Identifier
Values
0 => 0 => 0
1 => 1 => 0
00 => 00 => 0
01 => 01 => 0
10 => 01 => 0
11 => 11 => 0
000 => 000 => 0
001 => 001 => 0
010 => 001 => 0
011 => 011 => 0
100 => 001 => 0
101 => 011 => 0
110 => 011 => 0
111 => 111 => 0
0000 => 0000 => 0
0001 => 0001 => 0
0010 => 0001 => 0
0011 => 0011 => 0
0100 => 0001 => 0
0101 => 0101 => 2
0110 => 0011 => 0
0111 => 0111 => 0
1000 => 0001 => 0
1001 => 0011 => 0
1010 => 0011 => 0
1011 => 0111 => 0
1100 => 0011 => 0
1101 => 0111 => 0
1110 => 0111 => 0
1111 => 1111 => 0
00000 => 00000 => 0
00001 => 00001 => 0
00010 => 00001 => 0
00011 => 00011 => 0
00100 => 00001 => 0
00101 => 00101 => 3
00110 => 00011 => 0
00111 => 00111 => 0
01000 => 00001 => 0
01001 => 00101 => 3
01010 => 00101 => 3
01011 => 01011 => 2
01100 => 00011 => 0
01101 => 01011 => 2
01110 => 00111 => 0
01111 => 01111 => 0
10000 => 00001 => 0
10001 => 00011 => 0
10010 => 00011 => 0
10011 => 00111 => 0
10100 => 00011 => 0
10101 => 01011 => 2
10110 => 00111 => 0
10111 => 01111 => 0
11000 => 00011 => 0
11001 => 00111 => 0
11010 => 00111 => 0
11011 => 01111 => 0
11100 => 00111 => 0
11101 => 01111 => 0
11110 => 01111 => 0
11111 => 11111 => 0
000000 => 000000 => 0
000001 => 000001 => 0
000010 => 000001 => 0
000011 => 000011 => 0
000100 => 000001 => 0
000101 => 000101 => 4
000110 => 000011 => 0
000111 => 000111 => 0
001000 => 000001 => 0
001001 => 001001 => 3
001010 => 000101 => 4
001011 => 001011 => 3
001100 => 000011 => 0
001101 => 001101 => 4
001110 => 000111 => 0
001111 => 001111 => 0
010000 => 000001 => 0
010001 => 000101 => 4
010010 => 000101 => 4
010011 => 001101 => 4
010100 => 000101 => 4
010101 => 010101 => 6
010110 => 001011 => 3
010111 => 010111 => 2
011000 => 000011 => 0
011001 => 001011 => 3
011010 => 001011 => 3
011011 => 011011 => 3
011100 => 000111 => 0
011101 => 010111 => 2
011110 => 001111 => 0
011111 => 011111 => 0
100000 => 000001 => 0
100001 => 000011 => 0
100010 => 000011 => 0
100011 => 000111 => 0
100100 => 000011 => 0
100101 => 001011 => 3
100110 => 000111 => 0
>>> Load all 2014 entries. <<<
100111 => 001111 => 0
101000 => 000011 => 0
101001 => 001011 => 3
101010 => 001011 => 3
101011 => 010111 => 2
101100 => 000111 => 0
101101 => 010111 => 2
101110 => 001111 => 0
101111 => 011111 => 0
110000 => 000011 => 0
110001 => 000111 => 0
110010 => 000111 => 0
110011 => 001111 => 0
110100 => 000111 => 0
110101 => 010111 => 2
110110 => 001111 => 0
110111 => 011111 => 0
111000 => 000111 => 0
111001 => 001111 => 0
111010 => 001111 => 0
111011 => 011111 => 0
111100 => 001111 => 0
111101 => 011111 => 0
111110 => 011111 => 0
111111 => 111111 => 0
0000000 => 0000000 => 0
0000001 => 0000001 => 0
0000010 => 0000001 => 0
0000011 => 0000011 => 0
0000100 => 0000001 => 0
0000101 => 0000101 => 5
0000110 => 0000011 => 0
0000111 => 0000111 => 0
0001000 => 0000001 => 0
0001001 => 0001001 => 4
0001010 => 0000101 => 5
0001011 => 0001011 => 4
0001100 => 0000011 => 0
0001101 => 0001101 => 5
0001110 => 0000111 => 0
0001111 => 0001111 => 0
0010000 => 0000001 => 0
0010001 => 0001001 => 4
0010010 => 0001001 => 4
0010011 => 0010011 => 3
0010100 => 0000101 => 5
0010101 => 0010101 => 8
0010110 => 0001011 => 4
0010111 => 0010111 => 3
0011000 => 0000011 => 0
0011001 => 0010011 => 3
0011010 => 0001101 => 5
0011011 => 0011011 => 4
0011100 => 0000111 => 0
0011101 => 0011101 => 5
0011110 => 0001111 => 0
0011111 => 0011111 => 0
0100000 => 0000001 => 0
0100001 => 0000101 => 5
0100010 => 0000101 => 5
0100011 => 0001101 => 5
0100100 => 0000101 => 5
0100101 => 0010101 => 8
0100110 => 0001101 => 5
0100111 => 0011101 => 5
0101000 => 0000101 => 5
0101001 => 0010101 => 8
0101010 => 0010101 => 8
0101011 => 0101011 => 6
0101100 => 0001011 => 4
0101101 => 0101011 => 6
0101110 => 0010111 => 3
0101111 => 0101111 => 2
0110000 => 0000011 => 0
0110001 => 0001011 => 4
0110010 => 0001011 => 4
0110011 => 0011011 => 4
0110100 => 0001011 => 4
0110101 => 0101011 => 6
0110110 => 0011011 => 4
0110111 => 0110111 => 3
0111000 => 0000111 => 0
0111001 => 0010111 => 3
0111010 => 0010111 => 3
0111011 => 0110111 => 3
0111100 => 0001111 => 0
0111101 => 0101111 => 2
0111110 => 0011111 => 0
0111111 => 0111111 => 0
1000000 => 0000001 => 0
1000001 => 0000011 => 0
1000010 => 0000011 => 0
1000011 => 0000111 => 0
1000100 => 0000011 => 0
1000101 => 0001011 => 4
1000110 => 0000111 => 0
1000111 => 0001111 => 0
1001000 => 0000011 => 0
1001001 => 0010011 => 3
1001010 => 0001011 => 4
1001011 => 0010111 => 3
1001100 => 0000111 => 0
1001101 => 0011011 => 4
1001110 => 0001111 => 0
1001111 => 0011111 => 0
1010000 => 0000011 => 0
1010001 => 0001011 => 4
1010010 => 0001011 => 4
1010011 => 0011011 => 4
1010100 => 0001011 => 4
1010101 => 0101011 => 6
1010110 => 0010111 => 3
1010111 => 0101111 => 2
1011000 => 0000111 => 0
1011001 => 0010111 => 3
1011010 => 0010111 => 3
1011011 => 0110111 => 3
1011100 => 0001111 => 0
1011101 => 0101111 => 2
1011110 => 0011111 => 0
1011111 => 0111111 => 0
