,2] => 5
11110010 => 11110101 => [1,1,1,1,2,2,1] => 6
11110011 => 11110101 => [1,1,1,1,2,2,1] => 6
11110100 => 11111001 => [1,1,1,1,1,3,1] => 4
11110101 => 11111010 => [1,1,1,1,1,2,2] => 5
11110110 => 11111011 => [1,1,1,1,1,2,1,1] => 4
11110111 => 11111011 => [1,1,1,1,1,2,1,1] => 4
11111000 => 11111001 => [1,1,1,1,1,3,1] => 4
11111001 => 11111010 => [1,1,1,1,1,2,2] => 5
11111010 => 11111101 => [1,1,1,1,1,1,2,1] => 4
11111011 => 11111101 => [1,1,1,1,1,1,2,1] => 4
11111100 => 11111101 => [1,1,1,1,1,1,2,1] => 4
11111101 => 11111110 => [1,1,1,1,1,1,1,2] => 3
11111110 => 11111111 => [1,1,1,1,1,1,1,1,1] => 2
11111111 => 11111111 => [1,1,1,1,1,1,1,1,1] => 2
000000000 => 000000001 => [9,1] => 3
000000001 => 000000010 => [8,2] => 4
000000010 => 000000101 => [7,2,1] => 5
000000011 => 000000101 => [7,2,1] => 5
000000100 => 000001001 => [6,3,1] => 5
000000101 => 000001010 => [6,2,2] => 6
000000110 => 000001011 => [6,2,1,1] => 5
000000111 => 000001011 => [6,2,1,1] => 5
000001000 => 000010001 => [5,4,1] => 5
000001001 => 000010010 => [5,3,2] => 6
000001010 => 000010101 => [5,2,2,1] => 7
000001011 => 000010101 => [5,2,2,1] => 7
000001100 => 000010101 => [5,2,2,1] => 7
000001101 => 000010110 => [5,2,1,2] => 6
000001110 => 000010111 => [5,2,1,1,1] => 5
000001111 => 000010111 => [5,2,1,1,1] => 5
000010000 => 000100001 => [4,5,1] => 5
000010001 => 000100010 => [4,4,2] => 6
000010010 => 000100101 => [4,3,2,1] => 7
000010011 => 000100101 => [4,3,2,1] => 7
000010100 => 000101001 => [4,2,3,1] => 7
000010101 => 000101010 => [4,2,2,2] => 8
000010110 => 000101011 => [4,2,2,1,1] => 7
000010111 => 000101011 => [4,2,2,1,1] => 7
000011000 => 000101001 => [4,2,3,1] => 7
000011001 => 000101010 => [4,2,2,2] => 8
000011010 => 000101101 => [4,2,1,2,1] => 7
000011011 => 000101101 => [4,2,1,2,1] => 7
000011100 => 000101101 => [4,2,1,2,1] => 7
000011101 => 000101110 => [4,2,1,1,2] => 6
000011110 => 000101111 => [4,2,1,1,1,1] => 5
000011111 => 000101111 => [4,2,1,1,1,1] => 5
000100000 => 001000001 => [3,6,1] => 5
000100001 => 001000010 => [3,5,2] => 6
000100010 => 001000101 => [3,4,2,1] => 7
000100011 => 001000101 => [3,4,2,1] => 7
000100100 => 001001001 => [3,3,3,1] => 7
000100101 => 001001010 => [3,3,2,2] => 8
000100110 => 001001011 => [3,3,2,1,1] => 7
000100111 => 001001011 => [3,3,2,1,1] => 7
000101000 => 001010001 => [3,2,4,1] => 7
000101001 => 001010010 => [3,2,3,2] => 8
000101010 => 001010101 => [3,2,2,2,1] => 9
000101011 => 001010101 => [3,2,2,2,1] => 9
000101100 => 001010101 => [3,2,2,2,1] => 9
000101101 => 001010110 => [3,2,2,1,2] => 8
000101110 => 001010111 => [3,2,2,1,1,1] => 7
000101111 => 001010111 => [3,2,2,1,1,1] => 7
000110000 => 001010001 => [3,2,4,1] => 7
000110001 => 001010010 => [3,2,3,2] => 8
000110010 => 001010101 => [3,2,2,2,1] => 9
000110011 => 001010101 => [3,2,2,2,1] => 9
000110100 => 001011001 => [3,2,1,3,1] => 7
000110101 => 001011010 => [3,2,1,2,2] => 8
000110110 => 001011011 => [3,2,1,2,1,1] => 7
000110111 => 001011011 => [3,2,1,2,1,1] => 7
000111000 => 001011001 => [3,2,1,3,1] => 7
