Identifier
Identifier
Values
0000001110 => 2
0000010110 => 3
0000011000 => 2
0000100000 => 4
0000101000 => 3
0000101001 => 1
0000101100 => 3
0000101110 => 4
0000110000 => 4
0000110010 => 3
0000111100 => 4
0000111111 => 0
0001010010 => 4
0001010011 => 1
0001011111 => 0
0001100000 => 6
0001100100 => 6
0001100110 => 4
0001101000 => 2
0001101010 => 5
0001110010 => 1
0001111111 => 0
0010001011 => 4
0010001101 => 5
0010011010 => 5
0010100000 => 7
0010100001 => 5
0010100010 => 6
0010100101 => 4
0010100110 => 5
0010101100 => 7
0 => 0
1 => 0
00 => 0
01 => 0
10 => 0
11 => 0
000 => 0
001 => 0
010 => 0
011 => 0
100 => 1
101 => 0
110 => 1
111 => 0
0000 => 0
0001 => 0
0010 => 0
0011 => 0
0100 => 1
0101 => 0
0110 => 1
0111 => 0
1000 => 2
1001 => 1
1010 => 2
1011 => 0
1100 => 0
1101 => 1
1110 => 2
1111 => 0
00000 => 0
00001 => 0
00010 => 0
00011 => 0
00100 => 1
00101 => 0
00110 => 1
00111 => 0
01000 => 2
01001 => 1
01010 => 2
01011 => 0
01100 => 0
01101 => 1
01110 => 2
01111 => 0
10000 => 3
10001 => 2
10010 => 3
10011 => 1
10100 => 1
10101 => 2
10110 => 3
10111 => 0
11000 => 2
11001 => 0
11010 => 1
11011 => 1
11100 => 2
11101 => 2
11110 => 3
11111 => 0
000000 => 0
000001 => 0
000010 => 0
000011 => 0
000100 => 1
000101 => 0
000110 => 1
000111 => 0
001000 => 2
001001 => 1
001010 => 2
001011 => 0
001100 => 0
001101 => 1
001110 => 2
001111 => 0
010000 => 3
010001 => 2
010010 => 3
010011 => 1
010100 => 1
010101 => 2
010110 => 3
010111 => 0
011000 => 2
011001 => 0
011010 => 1
011011 => 1
011100 => 2
011101 => 2
011110 => 3
011111 => 0
100000 => 4
100001 => 3
100010 => 4
100011 => 2
100100 => 2
100101 => 3
100110 => 4
100111 => 1
101000 => 3
101001 => 1
101010 => 2
101011 => 2
101100 => 3
101101 => 3
101110 => 4
101111 => 0
110000 => 4
110001 => 2
110010 => 3
110011 => 0
110100 => 4
110101 => 1
110110 => 2
110111 => 1
111000 => 0
111001 => 2
111010 => 3
111011 => 2
111100 => 4
111101 => 3
111110 => 4
111111 => 0
0000000 => 0
0000001 => 0
0000010 => 0
0000011 => 0
0000100 => 1
0000101 => 0
0000110 => 1
0000111 => 0
0001000 => 2
0001001 => 1
0001010 => 2
0001011 => 0
0001100 => 0
0001101 => 1
0001110 => 2
0001111 => 0
0010000 => 3
0010001 => 2
0010010 => 3
0010011 => 1
0010100 => 1
0010101 => 2
0010110 => 3
0010111 => 0
0011000 => 2
0011001 => 0
0011010 => 1
0011011 => 1
0011100 => 2
0011101 => 2
0011110 => 3
0011111 => 0
0100000 => 4
0100001 => 3
0100010 => 4
0100011 => 2
0100100 => 2
0100101 => 3
0100110 => 4
0100111 => 1
0101000 => 3
0101001 => 1
0101010 => 2
0101011 => 2
0101100 => 3
0101101 => 3
0101110 => 4
0101111 => 0
0110000 => 4
0110001 => 2
0110010 => 3
0110011 => 0
0110100 => 4
0110101 => 1
0110110 => 2
0110111 => 1
0111000 => 0
0111001 => 2
0111010 => 3
0111011 => 2
0111100 => 4
0111101 => 3
0111110 => 4