1100000 => 0000011 => 0
1100001 => 0000111 => 0
1100010 => 0000111 => 0
1100011 => 0001111 => 0
1100100 => 0000111 => 0
1100101 => 0010111 => 3
1100110 => 0001111 => 0
1100111 => 0011111 => 0
1101000 => 0000111 => 0
1101001 => 0010111 => 3
1101010 => 0010111 => 3
1101011 => 0101111 => 2
1101100 => 0001111 => 0
1101101 => 0101111 => 2
1101110 => 0011111 => 0
1101111 => 0111111 => 0
1110000 => 0000111 => 0
1110001 => 0001111 => 0
1110010 => 0001111 => 0
1110011 => 0011111 => 0
1110100 => 0001111 => 0
1110101 => 0101111 => 2
1110110 => 0011111 => 0
1110111 => 0111111 => 0
1111000 => 0001111 => 0
1111001 => 0011111 => 0
1111010 => 0011111 => 0
1111011 => 0111111 => 0
1111100 => 0011111 => 0
1111101 => 0111111 => 0
1111110 => 0111111 => 0
1111111 => 1111111 => 0
00000000 => 00000000 => 0
00000001 => 00000001 => 0
00000010 => 00000001 => 0
00000011 => 00000011 => 0
00000100 => 00000001 => 0
00000101 => 00000101 => 6
00000110 => 00000011 => 0
00000111 => 00000111 => 0
00001000 => 00000001 => 0
00001001 => 00001001 => 5
00001010 => 00000101 => 6
00001011 => 00001011 => 5
00001100 => 00000011 => 0
00001101 => 00001101 => 6
00001110 => 00000111 => 0
00001111 => 00001111 => 0
00010000 => 00000001 => 0
00010001 => 00010001 => 4
00010010 => 00001001 => 5
00010011 => 00010011 => 4
00010100 => 00000101 => 6
00010101 => 00010101 => 10
00010110 => 00001011 => 5
00010111 => 00010111 => 4
00011000 => 00000011 => 0
00011001 => 00011001 => 5
00011010 => 00001101 => 6
00011011 => 00011011 => 5
00011100 => 00000111 => 0
00011101 => 00011101 => 6
00011110 => 00001111 => 0
00011111 => 00011111 => 0
00100000 => 00000001 => 0
00100001 => 00001001 => 5
00100010 => 00001001 => 5
00100011 => 00011001 => 5
00100100 => 00001001 => 5
00100101 => 00100101 => 9
00100110 => 00010011 => 4
00100111 => 00100111 => 3
00101000 => 00000101 => 6
00101001 => 00100101 => 9
00101010 => 00010101 => 10
00101011 => 00101011 => 8
00101100 => 00001011 => 5
00101101 => 00101011 => 8
00101110 => 00010111 => 4
00101111 => 00101111 => 3
00110000 => 00000011 => 0
00110001 => 00010011 => 4
00110010 => 00010011 => 4
00110011 => 00110011 => 4
00110100 => 00001101 => 6
00110101 => 00110101 => 10
00110110 => 00011011 => 5
00110111 => 00110111 => 4
00111000 => 00000111 => 0
00111001 => 00100111 => 3
00111010 => 00011101 => 6
00111011 => 00111011 => 5
00111100 => 00001111 => 0
00111101 => 00111101 => 6
00111110 => 00011111 => 0
00111111 => 00111111 => 0
01000000 => 00000001 => 0
01000001 => 00000101 => 6
01000010 => 00000101 => 6
01000011 => 00001101 => 6
01000100 => 00000101 => 6
01000101 => 00010101 => 10
01000110 => 00001101 => 6
01000111 => 00011101 => 6
01001000 => 00000101 => 6
01001001 => 00100101 => 9
01001010 => 00010101 => 10
01001011 => 00101011 => 8
01001100 => 00001101 => 6
01001101 => 00110101 => 10
01001110 => 00011101 => 6
01001111 => 00111101 => 6
01010000 => 00000101 => 6
01010001 => 00010101 => 10
01010010 => 00010101 => 10
01010011 => 00110101 => 10
01010100 => 00010101 => 10
01010101 => 01010101 => 12
01010110 => 00101011 => 8
01010111 => 01010111 => 6
01011000 => 00001011 => 5
01011001 => 00101011 => 8
01011010 => 00101011 => 8
01011011 => 01011011 => 7
01011100 => 00010111 => 4
01011101 => 01010111 => 6
01011110 => 00101111 => 3
01011111 => 01011111 => 2
01100000 => 00000011 => 0
01100001 => 00001011 => 5
01100010 => 00001011 => 5
01100011 => 00011011 => 5
01100100 => 00001011 => 5
01100101 => 00101011 => 8
01100110 => 00011011 => 5
01100111 => 00111011 => 5
01101000 => 00001011 => 5
01101001 => 00101011 => 8
01101010 => 00101011 => 8
01101011 => 01011011 => 7
01101100 => 00011011 => 5
01101101 => 01011011 => 7
01101110 => 00110111 => 4
01101111 => 01101111 => 3
01110000 => 00000111 => 0
01110001 => 00010111 => 4
01110010 => 00010111 => 4
01110011 => 00110111 => 4
01110100 => 00010111 => 4
01110101 => 01010111 => 6
01110110 => 00110111 => 4
01110111 => 01110111 => 4
01111000 => 00001111 => 0
01111001 => 00101111 => 3
01111010 => 00101111 => 3
01111011 => 01101111 => 3
01111100 => 00011111 => 0
01111101 => 01011111 => 2
01111110 => 00111111 => 0
01111111 => 01111111 => 0
10000000 => 00000001 => 0
10000001 => 00000011 => 0
10000010 => 00000011 => 0
10000011 => 00000111 => 0
10000100 => 00000011 => 0
10000101 => 00001011 => 5
10000110 => 00000111 => 0
10000111 => 00001111 => 0
10001000 => 00000011 => 0
10001001 => 00010011 => 4
10001010 => 00001011 => 5
10001011 => 00010111 => 4
10001100 => 00000111 => 0
10001101 => 00011011 => 5
10001110 => 00001111 => 0
10001111 => 00011111 => 0
10010000 => 00000011 => 0
10010001 => 00010011 => 4
10010010 => 00010011 => 4
10010011 => 00100111 => 3
10010100 => 00001011 => 5
10010101 => 00101011 => 8
10010110 => 00010111 => 4
10010111 => 00101111 => 3
10011000 => 00000111 => 0
10011001 => 00100111 => 3
10011010 => 00011011 => 5
10011011 => 00110111 => 4
10011100 => 00001111 => 0