000111001 => 001011010 => [3,2,1,2,2] => 8
000111010 => 001011101 => [3,2,1,1,2,1] => 7
000111011 => 001011101 => [3,2,1,1,2,1] => 7
000111100 => 001011101 => [3,2,1,1,2,1] => 7
000111101 => 001011110 => [3,2,1,1,1,2] => 6
000111110 => 001011111 => [3,2,1,1,1,1,1] => 5
000111111 => 001011111 => [3,2,1,1,1,1,1] => 5
001000000 => 010000001 => [2,7,1] => 5
001000001 => 010000010 => [2,6,2] => 6
001000010 => 010000101 => [2,5,2,1] => 7
001000011 => 010000101 => [2,5,2,1] => 7
001000100 => 010001001 => [2,4,3,1] => 7
001000101 => 010001010 => [2,4,2,2] => 8
001000110 => 010001011 => [2,4,2,1,1] => 7
001000111 => 010001011 => [2,4,2,1,1] => 7
001001000 => 010010001 => [2,3,4,1] => 7
001001001 => 010010010 => [2,3,3,2] => 8
001001010 => 010010101 => [2,3,2,2,1] => 9
001001011 => 010010101 => [2,3,2,2,1] => 9
001001100 => 010010101 => [2,3,2,2,1] => 9
001001101 => 010010110 => [2,3,2,1,2] => 8
001001110 => 010010111 => [2,3,2,1,1,1] => 7
001001111 => 010010111 => [2,3,2,1,1,1] => 7
001010000 => 010100001 => [2,2,5,1] => 7
001010001 => 010100010 => [2,2,4,2] => 8
001010010 => 010100101 => [2,2,3,2,1] => 9
001010011 => 010100101 => [2,2,3,2,1] => 9
001010100 => 010101001 => [2,2,2,3,1] => 9
001010101 => 010101010 => [2,2,2,2,2] => 10
001010110 => 010101011 => [2,2,2,2,1,1] => 9
001010111 => 010101011 => [2,2,2,2,1,1] => 9
001011000 => 010101001 => [2,2,2,3,1] => 9
001011001 => 010101010 => [2,2,2,2,2] => 10
001011010 => 010101101 => [2,2,2,1,2,1] => 9
001011011 => 010101101 => [2,2,2,1,2,1] => 9
001011100 => 010101101 => [2,2,2,1,2,1] => 9
001011101 => 010101110 => [2,2,2,1,1,2] => 8
001011110 => 010101111 => [2,2,2,1,1,1,1] => 7
001011111 => 010101111 => [2,2,2,1,1,1,1] => 7
001100000 => 010100001 => [2,2,5,1] => 7
001100001 => 010100010 => [2,2,4,2] => 8
001100010 => 010100101 => [2,2,3,2,1] => 9
001100011 => 010100101 => [2,2,3,2,1] => 9
001100100 => 010101001 => [2,2,2,3,1] => 9
001100101 => 010101010 => [2,2,2,2,2] => 10
001100110 => 010101011 => [2,2,2,2,1,1] => 9
001100111 => 010101011 => [2,2,2,2,1,1] => 9
001101000 => 010110001 => [2,2,1,4,1] => 7
001101001 => 010110010 => [2,2,1,3,2] => 8
001101010 => 010110101 => [2,2,1,2,2,1] => 9
001101011 => 010110101 => [2,2,1,2,2,1] => 9
001101100 => 010110101 => [2,2,1,2,2,1] => 9
001101101 => 010110110 => [2,2,1,2,1,2] => 8
001101110 => 010110111 => [2,2,1,2,1,1,1] => 7
001101111 => 010110111 => [2,2,1,2,1,1,1] => 7
001110000 => 010110001 => [2,2,1,4,1] => 7
001110001 => 010110010 => [2,2,1,3,2] => 8
001110010 => 010110101 => [2,2,1,2,2,1] => 9
001110011 => 010110101 => [2,2,1,2,2,1] => 9
001110100 => 010111001 => [2,2,1,1,3,1] => 7
001110101 => 010111010 => [2,2,1,1,2,2] => 8
001110110 => 010111011 => [2,2,1,1,2,1,1] => 7
001110111 => 010111011 => [2,2,1,1,2,1,1] => 7
001111000 => 010111001 => [2,2,1,1,3,1] => 7
001111001 => 010111010 => [2,2,1,1,2,2] => 8
001111010 => 010111101 => [2,2,1,1,1,2,1] => 7
001111011 => 010111101 => [2,2,1,1,1,2,1] => 7
001111100 => 010111101 => [2,2,1,1,1,2,1] => 7
001111101 => 010111110 => [2,2,1,1,1,1,2] => 6