0111111 => 0
1000000 => 5
1000001 => 4
1000010 => 5
1000011 => 3
1000100 => 3
1000101 => 4
1000110 => 5
1000111 => 2
1001000 => 4
1001001 => 2
1001010 => 3
1001011 => 3
1001100 => 4
1001101 => 4
1001110 => 5
1001111 => 1
1010000 => 5
1010001 => 3
1010010 => 4
1010011 => 1
1010100 => 5
1010101 => 2
1010110 => 3
1010111 => 2
1011000 => 1
1011001 => 3
1011010 => 4
1011011 => 3
1011100 => 5
1011101 => 4
1011110 => 5
1011111 => 0
1100000 => 6
1100001 => 4
1100010 => 5
1100011 => 2
1100100 => 6
1100101 => 3
1100110 => 4
1100111 => 0
1101000 => 2
1101001 => 4
1101010 => 5
1101011 => 1
1101100 => 6
1101101 => 2
1101110 => 3
1101111 => 1
1110000 => 3
1110001 => 0
1110010 => 1
1110011 => 2
1110100 => 2
1110101 => 3
1110110 => 4
1110111 => 2
1111000 => 3
1111001 => 4
1111010 => 5
1111011 => 3
1111100 => 6
1111101 => 4
1111110 => 5
1111111 => 0
00000000 => 0
00000001 => 0
00000010 => 0
00000011 => 0
00000100 => 1
00000101 => 0
00000110 => 1
00000111 => 0
00001000 => 2
00001001 => 1
00001010 => 2
00001011 => 0
00001100 => 0
00001101 => 1
00001110 => 2
00001111 => 0
00010000 => 3
00010001 => 2
00010010 => 3
00010011 => 1
00010100 => 1
00010101 => 2
00010110 => 3
00010111 => 0
00011000 => 2
00011001 => 0
00011010 => 1
00011011 => 1
00011100 => 2
00011101 => 2
00011110 => 3
00011111 => 0
00100000 => 4
00100001 => 3
00100010 => 4
00100011 => 2
00100100 => 2
00100101 => 3
00100110 => 4
00100111 => 1
00101000 => 3
00101001 => 1
00101010 => 2
00101011 => 2
00101100 => 3
00101101 => 3
00101110 => 4
00101111 => 0
00110000 => 4
00110001 => 2
00110010 => 3
00110011 => 0
00110100 => 4
00110101 => 1
00110110 => 2
00110111 => 1
00111000 => 0
00111001 => 2
00111010 => 3
00111011 => 2
00111100 => 4
00111101 => 3
00111110 => 4
00111111 => 0
01000000 => 5
01000001 => 4
01000010 => 5
01000011 => 3
01000100 => 3
01000101 => 4
01000110 => 5
01000111 => 2
01001000 => 4
01001001 => 2
01001010 => 3
01001011 => 3
01001100 => 4
01001101 => 4
01001110 => 5
01001111 => 1
01010000 => 5
01010001 => 3
01010010 => 4
01010011 => 1
01010100 => 5
01010101 => 2
01010110 => 3
01010111 => 2
01011000 => 1
01011001 => 3
01011010 => 4
01011011 => 3
01011100 => 5
01011101 => 4
01011110 => 5
01011111 => 0
01100000 => 6
01100001 => 4
01100010 => 5
01100011 => 2
01100100 => 6
01100101 => 3
01100110 => 4
01100111 => 0
01101000 => 2
01101001 => 4
01101010 => 5
01101011 => 1
01101100 => 6
01101101 => 2
01101110 => 3
01101111 => 1
01110000 => 3
01110001 => 0
01110010 => 1
01110011 => 2
01110100 => 2
01110101 => 3
01110110 => 4
01110111 => 2
01111000 => 3
01111001 => 4
01111010 => 5
01111011 => 3
01111100 => 6
01111101 => 4
01111110 => 5
01111111 => 0
10000000 => 6
10000001 => 5
10000010 => 6
10000011 => 4
10000100 => 4
10000101 => 5
10000110 => 6
10000111 => 3