10011101 => 00111011 => 5
10011110 => 00011111 => 0
10011111 => 00111111 => 0
10100000 => 00000011 => 0
10100001 => 00001011 => 5
10100010 => 00001011 => 5
10100011 => 00011011 => 5
10100100 => 00001011 => 5
10100101 => 00101011 => 8
10100110 => 00011011 => 5
10100111 => 00111011 => 5
10101000 => 00001011 => 5
10101001 => 00101011 => 8
10101010 => 00101011 => 8
10101011 => 01010111 => 6
10101100 => 00010111 => 4
10101101 => 01010111 => 6
10101110 => 00101111 => 3
10101111 => 01011111 => 2
10110000 => 00000111 => 0
10110001 => 00010111 => 4
10110010 => 00010111 => 4
10110011 => 00110111 => 4
10110100 => 00010111 => 4
10110101 => 01010111 => 6
10110110 => 00110111 => 4
10110111 => 01101111 => 3
10111000 => 00001111 => 0
10111001 => 00101111 => 3
10111010 => 00101111 => 3
10111011 => 01101111 => 3
10111100 => 00011111 => 0
10111101 => 01011111 => 2
10111110 => 00111111 => 0
10111111 => 01111111 => 0
11000000 => 00000011 => 0
11000001 => 00000111 => 0
11000010 => 00000111 => 0
11000011 => 00001111 => 0
11000100 => 00000111 => 0
11000101 => 00010111 => 4
11000110 => 00001111 => 0
11000111 => 00011111 => 0
11001000 => 00000111 => 0
11001001 => 00100111 => 3
11001010 => 00010111 => 4
11001011 => 00101111 => 3
11001100 => 00001111 => 0
11001101 => 00110111 => 4
11001110 => 00011111 => 0
11001111 => 00111111 => 0
11010000 => 00000111 => 0
11010001 => 00010111 => 4
11010010 => 00010111 => 4
11010011 => 00110111 => 4
11010100 => 00010111 => 4
11010101 => 01010111 => 6
11010110 => 00101111 => 3
11010111 => 01011111 => 2
11011000 => 00001111 => 0
11011001 => 00101111 => 3
11011010 => 00101111 => 3
11011011 => 01101111 => 3
11011100 => 00011111 => 0
11011101 => 01011111 => 2
11011110 => 00111111 => 0
11011111 => 01111111 => 0
11100000 => 00000111 => 0
11100001 => 00001111 => 0
11100010 => 00001111 => 0
11100011 => 00011111 => 0
11100100 => 00001111 => 0
11100101 => 00101111 => 3
11100110 => 00011111 => 0
11100111 => 00111111 => 0
11101000 => 00001111 => 0
11101001 => 00101111 => 3
11101010 => 00101111 => 3
11101011 => 01011111 => 2
11101100 => 00011111 => 0
11101101 => 01011111 => 2
11101110 => 00111111 => 0
11101111 => 01111111 => 0
11110000 => 00001111 => 0
11110001 => 00011111 => 0
11110010 => 00011111 => 0
11110011 => 00111111 => 0
11110100 => 00011111 => 0
11110101 => 01011111 => 2
11110110 => 00111111 => 0
11110111 => 01111111 => 0
11111000 => 00011111 => 0
11111001 => 00111111 => 0
11111010 => 00111111 => 0
11111011 => 01111111 => 0
11111100 => 00111111 => 0
11111101 => 01111111 => 0
11111110 => 01111111 => 0
11111111 => 11111111 => 0
000000000 => 000000000 => 0
000000001 => 000000001 => 0
000000010 => 000000001 => 0
000000011 => 000000011 => 0
000000100 => 000000001 => 0
000000101 => 000000101 => 7
000000110 => 000000011 => 0
000000111 => 000000111 => 0
000001000 => 000000001 => 0
000001001 => 000001001 => 6
000001010 => 000000101 => 7
000001011 => 000001011 => 6
000001100 => 000000011 => 0
000001101 => 000001101 => 7
000001110 => 000000111 => 0
000001111 => 000001111 => 0
000010000 => 000000001 => 0
000010001 => 000010001 => 5
000010010 => 000001001 => 6
000010011 => 000010011 => 5
000010100 => 000000101 => 7
000010101 => 000010101 => 12
000010110 => 000001011 => 6
000010111 => 000010111 => 5
000011000 => 000000011 => 0
000011001 => 000011001 => 6
000011010 => 000001101 => 7
000011011 => 000011011 => 6
000011100 => 000000111 => 0
000011101 => 000011101 => 7
000011110 => 000001111 => 0
000011111 => 000011111 => 0
000100000 => 000000001 => 0
000100001 => 000010001 => 5
000100010 => 000010001 => 5
000100011 => 000100011 => 4
000100100 => 000001001 => 6
000100101 => 000100101 => 11
000100110 => 000010011 => 5
000100111 => 000100111 => 4
000101000 => 000000101 => 7
000101001 => 000100101 => 11
000101010 => 000010101 => 12
000101011 => 000101011 => 10
000101100 => 000001011 => 6
000101101 => 000101011 => 10
000101110 => 000010111 => 5
000101111 => 000101111 => 4
000110000 => 000000011 => 0
000110001 => 000100011 => 4
000110010 => 000011001 => 6
000110011 => 000110011 => 5
000110100 => 000001101 => 7
000110101 => 000110101 => 12
000110110 => 000011011 => 6
000110111 => 000110111 => 5
000111000 => 000000111 => 0
000111001 => 000111001 => 6
000111010 => 000011101 => 7
000111011 => 000111011 => 6
000111100 => 000001111 => 0
000111101 => 000111101 => 7
000111110 => 000011111 => 0
000111111 => 000111111 => 0
001000000 => 000000001 => 0
001000001 => 000001001 => 6
001000010 => 000001001 => 6
001000011 => 000011001 => 6
001000100 => 000001001 => 6
001000101 => 000100101 => 11
001000110 => 000011001 => 6
001000111 => 000111001 => 6
001001000 => 000001001 => 6
001001001 => 001001001 => 9
001001010 => 000100101 => 11
001001011 => 001001011 => 9
001001100 => 000010011 => 5
001001101 => 001001101 => 10
001001110 => 000100111 => 4
001001111 => 001001111 => 3
001010000 => 000000101 => 7
001010001 => 000100101 => 11
001010010 => 000100101 => 11