001111110 => 010111111 => [2,2,1,1,1,1,1,1] => 5
001111111 => 010111111 => [2,2,1,1,1,1,1,1] => 5
010000000 => 100000001 => [1,8,1] => 4
010000001 => 100000010 => [1,7,2] => 5
010000010 => 100000101 => [1,6,2,1] => 6
010000011 => 100000101 => [1,6,2,1] => 6
010000100 => 100001001 => [1,5,3,1] => 6
010000101 => 100001010 => [1,5,2,2] => 7
010000110 => 100001011 => [1,5,2,1,1] => 6
010000111 => 100001011 => [1,5,2,1,1] => 6
010001000 => 100010001 => [1,4,4,1] => 6
010001001 => 100010010 => [1,4,3,2] => 7
010001010 => 100010101 => [1,4,2,2,1] => 8
010001011 => 100010101 => [1,4,2,2,1] => 8
010001100 => 100010101 => [1,4,2,2,1] => 8
010001101 => 100010110 => [1,4,2,1,2] => 7
010001110 => 100010111 => [1,4,2,1,1,1] => 6
010001111 => 100010111 => [1,4,2,1,1,1] => 6
010010000 => 100100001 => [1,3,5,1] => 6
010010001 => 100100010 => [1,3,4,2] => 7
010010010 => 100100101 => [1,3,3,2,1] => 8
010010011 => 100100101 => [1,3,3,2,1] => 8
010010100 => 100101001 => [1,3,2,3,1] => 8
010010101 => 100101010 => [1,3,2,2,2] => 9
010010110 => 100101011 => [1,3,2,2,1,1] => 8
010010111 => 100101011 => [1,3,2,2,1,1] => 8
010011000 => 100101001 => [1,3,2,3,1] => 8
010011001 => 100101010 => [1,3,2,2,2] => 9
010011010 => 100101101 => [1,3,2,1,2,1] => 8
010011011 => 100101101 => [1,3,2,1,2,1] => 8
010011100 => 100101101 => [1,3,2,1,2,1] => 8
010011101 => 100101110 => [1,3,2,1,1,2] => 7
010011110 => 100101111 => [1,3,2,1,1,1,1] => 6
010011111 => 100101111 => [1,3,2,1,1,1,1] => 6
010100000 => 101000001 => [1,2,6,1] => 6
010100001 => 101000010 => [1,2,5,2] => 7
010100010 => 101000101 => [1,2,4,2,1] => 8
010100011 => 101000101 => [1,2,4,2,1] => 8
010100100 => 101001001 => [1,2,3,3,1] => 8
010100101 => 101001010 => [1,2,3,2,2] => 9
010100110 => 101001011 => [1,2,3,2,1,1] => 8
010100111 => 101001011 => [1,2,3,2,1,1] => 8
010101000 => 101010001 => [1,2,2,4,1] => 8
010101001 => 101010010 => [1,2,2,3,2] => 9
010101010 => 101010101 => [1,2,2,2,2,1] => 10
010101011 => 101010101 => [1,2,2,2,2,1] => 10
010101100 => 101010101 => [1,2,2,2,2,1] => 10
010101101 => 101010110 => [1,2,2,2,1,2] => 9
010101110 => 101010111 => [1,2,2,2,1,1,1] => 8
010101111 => 101010111 => [1,2,2,2,1,1,1] => 8
010110000 => 101010001 => [1,2,2,4,1] => 8
010110001 => 101010010 => [1,2,2,3,2] => 9
010110010 => 101010101 => [1,2,2,2,2,1] => 10
010110011 => 101010101 => [1,2,2,2,2,1] => 10
010110100 => 101011001 => [1,2,2,1,3,1] => 8
010110101 => 101011010 => [1,2,2,1,2,2] => 9
010110110 => 101011011 => [1,2,2,1,2,1,1] => 8
010110111 => 101011011 => [1,2,2,1,2,1,1] => 8
010111000 => 101011001 => [1,2,2,1,3,1] => 8
010111001 => 101011010 => [1,2,2,1,2,2] => 9
010111010 => 101011101 => [1,2,2,1,1,2,1] => 8
010111011 => 101011101 => [1,2,2,1,1,2,1] => 8
010111100 => 101011101 => [1,2,2,1,1,2,1] => 8
010111101 => 101011110 => [1,2,2,1,1,1,2] => 7
010111110 => 101011111 => [1,2,2,1,1,1,1,1] => 6
010111111 => 101011111 => [1,2,2,1,1,1,1,1] => 6
011000000 => 101000001 => [1,2,6,1] => 6
011000001 => 101000010 => [1,2,5,2] => 7