10001000 => 5
10001001 => 3
10001010 => 4
10001011 => 4
10001100 => 5
10001101 => 5
10001110 => 6
10001111 => 2
10010000 => 6
10010001 => 4
10010010 => 5
10010011 => 2
10010100 => 6
10010101 => 3
10010110 => 4
10010111 => 3
10011000 => 2
10011001 => 4
10011010 => 5
10011011 => 4
10011100 => 6
10011101 => 5
10011110 => 6
10011111 => 1
10100000 => 7
10100001 => 5
10100010 => 6
10100011 => 3
10100100 => 7
10100101 => 4
10100110 => 5
10100111 => 1
10101000 => 3
10101001 => 5
10101010 => 6
10101011 => 2
10101100 => 7
10101101 => 3
10101110 => 4
10101111 => 2
10110000 => 4
10110001 => 1
10110010 => 2
10110011 => 3
10110100 => 3
10110101 => 4
10110110 => 5
10110111 => 3
10111000 => 4
10111001 => 5
10111010 => 6
10111011 => 4
10111100 => 7
10111101 => 5
10111110 => 6
10111111 => 0
11000000 => 8
11000001 => 6
11000010 => 7
11000011 => 4
11000100 => 8
11000101 => 5
11000110 => 6
11000111 => 2
11001000 => 4
11001001 => 6
11001010 => 7
11001011 => 3
11001100 => 8
11001101 => 4
11001110 => 5
11001111 => 0
11010000 => 5
11010001 => 2
11010010 => 3
11010011 => 4
11010100 => 4
11010101 => 5
11010110 => 6
11010111 => 1
11011000 => 5
11011001 => 6
11011010 => 7
11011011 => 2
11011100 => 8
11011101 => 3
11011110 => 4
11011111 => 1
11100000 => 6
11100001 => 3
11100010 => 4
11100011 => 0
11100100 => 5
11100101 => 1
11100110 => 2
11100111 => 2
11101000 => 6
11101001 => 2
11101010 => 3
11101011 => 3
11101100 => 4
11101101 => 4
11101110 => 5
11101111 => 2
11110000 => 0
11110001 => 3
11110010 => 4
11110011 => 4
11110100 => 5
11110101 => 5
11110110 => 6
11110111 => 3
11111000 => 6
11111001 => 6
11111010 => 7
11111011 => 4
11111100 => 8
11111101 => 5
11111110 => 6
11111111 => 0
000000000 => 0
000000001 => 0
000000010 => 0
000000011 => 0
000000100 => 1
000000101 => 0
000000110 => 1
000000111 => 0
000001000 => 2
000001001 => 1
000001010 => 2
000001011 => 0
000001100 => 0
000001101 => 1
000001110 => 2
000001111 => 0
000010000 => 3
000010001 => 2
000010010 => 3
000010011 => 1
000010100 => 1
000010101 => 2
000010110 => 3
000010111 => 0
000011000 => 2
000011001 => 0
000011010 => 1
000011011 => 1
000011100 => 2
000011101 => 2
000011110 => 3
000011111 => 0
000100000 => 4
000100001 => 3
000100010 => 4
000100011 => 2
000100100 => 2
000100101 => 3
000100110 => 4
000100111 => 1
000101000 => 3
000101001 => 1
000101010 => 2
000101011 => 2
000101100 => 3
000101101 => 3
000101110 => 4
000101111 => 0
000110000 => 4
000110001 => 2
000110010 => 3
000110011 => 0
000110100 => 4
000110101 => 1
000110110 => 2
000110111 => 1
000111000 => 0
000111001 => 2
000111010 => 3
000111011 => 2
000111100 => 4
000111101 => 3
000111110 => 4
000111111 => 0
001000000 => 5
001000001 => 4
001000010 => 5
001000011 => 3
001000100 => 3
001000101 => 4