001010011 => 001001101 => 10
001010100 => 000010101 => 12
001010101 => 001010101 => 15
001010110 => 000101011 => 10
001010111 => 001010111 => 8
001011000 => 000001011 => 6
001011001 => 001001011 => 9
001011010 => 000101011 => 10
001011011 => 001011011 => 9
001011100 => 000010111 => 5
001011101 => 001010111 => 8
001011110 => 000101111 => 4
001011111 => 001011111 => 3
001100000 => 000000011 => 0
001100001 => 000010011 => 5
001100010 => 000010011 => 5
001100011 => 000110011 => 5
001100100 => 000010011 => 5
001100101 => 001001101 => 10
001100110 => 000110011 => 5
001100111 => 001100111 => 4
001101000 => 000001101 => 7
001101001 => 001001101 => 10
001101010 => 000110101 => 12
001101011 => 001101011 => 10
001101100 => 000011011 => 6
001101101 => 001101011 => 10
001101110 => 000110111 => 5
001101111 => 001101111 => 4
001110000 => 000000111 => 0
001110001 => 000100111 => 4
001110010 => 000100111 => 4
001110011 => 001100111 => 4
001110100 => 000011101 => 7
001110101 => 001110101 => 12
001110110 => 000111011 => 6
001110111 => 001110111 => 5
001111000 => 000001111 => 0
001111001 => 001001111 => 3
001111010 => 000111101 => 7
001111011 => 001111011 => 6
001111100 => 000011111 => 0
001111101 => 001111101 => 7
001111110 => 000111111 => 0
001111111 => 001111111 => 0
010000000 => 000000001 => 0
010000001 => 000000101 => 7
010000010 => 000000101 => 7
010000011 => 000001101 => 7
010000100 => 000000101 => 7
010000101 => 000010101 => 12
010000110 => 000001101 => 7
010000111 => 000011101 => 7
010001000 => 000000101 => 7
010001001 => 000100101 => 11
010001010 => 000010101 => 12
010001011 => 000101011 => 10
010001100 => 000001101 => 7
010001101 => 000110101 => 12
010001110 => 000011101 => 7
010001111 => 000111101 => 7
010010000 => 000000101 => 7
010010001 => 000100101 => 11
010010010 => 000100101 => 11
010010011 => 001001101 => 10
010010100 => 000010101 => 12
010010101 => 001010101 => 15
010010110 => 000101011 => 10
010010111 => 001010111 => 8
010011000 => 000001101 => 7
010011001 => 001001101 => 10
010011010 => 000110101 => 12
010011011 => 001101011 => 10
010011100 => 000011101 => 7
010011101 => 001110101 => 12
010011110 => 000111101 => 7
010011111 => 001111101 => 7
010100000 => 000000101 => 7
010100001 => 000010101 => 12
010100010 => 000010101 => 12
010100011 => 000110101 => 12
010100100 => 000010101 => 12
010100101 => 001010101 => 15
010100110 => 000110101 => 12
010100111 => 001110101 => 12
010101000 => 000010101 => 12
010101001 => 001010101 => 15
010101010 => 001010101 => 15
010101011 => 010101011 => 12
010101100 => 000101011 => 10
010101101 => 010101011 => 12
010101110 => 001010111 => 8
010101111 => 010101111 => 6
010110000 => 000001011 => 6
010110001 => 000101011 => 10
010110010 => 000101011 => 10
010110011 => 001101011 => 10
010110100 => 000101011 => 10
010110101 => 010101011 => 12
010110110 => 001011011 => 9
010110111 => 010110111 => 7
010111000 => 000010111 => 5
010111001 => 001010111 => 8
010111010 => 001010111 => 8
010111011 => 010110111 => 7
010111100 => 000101111 => 4
010111101 => 010101111 => 6
010111110 => 001011111 => 3
010111111 => 010111111 => 2
011000000 => 000000011 => 0
011000001 => 000001011 => 6
011000010 => 000001011 => 6
011000011 => 000011011 => 6
011000100 => 000001011 => 6
011000101 => 000101011 => 10
011000110 => 000011011 => 6
011000111 => 000111011 => 6
011001000 => 000001011 => 6
011001001 => 001001011 => 9
011001010 => 000101011 => 10
011001011 => 001011011 => 9
011001100 => 000011011 => 6
011001101 => 001101011 => 10
011001110 => 000111011 => 6
011001111 => 001111011 => 6
011010000 => 000001011 => 6
011010001 => 000101011 => 10
011010010 => 000101011 => 10
011010011 => 001101011 => 10
011010100 => 000101011 => 10
011010101 => 010101011 => 12
011010110 => 001011011 => 9
011010111 => 010110111 => 7
011011000 => 000011011 => 6
011011001 => 001011011 => 9
011011010 => 001011011 => 9
011011011 => 011011011 => 9
011011100 => 000110111 => 5
011011101 => 010110111 => 7
011011110 => 001101111 => 4
011011111 => 011011111 => 3
011100000 => 000000111 => 0
011100001 => 000010111 => 5
011100010 => 000010111 => 5
011100011 => 000110111 => 5
011100100 => 000010111 => 5
011100101 => 001010111 => 8
011100110 => 000110111 => 5
011100111 => 001110111 => 5
011101000 => 000010111 => 5
011101001 => 001010111 => 8
011101010 => 001010111 => 8
011101011 => 010110111 => 7
011101100 => 000110111 => 5
011101101 => 010110111 => 7
011101110 => 001110111 => 5
011101111 => 011101111 => 4
011110000 => 000001111 => 0
011110001 => 000101111 => 4
011110010 => 000101111 => 4
011110011 => 001101111 => 4
011110100 => 000101111 => 4
011110101 => 010101111 => 6
011110110 => 001101111 => 4
011110111 => 011101111 => 4
011111000 => 000011111 => 0
011111001 => 001011111 => 3
011111010 => 001011111 => 3
011111011 => 011011111 => 3
011111100 => 000111111 => 0
011111101 => 010111111 => 2
011111110 => 001111111 => 0