011000010 => 101000101 => [1,2,4,2,1] => 8
011000011 => 101000101 => [1,2,4,2,1] => 8
011000100 => 101001001 => [1,2,3,3,1] => 8
011000101 => 101001010 => [1,2,3,2,2] => 9
011000110 => 101001011 => [1,2,3,2,1,1] => 8
011000111 => 101001011 => [1,2,3,2,1,1] => 8
011001000 => 101010001 => [1,2,2,4,1] => 8
011001001 => 101010010 => [1,2,2,3,2] => 9
011001010 => 101010101 => [1,2,2,2,2,1] => 10
011001011 => 101010101 => [1,2,2,2,2,1] => 10
011001100 => 101010101 => [1,2,2,2,2,1] => 10
011001101 => 101010110 => [1,2,2,2,1,2] => 9
011001110 => 101010111 => [1,2,2,2,1,1,1] => 8
011001111 => 101010111 => [1,2,2,2,1,1,1] => 8
011010000 => 101100001 => [1,2,1,5,1] => 6
011010001 => 101100010 => [1,2,1,4,2] => 7
011010010 => 101100101 => [1,2,1,3,2,1] => 8
011010011 => 101100101 => [1,2,1,3,2,1] => 8
011010100 => 101101001 => [1,2,1,2,3,1] => 8
011010101 => 101101010 => [1,2,1,2,2,2] => 9
011010110 => 101101011 => [1,2,1,2,2,1,1] => 8
011010111 => 101101011 => [1,2,1,2,2,1,1] => 8
011011000 => 101101001 => [1,2,1,2,3,1] => 8
011011001 => 101101010 => [1,2,1,2,2,2] => 9
011011010 => 101101101 => [1,2,1,2,1,2,1] => 8
011011011 => 101101101 => [1,2,1,2,1,2,1] => 8
011011100 => 101101101 => [1,2,1,2,1,2,1] => 8
011011101 => 101101110 => [1,2,1,2,1,1,2] => 7
011011110 => 101101111 => [1,2,1,2,1,1,1,1] => 6
011011111 => 101101111 => [1,2,1,2,1,1,1,1] => 6
011100000 => 101100001 => [1,2,1,5,1] => 6
011100001 => 101100010 => [1,2,1,4,2] => 7
011100010 => 101100101 => [1,2,1,3,2,1] => 8
011100011 => 101100101 => [1,2,1,3,2,1] => 8
011100100 => 101101001 => [1,2,1,2,3,1] => 8
011100101 => 101101010 => [1,2,1,2,2,2] => 9
011100110 => 101101011 => [1,2,1,2,2,1,1] => 8
011100111 => 101101011 => [1,2,1,2,2,1,1] => 8
011101000 => 101110001 => [1,2,1,1,4,1] => 6
011101001 => 101110010 => [1,2,1,1,3,2] => 7
011101010 => 101110101 => [1,2,1,1,2,2,1] => 8
011101011 => 101110101 => [1,2,1,1,2,2,1] => 8
011101100 => 101110101 => [1,2,1,1,2,2,1] => 8
011101101 => 101110110 => [1,2,1,1,2,1,2] => 7
011101110 => 101110111 => [1,2,1,1,2,1,1,1] => 6
011101111 => 101110111 => [1,2,1,1,2,1,1,1] => 6
011110000 => 101110001 => [1,2,1,1,4,1] => 6
011110001 => 101110010 => [1,2,1,1,3,2] => 7
011110010 => 101110101 => [1,2,1,1,2,2,1] => 8
011110011 => 101110101 => [1,2,1,1,2,2,1] => 8
011110100 => 101111001 => [1,2,1,1,1,3,1] => 6
011110101 => 101111010 => [1,2,1,1,1,2,2] => 7
011110110 => 101111011 => [1,2,1,1,1,2,1,1] => 6
011110111 => 101111011 => [1,2,1,1,1,2,1,1] => 6
011111000 => 101111001 => [1,2,1,1,1,3,1] => 6
011111001 => 101111010 => [1,2,1,1,1,2,2] => 7
011111010 => 101111101 => [1,2,1,1,1,1,2,1] => 6
011111011 => 101111101 => [1,2,1,1,1,1,2,1] => 6
011111100 => 101111101 => [1,2,1,1,1,1,2,1] => 6
011111101 => 101111110 => [1,2,1,1,1,1,1,2] => 5
011111110 => 101111111 => [1,2,1,1,1,1,1,1,1] => 4
011111111 => 101111111 => [1,2,1,1,1,1,1,1,1] => 4
100000000 => 100000001 => [1,8,1] => 4
100000001 => 100000010 => [1,7,2] => 5
100000010 => 100000101 => [1,6,2,1] => 6
100000011 => 100000101 => [1,6,2,1] => 6
100000100 => 100001001 => [1,5,3,1] => 6