001000110 => 5
001000111 => 2
001001000 => 4
001001001 => 2
001001010 => 3
001001011 => 3
001001100 => 4
001001101 => 4
001001110 => 5
001001111 => 1
001010000 => 5
001010001 => 3
001010010 => 4
001010011 => 1
001010100 => 5
001010101 => 2
001010110 => 3
001010111 => 2
001011000 => 1
001011001 => 3
001011010 => 4
001011011 => 3
001011100 => 5
001011101 => 4
001011110 => 5
001011111 => 0
001100000 => 6
001100001 => 4
001100010 => 5
001100011 => 2
001100100 => 6
001100101 => 3
001100110 => 4
001100111 => 0
001101000 => 2
001101001 => 4
001101010 => 5
001101011 => 1
001101100 => 6
001101101 => 2
001101110 => 3
001101111 => 1
001110000 => 3
001110001 => 0
001110010 => 1
001110011 => 2
001110100 => 2
001110101 => 3
001110110 => 4
001110111 => 2
001111000 => 3
001111001 => 4
001111010 => 5
001111011 => 3
001111100 => 6
001111101 => 4
001111110 => 5
001111111 => 0
010000000 => 6
010000001 => 5
010000010 => 6
010000011 => 4
010000100 => 4
010000101 => 5
010000110 => 6
010000111 => 3
010001000 => 5
010001001 => 3
010001010 => 4
010001011 => 4
010001100 => 5
010001101 => 5
010001110 => 6
010001111 => 2
010010000 => 6
010010001 => 4
010010010 => 5
010010011 => 2
010010100 => 6
010010101 => 3
010010110 => 4
010010111 => 3
010011000 => 2
010011001 => 4
010011010 => 5
010011011 => 4
010011100 => 6
010011101 => 5
010011110 => 6
010011111 => 1
010100000 => 7
010100001 => 5
010100010 => 6
010100011 => 3
010100100 => 7
010100101 => 4
010100110 => 5
010100111 => 1
010101000 => 3
010101001 => 5
010101010 => 6
010101011 => 2
010101100 => 7
010101101 => 3
010101110 => 4
010101111 => 2
010110000 => 4
010110001 => 1
010110010 => 2
010110011 => 3
010110100 => 3
010110101 => 4
010110110 => 5
010110111 => 3
010111000 => 4
010111001 => 5
010111010 => 6
010111011 => 4
010111100 => 7
010111101 => 5
010111110 => 6
010111111 => 0
011000000 => 8
011000001 => 6
011000010 => 7
011000011 => 4
011000100 => 8
011000101 => 5
011000110 => 6
011000111 => 2
011001000 => 4
011001001 => 6
011001010 => 7
011001011 => 3
011001100 => 8
011001101 => 4
011001110 => 5
011001111 => 0
011010000 => 5
011010001 => 2
011010010 => 3
011010011 => 4
011010100 => 4
011010101 => 5
011010110 => 6
011010111 => 1
011011000 => 5
011011001 => 6
011011010 => 7
011011011 => 2
011011100 => 8
011011101 => 3
011011110 => 4
011011111 => 1
011100000 => 6
011100001 => 3
011100010 => 4
011100011 => 0
011100100 => 5
011100101 => 1
011100110 => 2
011100111 => 2
011101000 => 6
011101001 => 2
011101010 => 3
011101011 => 3
011101100 => 4
011101101 => 4
011101110 => 5
011101111 => 2
011110000 => 0
011110001 => 3
011110010 => 4
011110011 => 4
011110100 => 5
011110101 => 5
011110110 => 6
011110111 => 3
011111000 => 6
011111001 => 6
011111010 => 7
011111011 => 4
011111100 => 8