011111111 => 011111111 => 0
100000000 => 000000001 => 0
100000001 => 000000011 => 0
100000010 => 000000011 => 0
100000011 => 000000111 => 0
100000100 => 000000011 => 0
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000111010101 => 000111010101 => 24
000111010011 => 000111001101 => 16
000111001101 => 000111001101 => 16
000111001011 => 000111001011 => 15
000111000111 => 000111000111 => 6
000110110101 => 000110101011 => 21
000110110011 => 000110011011 => 14
000110101101 => 000110101011 => 21
000110101011 => 000110101011 => 21
000110100111 => 000110011101 => 15
000110011101 => 000110011101 => 15
000110011011 => 000110011011 => 14
000110010111 => 000110010111 => 13
000110001111 => 000110001111 => 5
000101110101 => 000101010111 => 18
000101110011 => 000100110111 => 12
000101101101 => 000101011011 => 19
000101101011 => 000101011011 => 19
000101100111 => 000100111011 => 13
000101011101 => 000101010111 => 18
000101011011 => 000101011011 => 19
000101010111 => 000101010111 => 18
000101001111 => 000100111101 => 14
000100111101 => 000100111101 => 14
000100111011 => 000100111011 => 13
000100110111 => 000100110111 => 12
000100101111 => 000100101111 => 11
000100011111 => 000100011111 => 4
000011110101 => 000011110101 => 18
000011110011 => 000011110011 => 8
000011101101 => 000011101011 => 16
000011101011 => 000011101011 => 16
000011100111 => 000011100111 => 7
000011011101 => 000011010111 => 14
000011011011 => 000011011011 => 15
000011010111 => 000011010111 => 14
000011001111 => 000011001111 => 6
000010111101 => 000010101111 => 12
000010111011 => 000010110111 => 13
000010110111 => 000010110111 => 13
000010101111 => 000010101111 => 12
000010011111 => 000010011111 => 5
000001111101 => 000001111101 => 10
000001111011 => 000001111011 => 9
000001110111 => 000001110111 => 8
000001101111 => 000001101111 => 7
000001011111 => 000001011111 => 6
000000111111 => 000000111111 => 0
111110000001 => 000000111111 => 0
111001100001 => 000010011111 => 5
111000011001 => 000011001111 => 6
111000000111 => 000000111111 => 0
111000001101 => 000001101111 => 7
111000110001 => 000100011111 => 4
111000100101 => 000100101111 => 11
111011000001 => 000001011111 => 6
111010010001 => 000100101111 => 11
111010000101 => 000010101111 => 12
100111100001 => 000010011111 => 5
100110011001 => 001001100111 => 10
100110000111 => 000011100111 => 7
100110001101 => 000110011011 => 14
100110110001 => 000100110111 => 12
100110100101 => 001001101011 => 19
100001111001 => 000011110011 => 8
100001100111 => 000011001111 => 6
100001101101 => 000011010111 => 14
100000011111 => 000000111111 => 0
100000110111 => 000001101111 => 7
100000111101 => 000001111011 => 9
100011011001 => 000110010111 => 13
100011000111 => 000110001111 => 5
100011001101 => 000110011011 => 14
100011110001 => 000100011111 => 4
100011100101 => 000111001011 => 15
100010010111 => 000100101111 => 11
100010011101 => 000100111011 => 13
100010110101 => 000101010111 => 18
101101100001 => 000010110111 => 13
101100011001 => 000110010111 => 13
101100000111 => 000001110111 => 8
101100001101 => 000011010111 => 14
101100110001 => 000100110111 => 12
101100100101 => 001001010111 => 17
101111000001 => 000001011111 => 6
101110010001 => 000100101111 => 11
101110000101 => 000010101111 => 12
101001011001 => 001001010111 => 17
101001000111 => 000111001011 => 15
101001001101 => 001001101011 => 19
101001110001 => 000100111011 => 13
101001100101 => 001001101011 => 19
101000010111 => 000010101111 => 12
101000011101 => 000011101011 => 16
101000110101 => 000110101011 => 21
101011010001 => 000101010111 => 18
101011000101 => 000101010111 => 18
101010010101 => 001010101011 => 24
0000000000 => 0000000000 => 0
0000000110 => 0000000011 => 0
0000011000 => 0000000011 => 0
0000011110 => 0000001111 => 0
0000010010 => 0000001001 => 7
0001100000 => 0000000011 => 0
0001100110 => 0000110011 => 6
0001111000 => 0000001111 => 0
0001111110 => 0000111111 => 0
0001110010 => 0000111001 => 7
0001001000 => 0000001001 => 7
0001001110 => 0000100111 => 5
0001000010 => 0000010001 => 6
0001011010 => 0000101011 => 12
0110000000 => 0000000011 => 0
0110000110 => 0000011011 => 7
0110011000 => 0000011011 => 7
0110011110 => 0001111011 => 7
0110010010 => 0001001011 => 11
0111100000 => 0000001111 => 0
0111100110 => 0001101111 => 5
0111111000 => 0000111111 => 0
0111110010 => 0001011111 => 4
0111001000 => 0000010111 => 6
0111001110 => 0001110111 => 6
0111000010 => 0000010111 => 6
0100100000 => 0000000101 => 8
0100100110 => 0001001101 => 12
0100111000 => 0000011101 => 8
0100111110 => 0001111101 => 8
0100110010 => 0001001101 => 12
0100001000 => 0000000101 => 8
0100001110 => 0000011101 => 8
0100000010 => 0000000101 => 8
0100011010 => 0000110101 => 14
0101101000 => 0000101011 => 12
0101100010 => 0000101011 => 12
0101111010 => 0010101111 => 8
0101001010 => 0001010101 => 18
000001111110 => 000000111111 => 0
000110011110 => 000011001111 => 6
000111100110 => 000011110011 => 8