100000101 => 100001010 => [1,5,2,2] => 7
100000110 => 100001011 => [1,5,2,1,1] => 6
100000111 => 100001011 => [1,5,2,1,1] => 6
100001000 => 100010001 => [1,4,4,1] => 6
100001001 => 100010010 => [1,4,3,2] => 7
100001010 => 100010101 => [1,4,2,2,1] => 8
100001011 => 100010101 => [1,4,2,2,1] => 8
100001100 => 100010101 => [1,4,2,2,1] => 8
100001101 => 100010110 => [1,4,2,1,2] => 7
100001110 => 100010111 => [1,4,2,1,1,1] => 6
100001111 => 100010111 => [1,4,2,1,1,1] => 6
100010000 => 100100001 => [1,3,5,1] => 6
100010001 => 100100010 => [1,3,4,2] => 7
100010010 => 100100101 => [1,3,3,2,1] => 8
100010011 => 100100101 => [1,3,3,2,1] => 8
100010100 => 100101001 => [1,3,2,3,1] => 8
100010101 => 100101010 => [1,3,2,2,2] => 9
100010110 => 100101011 => [1,3,2,2,1,1] => 8
100010111 => 100101011 => [1,3,2,2,1,1] => 8
100011000 => 100101001 => [1,3,2,3,1] => 8
100011001 => 100101010 => [1,3,2,2,2] => 9
100011010 => 100101101 => [1,3,2,1,2,1] => 8
100011011 => 100101101 => [1,3,2,1,2,1] => 8
100011100 => 100101101 => [1,3,2,1,2,1] => 8
100011101 => 100101110 => [1,3,2,1,1,2] => 7
100011110 => 100101111 => [1,3,2,1,1,1,1] => 6
100011111 => 100101111 => [1,3,2,1,1,1,1] => 6
100100000 => 101000001 => [1,2,6,1] => 6
100100001 => 101000010 => [1,2,5,2] => 7
100100010 => 101000101 => [1,2,4,2,1] => 8
100100011 => 101000101 => [1,2,4,2,1] => 8
100100100 => 101001001 => [1,2,3,3,1] => 8
100100101 => 101001010 => [1,2,3,2,2] => 9
100100110 => 101001011 => [1,2,3,2,1,1] => 8
100100111 => 101001011 => [1,2,3,2,1,1] => 8
100101000 => 101010001 => [1,2,2,4,1] => 8
100101001 => 101010010 => [1,2,2,3,2] => 9
100101010 => 101010101 => [1,2,2,2,2,1] => 10
100101011 => 101010101 => [1,2,2,2,2,1] => 10
100101100 => 101010101 => [1,2,2,2,2,1] => 10
100101101 => 101010110 => [1,2,2,2,1,2] => 9
100101110 => 101010111 => [1,2,2,2,1,1,1] => 8
100101111 => 101010111 => [1,2,2,2,1,1,1] => 8
100110000 => 101010001 => [1,2,2,4,1] => 8
100110001 => 101010010 => [1,2,2,3,2] => 9
100110010 => 101010101 => [1,2,2,2,2,1] => 10
100110011 => 101010101 => [1,2,2,2,2,1] => 10
100110100 => 101011001 => [1,2,2,1,3,1] => 8
100110101 => 101011010 => [1,2,2,1,2,2] => 9
100110110 => 101011011 => [1,2,2,1,2,1,1] => 8
100110111 => 101011011 => [1,2,2,1,2,1,1] => 8
100111000 => 101011001 => [1,2,2,1,3,1] => 8
100111001 => 101011010 => [1,2,2,1,2,2] => 9
100111010 => 101011101 => [1,2,2,1,1,2,1] => 8
100111011 => 101011101 => [1,2,2,1,1,2,1] => 8
100111100 => 101011101 => [1,2,2,1,1,2,1] => 8
100111101 => 101011110 => [1,2,2,1,1,1,2] => 7
100111110 => 101011111 => [1,2,2,1,1,1,1,1] => 6
100111111 => 101011111 => [1,2,2,1,1,1,1,1] => 6
101000000 => 110000001 => [1,1,7,1] => 4
101000001 => 110000010 => [1,1,6,2] => 5
101000010 => 110000101 => [1,1,5,2,1] => 6
101000011 => 110000101 => [1,1,5,2,1] => 6
101000100 => 110001001 => [1,1,4,3,1] => 6
101000101 => 110001010 => [1,1,4,2,2] => 7
101000110 => 110001011 => [1,1,4,2,1,1] => 6
101000111 => 110001011 => [1,1,4,2,1,1] => 6
101001000 => 110010001 => [1,1,3,4,1] => 6