011111101 => 5
011111110 => 6
011111111 => 0
100000000 => 7
100000001 => 6
100000010 => 7
100000011 => 5
100000100 => 5
100000101 => 6
100000110 => 7
100000111 => 4
100001000 => 6
100001001 => 4
100001010 => 5
100001011 => 5
100001100 => 6
100001101 => 6
100001110 => 7
100001111 => 3
100010000 => 7
100010001 => 5
100010010 => 6
100010011 => 3
100010100 => 7
100010101 => 4
100010110 => 5
100010111 => 4
100011000 => 3
100011001 => 5
100011010 => 6
100011011 => 5
100011100 => 7
100011101 => 6
100011110 => 7
100011111 => 2
100100000 => 8
100100001 => 6
100100010 => 7
100100011 => 4
100100100 => 8
100100101 => 5
100100110 => 6
100100111 => 2
100101000 => 4
100101001 => 6
100101010 => 7
100101011 => 3
100101100 => 8
100101101 => 4
100101110 => 5
100101111 => 3
100110000 => 5
100110001 => 2
100110010 => 3
100110011 => 4
100110100 => 4
100110101 => 5
100110110 => 6
100110111 => 4
100111000 => 5
100111001 => 6
100111010 => 7
100111011 => 5
100111100 => 8
100111101 => 6
100111110 => 7
100111111 => 1
101000000 => 9
101000001 => 7
101000010 => 8
101000011 => 5
101000100 => 9
101000101 => 6
101000110 => 7
101000111 => 3
101001000 => 5
101001001 => 7
101001010 => 8
101001011 => 4
101001100 => 9
101001101 => 5
101001110 => 6
101001111 => 1
101010000 => 6
101010001 => 3
101010010 => 4
101010011 => 5
101010100 => 5
101010101 => 6
101010110 => 7
101010111 => 2
101011000 => 6
101011001 => 7
101011010 => 8
101011011 => 3
101011100 => 9
101011101 => 4
101011110 => 5
101011111 => 2
101100000 => 7
101100001 => 4
101100010 => 5
101100011 => 1
101100100 => 6
101100101 => 2
101100110 => 3
101100111 => 3
101101000 => 7
101101001 => 3
101101010 => 4
101101011 => 4
101101100 => 5
101101101 => 5
101101110 => 6
101101111 => 3
101110000 => 1
101110001 => 4
101110010 => 5
101110011 => 5
101110100 => 6
101110101 => 6
101110110 => 7
101110111 => 4
101111000 => 7
101111001 => 7
101111010 => 8
101111011 => 5
101111100 => 9
101111101 => 6
101111110 => 7
101111111 => 0
110000000 => 10
110000001 => 8
110000010 => 9
110000011 => 6
110000100 => 10
110000101 => 7
110000110 => 8
110000111 => 4
110001000 => 6
110001001 => 8
110001010 => 9
110001011 => 5
110001100 => 10
110001101 => 6
110001110 => 7
110001111 => 2
110010000 => 7
110010001 => 4
110010010 => 5
110010011 => 6
110010100 => 6
110010101 => 7
110010110 => 8
110010111 => 3
110011000 => 7
110011001 => 8
110011010 => 9
110011011 => 4
110011100 => 10
110011101 => 5
110011110 => 6
110011111 => 0
110100000 => 8
110100001 => 5
110100010 => 6
110100011 => 2
110100100 => 7
110100101 => 3
110100110 => 4
110100111 => 4
110101000 => 8
110101001 => 4
110101010 => 5
110101011 => 5
110101100 => 6
110101101 => 6
110101110 => 7
110101111 => 1
110110000 => 2
110110001 => 5
110110010 => 6
110110011 => 6