000111111000 => 000000111111 => 0
000111001110 => 000011100111 => 7
000111011010 => 000011101011 => 16
000100111110 => 000010011111 => 5
000101101110 => 000010110111 => 13
000101111010 => 000010101111 => 12
011000011110 => 000001111011 => 9
011001100110 => 000110011011 => 14
011001111000 => 000001111011 => 9
011001110010 => 000100111011 => 13
011001001110 => 000100111011 => 13
011001011010 => 000101011011 => 19
011110000110 => 000001101111 => 7
011110011000 => 000001101111 => 7
011110010010 => 000100101111 => 11
011111100000 => 000000111111 => 0
011111001000 => 000001011111 => 6
011111000010 => 000001011111 => 6
011100100110 => 000100110111 => 12
011100111000 => 000001110111 => 8
011100110010 => 000100110111 => 12
011100001110 => 000001110111 => 8
011100011010 => 000011010111 => 14
011101101000 => 000010110111 => 13
011101100010 => 000010110111 => 13
011101001010 => 000101010111 => 18
010010011110 => 000100111101 => 14
010011100110 => 000110011101 => 15
010011111000 => 000001111101 => 10
010011110010 => 000100111101 => 14
010011001110 => 000110011101 => 15
010011011010 => 000110101011 => 21
010000111110 => 000001111101 => 10
010001101110 => 000011010111 => 14
010001111010 => 000011110101 => 18
010110100110 => 000110101011 => 21
010110111000 => 000010110111 => 13
010110110010 => 000101011011 => 19
010110001110 => 000011101011 => 16
010110011010 => 000110101011 => 21
010111101000 => 000010101111 => 12
010111100010 => 000010101111 => 12
010111001010 => 000101010111 => 18
010100101110 => 000101010111 => 18
010100111010 => 000111010101 => 24
010101101010 => 001010101011 => 24
0010101010 => 0001010101 => 18
0010101000 => 0000010101 => 14
0010101100 => 0000101011 => 12
0010100100 => 0000100101 => 13
0010110100 => 0000101011 => 12
0010010100 => 0000100101 => 13
0011010100 => 0000110101 => 14
0001010100 => 0000010101 => 14
0101010100 => 0001010101 => 18
0010101110 => 0001010111 => 10
0010100000 => 0000000101 => 8
0010111100 => 0000101111 => 5
0010000100 => 0000001001 => 7
0011110100 => 0000111101 => 8
0000010100 => 0000000101 => 8
0111010100 => 0001010111 => 10
0000000010 => 0000000001 => 0
0000001110 => 0000000111 => 0
0000111110 => 0000011111 => 0
0011111110 => 0001111111 => 0
00000000010 => 00000000001 => 0
0000000100 => 0000000001 => 0
0000001010 => 0000000101 => 8
0000010110 => 0000001011 => 7
0000101110 => 0000010111 => 6
0001011110 => 0000101111 => 5
0010111110 => 0001011111 => 4
0010110010 => 0001001011 => 11
0010111000 => 0000010111 => 6
0011001010 => 0001001101 => 12
0011001100 => 0000110011 => 6
0011010010 => 0001001101 => 12
0011011000 => 0000011011 => 7
0011100010 => 0000100111 => 5
0011100100 => 0000100111 => 5
0011101000 => 0000011101 => 8
0011110000 => 0000001111 => 0
0100101010 => 0001010101 => 18
0100101100 => 0000101011 => 12
0100110100 => 0000110101 => 14
0101001100 => 0000110101 => 14
0101010010 => 0001010101 => 18
0101011000 => 0000101011 => 12
0101100100 => 0000101011 => 12
0101110000 => 0000010111 => 6
0110001010 => 0000101011 => 12
0110001100 => 0000011011 => 7
0110010100 => 0000101011 => 12
0110100010 => 0000101011 => 12
0110100100 => 0000101011 => 12
0110101000 => 0000101011 => 12
0110110000 => 0000011011 => 7
0111000100 => 0000010111 => 6
0111010000 => 0000010111 => 6
01001001001 => 00100100101 => 18
01000001000 => 00000000101 => 9
01000010000 => 00000000101 => 9
00100100101 => 00100100101 => 18
00100101001 => 00100100101 => 18
00100010001 => 00010001001 => 12
00101001001 => 00100100101 => 18
00010001001 => 00010001001 => 12
00010010001 => 00010001001 => 12
00001010000 => 00000000101 => 9
00000100000 => 00000000001 => 0
0100000000 => 0000000001 => 0
0100000011 => 0000001101 => 8
0100000111 => 0000011101 => 8
0100011111 => 0001111101 => 8
0100111111 => 0011111101 => 8
0101111111 => 0101111111 => 2
01000000000 => 00000000001 => 0
01000000011 => 00000001101 => 9
0100000101 => 0000010101 => 14
01000000111 => 00000011101 => 9
0100001011 => 0000101011 => 12
01000001111 => 00000111101 => 9
01000011111 => 00001111101 => 9
0100101111 => 0010101111 => 8
01000111111 => 00011111101 => 9
0101011111 => 0101011111 => 6
01001111111 => 00111111101 => 9
0110111111 => 0110111111 => 3
01011111111 => 01011111111 => 2
0101010110 => 0010101011 => 15
0101011001 => 0010101011 => 15
0101011010 => 0010101011 => 15
0101011100 => 0001010111 => 10
0101100101 => 0010101011 => 15
0101100110 => 0001101011 => 12
0101101001 => 0010101011 => 15
0101101010 => 0010101011 => 15
0101101100 => 0001011011 => 11
0101110001 => 0001010111 => 10
0101110010 => 0001010111 => 10
0101110100 => 0001010111 => 10
0101111000 => 0000101111 => 5
0110010101 => 0010101011 => 15
0110010110 => 0001011011 => 11
0110011001 => 0010011011 => 10
0110011010 => 0001101011 => 12
0110011100 => 0000111011 => 7
0110100101 => 0010101011 => 15
0110100110 => 0001101011 => 12
0110101001 => 0010101011 => 15
0110101010 => 0010101011 => 15