101001001 => 110010010 => [1,1,3,3,2] => 7
101001010 => 110010101 => [1,1,3,2,2,1] => 8
101001011 => 110010101 => [1,1,3,2,2,1] => 8
101001100 => 110010101 => [1,1,3,2,2,1] => 8
101001101 => 110010110 => [1,1,3,2,1,2] => 7
101001110 => 110010111 => [1,1,3,2,1,1,1] => 6
101001111 => 110010111 => [1,1,3,2,1,1,1] => 6
101010000 => 110100001 => [1,1,2,5,1] => 6
101010001 => 110100010 => [1,1,2,4,2] => 7
101010010 => 110100101 => [1,1,2,3,2,1] => 8
101010011 => 110100101 => [1,1,2,3,2,1] => 8
101010100 => 110101001 => [1,1,2,2,3,1] => 8
101010101 => 110101010 => [1,1,2,2,2,2] => 9
101010110 => 110101011 => [1,1,2,2,2,1,1] => 8
101010111 => 110101011 => [1,1,2,2,2,1,1] => 8
101011000 => 110101001 => [1,1,2,2,3,1] => 8
101011001 => 110101010 => [1,1,2,2,2,2] => 9
101011010 => 110101101 => [1,1,2,2,1,2,1] => 8
101011011 => 110101101 => [1,1,2,2,1,2,1] => 8
101011100 => 110101101 => [1,1,2,2,1,2,1] => 8
101011101 => 110101110 => [1,1,2,2,1,1,2] => 7
101011110 => 110101111 => [1,1,2,2,1,1,1,1] => 6
101011111 => 110101111 => [1,1,2,2,1,1,1,1] => 6
101100000 => 110100001 => [1,1,2,5,1] => 6
101100001 => 110100010 => [1,1,2,4,2] => 7
101100010 => 110100101 => [1,1,2,3,2,1] => 8
101100011 => 110100101 => [1,1,2,3,2,1] => 8
101100100 => 110101001 => [1,1,2,2,3,1] => 8
101100101 => 110101010 => [1,1,2,2,2,2] => 9
101100110 => 110101011 => [1,1,2,2,2,1,1] => 8
101100111 => 110101011 => [1,1,2,2,2,1,1] => 8
101101000 => 110110001 => [1,1,2,1,4,1] => 6
101101001 => 110110010 => [1,1,2,1,3,2] => 7
101101010 => 110110101 => [1,1,2,1,2,2,1] => 8
101101011 => 110110101 => [1,1,2,1,2,2,1] => 8
101101100 => 110110101 => [1,1,2,1,2,2,1] => 8
101101101 => 110110110 => [1,1,2,1,2,1,2] => 7
101101110 => 110110111 => [1,1,2,1,2,1,1,1] => 6
101101111 => 110110111 => [1,1,2,1,2,1,1,1] => 6
101110000 => 110110001 => [1,1,2,1,4,1] => 6
101110001 => 110110010 => [1,1,2,1,3,2] => 7
101110010 => 110110101 => [1,1,2,1,2,2,1] => 8
101110011 => 110110101 => [1,1,2,1,2,2,1] => 8
101110100 => 110111001 => [1,1,2,1,1,3,1] => 6
101110101 => 110111010 => [1,1,2,1,1,2,2] => 7
101110110 => 110111011 => [1,1,2,1,1,2,1,1] => 6
101110111 => 110111011 => [1,1,2,1,1,2,1,1] => 6
101111000 => 110111001 => [1,1,2,1,1,3,1] => 6
101111001 => 110111010 => [1,1,2,1,1,2,2] => 7
101111010 => 110111101 => [1,1,2,1,1,1,2,1] => 6
101111011 => 110111101 => [1,1,2,1,1,1,2,1] => 6
101111100 => 110111101 => [1,1,2,1,1,1,2,1] => 6
101111101 => 110111110 => [1,1,2,1,1,1,1,2] => 5
101111110 => 110111111 => [1,1,2,1,1,1,1,1,1] => 4
101111111 => 110111111 => [1,1,2,1,1,1,1,1,1] => 4
110000000 => 110000001 => [1,1,7,1] => 4
110000001 => 110000010 => [1,1,6,2] => 5
110000010 => 110000101 => [1,1,5,2,1] => 6
110000011 => 110000101 => [1,1,5,2,1] => 6
110000100 => 110001001 => [1,1,4,3,1] => 6
110000101 => 110001010 => [1,1,4,2,2] => 7
110000110 => 110001011 => [1,1,4,2,1,1] => 6
110000111 => 110001011 => [1,1,4,2,1,1] => 6
110001000 => 110010001 => [1,1,3,4,1] => 6
110001001 => 110010010 => [1,1,3,3,2] => 7
110001010 => 110010101 => [1,1,3,2,2,1] => 8