110110100 => 7
110110101 => 7
110110110 => 8
110110111 => 2
110111000 => 8
110111001 => 8
110111010 => 9
110111011 => 3
110111100 => 10
110111101 => 4
110111110 => 5
110111111 => 1
111000000 => 9
111000001 => 6
111000010 => 7
111000011 => 3
111000100 => 8
111000101 => 4
111000110 => 5
111000111 => 0
111001000 => 9
111001001 => 5
111001010 => 6
111001011 => 1
111001100 => 7
111001101 => 2
111001110 => 3
111001111 => 2
111010000 => 3
111010001 => 6
111010010 => 7
111010011 => 2
111010100 => 8
111010101 => 3
111010110 => 4
111010111 => 3
111011000 => 9
111011001 => 4
111011010 => 5
111011011 => 4
111011100 => 6
111011101 => 5
111011110 => 6
111011111 => 2
111100000 => 4
111100001 => 0
111100010 => 1
111100011 => 3
111100100 => 2
111100101 => 4
111100110 => 5
111100111 => 4
111101000 => 3
111101001 => 5
111101010 => 6
111101011 => 5
111101100 => 7
111101101 => 6
111101110 => 7
111101111 => 3
111110000 => 4
111110001 => 6
111110010 => 7
111110011 => 6
111110100 => 8
111110101 => 7
111110110 => 8
111110111 => 4
111111000 => 9
111111001 => 8
111111010 => 9
111111011 => 5
111111100 => 10
111111101 => 6
111111110 => 7
111111111 => 0
1010101010 => 6
1010101100 => 7
1010110010 => 7
1010110100 => 8
1010111000 => 9
1011001010 => 7
1011001100 => 8
1011010010 => 8
1011010100 => 9
1011011000 => 10
1011100010 => 2
1011100100 => 3
1011101000 => 4
1011110000 => 5
1100101010 => 7
1100101100 => 8
1100110010 => 8
1100110100 => 9
1100111000 => 10
1101001010 => 8
1101001100 => 9
1101010010 => 9
1101010100 => 10
1101011000 => 11
1101100010 => 3
1101100100 => 4
1101101000 => 5
1101110000 => 6
1110001010 => 9
1110001100 => 10
1110010010 => 10
1110010100 => 11
1110011000 => 12
1110100010 => 4
1110100100 => 5
1110101000 => 6
1110110000 => 7
1111000010 => 5
1111000100 => 6
1111001000 => 7
1111010000 => 8
1111100000 => 0
1111111110 => 8
1111111101 => 7
1111000001 => 4
1110111110 => 7
1110100001 => 3
1110011110 => 4
1110010001 => 9
1110001001 => 8
1110000101 => 7
1101111110 => 6
1101100001 => 2
1101010001 => 8
1101001110 => 5
1101001001 => 7
1101000101 => 6
1100110001 => 7
1100101001 => 6
1100100110 => 6
1100100101 => 5
1100011001 => 10
1100010101 => 9
1100010010 => 7
1100001000 => 8
1011111110 => 8
1011111101 => 7
1011100001 => 1
1011010001 => 7
1011001001 => 6
1011000101 => 5
1010111110 => 6
1010110001 => 6
1010101001 => 5
1010100110 => 5
1010100101 => 4
1010011010 => 10
1010011001 => 9
1010010110 => 9
1010010101 => 8
1010001110 => 8
1001111110 => 8
1001111000 => 8
1001110100 => 7
1001110001 => 5
1001101100 => 6
1001101010 => 5
1001101001 => 4
1001100110 => 4
1001100101 => 3
1001011110 => 6
1001011010 => 9
1001011001 => 8
1001010110 => 8
1001010101 => 7
1001001110 => 7
1000111110 => 8
1000111100 => 9
1000111010 => 8