0110101100 => 0001011011 => 11
0110110001 => 0001011011 => 11
0110110010 => 0001011011 => 11
0110110100 => 0001011011 => 11
0110111000 => 0000110111 => 6
0111000101 => 0001010111 => 10
0111000110 => 0000110111 => 6
0111001001 => 0010010111 => 9
0111001010 => 0001010111 => 10
0111001100 => 0000110111 => 6
0111010010 => 0001010111 => 10
0111011000 => 0000110111 => 6
0111100010 => 0000101111 => 5
0111100100 => 0000101111 => 5
0111101000 => 0000101111 => 5
0111110000 => 0000011111 => 0
010101010110 => 001010101011 => 24
010101011001 => 001010101011 => 24
010101011010 => 001010101011 => 24
010101011100 => 000101010111 => 18
010101100101 => 001010101011 => 24
010101100110 => 000110101011 => 21
010101101001 => 001010101011 => 24
010101101100 => 000101011011 => 19
010101110001 => 000101010111 => 18
010101110010 => 000101010111 => 18
010101110100 => 000101010111 => 18
010101111000 => 000010101111 => 12
010110010101 => 001010101011 => 24
010110010110 => 000101011011 => 19
010110011001 => 001001101011 => 19
010110011100 => 000011101011 => 16
010110100101 => 001010101011 => 24
010110101001 => 001010101011 => 24
010110101010 => 001010101011 => 24
010110101100 => 000101011011 => 19
010110110001 => 000101011011 => 19
010110110100 => 000101011011 => 19
010111000101 => 000101010111 => 18
010111000110 => 000011010111 => 14
010111001001 => 001001010111 => 17
010111001100 => 000011010111 => 14
010111010001 => 000101010111 => 18
010111010010 => 000101010111 => 18
010111010100 => 000101010111 => 18
010111011000 => 000010110111 => 13
010111100001 => 000010101111 => 12
010111100100 => 000010101111 => 12
010111110000 => 000001011111 => 6
011001010101 => 001010101011 => 24
011001010110 => 000101011011 => 19
011001011001 => 001001011011 => 18
011001011100 => 000010110111 => 13
011001100101 => 001001101011 => 19
011001101001 => 001001101011 => 19
011001101010 => 000110101011 => 21
011001101100 => 000011011011 => 15
011001110001 => 000100111011 => 13
011001110100 => 000011101011 => 16
011010010101 => 001010101011 => 24
011010010110 => 000101011011 => 19
011010011001 => 001001101011 => 19
011010011010 => 000110101011 => 21
011010011100 => 000011101011 => 16
011010100101 => 001010101011 => 24
011010100110 => 000110101011 => 21
011010101001 => 001010101011 => 24
011010101010 => 001010101011 => 24
011010101100 => 000101011011 => 19
011010110001 => 000101011011 => 19
011010110010 => 000101011011 => 19
011010110100 => 000101011011 => 19
011010111000 => 000010110111 => 13
011011000101 => 000101011011 => 19
011011000110 => 000011011011 => 15
011011001001 => 001001011011 => 18
011011001010 => 000101011011 => 19
011011001100 => 000011011011 => 15
011011010001 => 000101011011 => 19
011011010010 => 000101011011 => 19
011011010100 => 000101011011 => 19
011011011000 => 000011011011 => 15
011011100001 => 000010110111 => 13
011011100010 => 000010110111 => 13
011011100100 => 000010110111 => 13
011011101000 => 000010110111 => 13
011011110000 => 000001101111 => 7
011100010101 => 000101010111 => 18
011100010110 => 000010110111 => 13
011100011001 => 000110010111 => 13
011100011100 => 000001110111 => 8
011100100101 => 001001010111 => 17
011100101001 => 001001010111 => 17
011100101010 => 000101010111 => 18
011100101100 => 000010110111 => 13
011100110001 => 000100110111 => 12
011100110100 => 000011010111 => 14
011101000101 => 000101010111 => 18
011101000110 => 000011010111 => 14
011101001001 => 001001010111 => 17
011101001100 => 000011010111 => 14
011101010001 => 000101010111 => 18
011101010010 => 000101010111 => 18
011101010100 => 000101010111 => 18
011101011000 => 000010110111 => 13
011101100001 => 000010110111 => 13
011101100100 => 000010110111 => 13
011101110000 => 000001110111 => 8
011110000101 => 000010101111 => 12
011110001001 => 000100101111 => 11
011110001010 => 000010101111 => 12
011110001100 => 000001101111 => 7
011110010001 => 000100101111 => 11
011110010100 => 000010101111 => 12
011110100001 => 000010101111 => 12
011110100010 => 000010101111 => 12
011110100100 => 000010101111 => 12
011110101000 => 000010101111 => 12
011110110000 => 000001101111 => 7
011111000001 => 000001011111 => 6
011111000100 => 000001011111 => 6
011111010000 => 000001011111 => 6
0100000100 => 0000000101 => 8
0011100110 => 0001100111 => 5
0011101010 => 0001110101 => 14
0011101100 => 0000111011 => 7
0001101110 => 0000110111 => 6
0010110110 => 0001011011 => 11
0011110010 => 0001001111 => 4
0001110110 => 0000111011 => 7
0100111010 => 0001110101 => 14
0010111010 => 0001010111 => 10
0011111000 => 0000011111 => 0
0001111010 => 0000111101 => 8
0100111100 => 0000111101 => 8
0001111100 => 0000011111 => 0
001111000110 => 000011001111 => 6
001111001010 => 000100111101 => 14
100111001100 => 000011001111 => 6
001111001100 => 000011001111 => 6
001011010110 => 000101011011 => 19
001111010010 => 000100111101 => 14
100111010100 => 000011101011 => 16
001111010100 => 000011110101 => 18