110001011 => 110010101 => [1,1,3,2,2,1] => 8
110001100 => 110010101 => [1,1,3,2,2,1] => 8
110001101 => 110010110 => [1,1,3,2,1,2] => 7
110001110 => 110010111 => [1,1,3,2,1,1,1] => 6
110001111 => 110010111 => [1,1,3,2,1,1,1] => 6
110010000 => 110100001 => [1,1,2,5,1] => 6
110010001 => 110100010 => [1,1,2,4,2] => 7
110010010 => 110100101 => [1,1,2,3,2,1] => 8
110010011 => 110100101 => [1,1,2,3,2,1] => 8
110010100 => 110101001 => [1,1,2,2,3,1] => 8
110010101 => 110101010 => [1,1,2,2,2,2] => 9
110010110 => 110101011 => [1,1,2,2,2,1,1] => 8
110010111 => 110101011 => [1,1,2,2,2,1,1] => 8
110011000 => 110101001 => [1,1,2,2,3,1] => 8
110011001 => 110101010 => [1,1,2,2,2,2] => 9
110011010 => 110101101 => [1,1,2,2,1,2,1] => 8
110011011 => 110101101 => [1,1,2,2,1,2,1] => 8
110011100 => 110101101 => [1,1,2,2,1,2,1] => 8
110011101 => 110101110 => [1,1,2,2,1,1,2] => 7
110011110 => 110101111 => [1,1,2,2,1,1,1,1] => 6
110011111 => 110101111 => [1,1,2,2,1,1,1,1] => 6
110100000 => 111000001 => [1,1,1,6,1] => 4
110100001 => 111000010 => [1,1,1,5,2] => 5
110100010 => 111000101 => [1,1,1,4,2,1] => 6
110100011 => 111000101 => [1,1,1,4,2,1] => 6
110100100 => 111001001 => [1,1,1,3,3,1] => 6
110100101 => 111001010 => [1,1,1,3,2,2] => 7
110100110 => 111001011 => [1,1,1,3,2,1,1] => 6
110100111 => 111001011 => [1,1,1,3,2,1,1] => 6
110101000 => 111010001 => [1,1,1,2,4,1] => 6
110101001 => 111010010 => [1,1,1,2,3,2] => 7
110101010 => 111010101 => [1,1,1,2,2,2,1] => 8
110101011 => 111010101 => [1,1,1,2,2,2,1] => 8
110101100 => 111010101 => [1,1,1,2,2,2,1] => 8
110101101 => 111010110 => [1,1,1,2,2,1,2] => 7
110101110 => 111010111 => [1,1,1,2,2,1,1,1] => 6
110101111 => 111010111 => [1,1,1,2,2,1,1,1] => 6
110110000 => 111010001 => [1,1,1,2,4,1] => 6
110110001 => 111010010 => [1,1,1,2,3,2] => 7
110110010 => 111010101 => [1,1,1,2,2,2,1] => 8
110110011 => 111010101 => [1,1,1,2,2,2,1] => 8
110110100 => 111011001 => [1,1,1,2,1,3,1] => 6
110110101 => 111011010 => [1,1,1,2,1,2,2] => 7
110110110 => 111011011 => [1,1,1,2,1,2,1,1] => 6
110110111 => 111011011 => [1,1,1,2,1,2,1,1] => 6
110111000 => 111011001 => [1,1,1,2,1,3,1] => 6
110111001 => 111011010 => [1,1,1,2,1,2,2] => 7
110111010 => 111011101 => [1,1,1,2,1,1,2,1] => 6
110111011 => 111011101 => [1,1,1,2,1,1,2,1] => 6
110111100 => 111011101 => [1,1,1,2,1,1,2,1] => 6
110111101 => 111011110 => [1,1,1,2,1,1,1,2] => 5
110111110 => 111011111 => [1,1,1,2,1,1,1,1,1] => 4
110111111 => 111011111 => [1,1,1,2,1,1,1,1,1] => 4
111000000 => 111000001 => [1,1,1,6,1] => 4
111000001 => 111000010 => [1,1,1,5,2] => 5
111000010 => 111000101 => [1,1,1,4,2,1] => 6
111000011 => 111000101 => [1,1,1,4,2,1] => 6
111000100 => 111001001 => [1,1,1,3,3,1] => 6
111000101 => 111001010 => [1,1,1,3,2,2] => 7
111000110 => 111001011 => [1,1,1,3,2,1,1] => 6
111000111 => 111001011 => [1,1,1,3,2,1,1] => 6
111001000 => 111010001 => [1,1,1,2,4,1] => 6
111001001 => 111010010 => [1,1,1,2,3,2] => 7
111001010 => 111010101 => [1,1,1,2,2,2,1] => 8
111001011 => 111010101 => [1,1,1,2,2,2,1] => 8
111001100 => 111010101 => [1,1,1,2,2,2,1] => 8