000111010110 => 000011101011 => 16
001011011010 => 000101011011 => 19
100111011000 => 000001110111 => 8
001111011000 => 000001111011 => 9
100011011100 => 000001101111 => 7
010011011100 => 000011010111 => 14
001011011100 => 000010110111 => 13
000111011100 => 000001110111 => 8
000011011110 => 000001101111 => 7
001101100110 => 000110011011 => 14
001101101010 => 000110101011 => 21
100101101100 => 000010110111 => 13
001101101100 => 000011011011 => 15
001011100110 => 000100110111 => 12
001111100010 => 000010011111 => 5
100111100100 => 000010011111 => 5
001111100100 => 000010011111 => 5
010011101010 => 000111010101 => 24
001011101010 => 000101010111 => 18
100111101000 => 000001111011 => 9
001111101000 => 000001111101 => 10
000111101010 => 000011110101 => 18
100011101100 => 000001110111 => 8
010011101100 => 000011101011 => 16
001011101100 => 000010110111 => 13
000111101100 => 000001111011 => 9
000011101110 => 000001110111 => 8
101001110100 => 000011101011 => 16
001001110110 => 000100111011 => 13
001101110010 => 000100110111 => 12
100101110100 => 000010101111 => 12
001101110100 => 000011010111 => 14
000101110110 => 000010110111 => 13
001011110010 => 000100101111 => 11
100111110000 => 000000111111 => 0
001111110000 => 000000111111 => 0
100011110100 => 000001111011 => 9
010011110100 => 000011110101 => 18
001011110100 => 000010101111 => 12
000111110100 => 000001111101 => 10
000011110110 => 000001111011 => 9
110001111000 => 000000111111 => 0
101001111000 => 000001111011 => 9
001001111010 => 000100111101 => 14
100101111000 => 000001011111 => 6
001101111000 => 000001101111 => 7
100011111000 => 000000111111 => 0
001011111000 => 000001011111 => 6
000011111010 => 000001111101 => 10
010001111100 => 000001111101 => 10
001001111100 => 000010011111 => 5
000101111100 => 000001011111 => 6
000011111100 => 000000111111 => 0
0000000101 => 0000000101 => 8
0000001101 => 0000001101 => 8
0000011101 => 0000011101 => 8
0001111101 => 0001111101 => 8
0011111101 => 0011111101 => 8
00000000101 => 00000000101 => 9
0000001001 => 0000001001 => 7
00000001101 => 00000001101 => 9
0000010101 => 0000010101 => 14
00000011101 => 00000011101 => 9
0000101101 => 0000101011 => 12
00000111101 => 00000111101 => 9
00001111101 => 00001111101 => 9
0010111101 => 0010101111 => 8
00011111101 => 00011111101 => 9
0101111101 => 0101011111 => 6
00111111101 => 00111111101 => 9
11111111101 => 01111111111 => 0
100101010101 => 001010101011 => 24
100101011001 => 001001010111 => 17
100101100101 => 001001010111 => 17
100101101001 => 001001010111 => 17
100101110001 => 000100101111 => 11
100110010101 => 001001101011 => 19
100110101001 => 001001101011 => 19
100111000101 => 000100111011 => 13
100111001001 => 001001001111 => 9
100111010001 => 000100111011 => 13
101001010101 => 001010101011 => 24
101001101001 => 001001101011 => 19
101010011001 => 001001101011 => 19
101010100101 => 001010101011 => 24
101010101001 => 001010101011 => 24
101010110001 => 000101010111 => 18
101011001001 => 001001010111 => 17
101011100001 => 000010101111 => 12
101100010101 => 000101010111 => 18
101100101001 => 001001010111 => 17
101101000101 => 000101010111 => 18
101101001001 => 001001010111 => 17
101101010001 => 000101010111 => 18
101110001001 => 000100101111 => 11
101110100001 => 000010101111 => 12
110001010101 => 000101010111 => 18
110001011001 => 000100101111 => 11
110001100101 => 000110010111 => 13
110001101001 => 000110010111 => 13
110001110001 => 000100011111 => 4
110010010101 => 001001010111 => 17
110010011001 => 001001001111 => 9
110010100101 => 001001010111 => 17
110010101001 => 001001010111 => 17
110010110001 => 000100101111 => 11
110011000101 => 000100110111 => 12
110011001001 => 001001001111 => 9
110011010001 => 000100110111 => 12
110011100001 => 000010011111 => 5
110100010101 => 000101010111 => 18
110100011001 => 000110010111 => 13
110100100101 => 001001010111 => 17
110100101001 => 001001010111 => 17
110100110001 => 000100110111 => 12
110101000101 => 000101010111 => 18
110101001001 => 001001010111 => 17
110101010001 => 000101010111 => 18
110101100001 => 000010101111 => 12
110110000101 => 000010101111 => 12
110110001001 => 000100101111 => 11
110110010001 => 000100101111 => 11
110110100001 => 000010101111 => 12
110111000001 => 000001011111 => 6
111000010101 => 000010101111 => 12
111000101001 => 000100101111 => 11
111001000101 => 000100101111 => 11
111001001001 => 001001001111 => 9
111001010001 => 000100101111 => 11
111010001001 => 000100101111 => 11
111010100001 => 000010101111 => 12
111100000101 => 000001011111 => 6
111100001001 => 000010011111 => 5
111100010001 => 000100011111 => 4
111100100001 => 000010011111 => 5
111101000001 => 000001011111 => 6
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Description
The major index of a binary word.
This is the sum of the positions of descents, i.e., a one followed by a zero.
For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.