111001101 => 111010110 => [1,1,1,2,2,1,2] => 7
111001110 => 111010111 => [1,1,1,2,2,1,1,1] => 6
111001111 => 111010111 => [1,1,1,2,2,1,1,1] => 6
111010000 => 111100001 => [1,1,1,1,5,1] => 4
111010001 => 111100010 => [1,1,1,1,4,2] => 5
111010010 => 111100101 => [1,1,1,1,3,2,1] => 6
111010011 => 111100101 => [1,1,1,1,3,2,1] => 6
111010100 => 111101001 => [1,1,1,1,2,3,1] => 6
111010101 => 111101010 => [1,1,1,1,2,2,2] => 7
111010110 => 111101011 => [1,1,1,1,2,2,1,1] => 6
111010111 => 111101011 => [1,1,1,1,2,2,1,1] => 6
111011000 => 111101001 => [1,1,1,1,2,3,1] => 6
111011001 => 111101010 => [1,1,1,1,2,2,2] => 7
111011010 => 111101101 => [1,1,1,1,2,1,2,1] => 6
111011011 => 111101101 => [1,1,1,1,2,1,2,1] => 6
111011100 => 111101101 => [1,1,1,1,2,1,2,1] => 6
111011101 => 111101110 => [1,1,1,1,2,1,1,2] => 5
111011110 => 111101111 => [1,1,1,1,2,1,1,1,1] => 4
111011111 => 111101111 => [1,1,1,1,2,1,1,1,1] => 4
111100000 => 111100001 => [1,1,1,1,5,1] => 4
111100001 => 111100010 => [1,1,1,1,4,2] => 5
111100010 => 111100101 => [1,1,1,1,3,2,1] => 6
111100011 => 111100101 => [1,1,1,1,3,2,1] => 6
111100100 => 111101001 => [1,1,1,1,2,3,1] => 6
111100101 => 111101010 => [1,1,1,1,2,2,2] => 7
111100110 => 111101011 => [1,1,1,1,2,2,1,1] => 6
111100111 => 111101011 => [1,1,1,1,2,2,1,1] => 6
111101000 => 111110001 => [1,1,1,1,1,4,1] => 4
111101001 => 111110010 => [1,1,1,1,1,3,2] => 5
111101010 => 111110101 => [1,1,1,1,1,2,2,1] => 6
111101011 => 111110101 => [1,1,1,1,1,2,2,1] => 6
111101100 => 111110101 => [1,1,1,1,1,2,2,1] => 6
111101101 => 111110110 => [1,1,1,1,1,2,1,2] => 5
111101110 => 111110111 => [1,1,1,1,1,2,1,1,1] => 4
111101111 => 111110111 => [1,1,1,1,1,2,1,1,1] => 4
111110000 => 111110001 => [1,1,1,1,1,4,1] => 4
111110001 => 111110010 => [1,1,1,1,1,3,2] => 5
111110010 => 111110101 => [1,1,1,1,1,2,2,1] => 6
111110011 => 111110101 => [1,1,1,1,1,2,2,1] => 6
111110100 => 111111001 => [1,1,1,1,1,1,3,1] => 4
111110101 => 111111010 => [1,1,1,1,1,1,2,2] => 5
111110110 => 111111011 => [1,1,1,1,1,1,2,1,1] => 4
111110111 => 111111011 => [1,1,1,1,1,1,2,1,1] => 4
111111000 => 111111001 => [1,1,1,1,1,1,3,1] => 4
111111001 => 111111010 => [1,1,1,1,1,1,2,2] => 5
111111010 => 111111101 => [1,1,1,1,1,1,1,2,1] => 4
111111011 => 111111101 => [1,1,1,1,1,1,1,2,1] => 4
111111100 => 111111101 => [1,1,1,1,1,1,1,2,1] => 4
111111101 => 111111110 => [1,1,1,1,1,1,1,1,2] => 3
111111110 => 111111111 => [1,1,1,1,1,1,1,1,1,1] => 2
111111111 => 111111111 => [1,1,1,1,1,1,1,1,1,1] => 2
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Description
The number of corners of the ribbon associated with an integer composition.
We associate a ribbon shape to a composition $c=(c_1,\dots,c_n)$ with $c_i$ cells in the $i$-th row from bottom to top, such that the cells in two rows overlap in precisely one cell.
This statistic records the total number of corners of the ribbon shape.
Map
valleys-to-peaks
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.
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.