1000110110 => 7
1000101110 => 6
1000011110 => 8
1000010110 => 6
1000001110 => 8
1000001010 => 6
1000000110 => 8
1000000100 => 6
1000000010 => 8
1000000000 => 8
0000111110 => 4
0001111010 => 5
0001111100 => 6
0001110110 => 4
0011110010 => 4
0011110100 => 5
0010111010 => 6
0010111100 => 7
0011111000 => 6
0001101110 => 3
0011101010 => 3
0011101100 => 4
0011100110 => 2
0111100010 => 1
0111100100 => 2
0100111010 => 7
0100111100 => 8
0111101000 => 3
0010110110 => 5
0110110010 => 6
0110110100 => 7
0101101010 => 4
0101101100 => 5
0110111000 => 8
0101110010 => 5
0101110100 => 6
0101111000 => 7
0111110000 => 4
0101010101 => 6
0000011111 => 0
0100001111 => 3
0000110111 => 1
0000101111 => 0
0101000111 => 3
0000111011 => 2
0100011011 => 5
0001101011 => 1
0001011011 => 3
0100010111 => 4
0001100111 => 0
0001001111 => 1
0001010111 => 2
0101010011 => 5
0000111101 => 3
0100011101 => 6
0001101101 => 2
0001011101 => 4
0101001101 => 5
0001110101 => 3
0100110101 => 5
0011010101 => 5
0010110101 => 4
0100101101 => 4
0011000111 => 2
0010001111 => 2
0010101101 => 3
0101001011 => 4
0001110011 => 2
0100110011 => 4
0011010011 => 4
0010110011 => 3
0100100111 => 2
0011001101 => 4
0010011101 => 5
0010100111 => 1
0100101011 => 3
0011001011 => 3
0010011011 => 4
0010010111 => 3
0010101011 => 2
0111100001 => 0
0111000101 => 4
0110110001 => 5
0111010001 => 6
0110010101 => 7
0101110001 => 4
0101100101 => 2
0101011001 => 7
0101101001 => 3
0110100101 => 3
0110101001 => 4
0110011001 => 8
0111001001 => 5
0111011000 => 9
0110101100 => 6
0111001100 => 7
0111010100 => 8
0101011100 => 9
0101010110 => 7
0101011010 => 8
0111000110 => 5
0110011100 => 10
0110010110 => 8
0110011010 => 9
0101100110 => 3
0111001010 => 6
0110100110 => 4
0111010010 => 7
0110101010 => 5
0001011110 => 5
0010101110 => 4
0010011110 => 6
0001111001 => 4
0000000010 => 0
0100000100 => 5
0000000001 => 0
0100000001 => 6
0110000001 => 8
0111000001 => 6
0111110001 => 6
0111111001 => 8
0111111101 => 6
0111111111 => 0
0010000001 => 5
0101000001 => 7
0110100001 => 5
0111101001 => 5
0111110101 => 7
0111111011 => 5
0000000101 => 0
0000001101 => 1
0000011101 => 2
0001111101 => 4
0011111101 => 5
0000001001 => 1
0000010101 => 2
0000101101 => 3
0010111101 => 5
0101111101 => 6
0100000000 => 7
0100000011 => 5
0100000111 => 4
0100011111 => 2
0100111111 => 1
0101111111 => 0
0100000010 => 7
0100000101 => 6
0100001011 => 5
0100101111 => 3
0101011111 => 2
0110111111 => 1
0000000000 => 0
0010001100 => 5
0001000011 => 3
0010000010 => 6
0001000001 => 4
0001100001 => 4
0010110001 => 1
0000000100 => 1
0001101001 => 4
0000110001 => 2
0000010001 => 2
0000111010 => 3
0000011010 => 1
0000001010 => 2
0001011010 => 4
0000101010 => 2
0000010010 => 3
0010011111 => 1
0000100111 => 1
0000010011 => 1
0010000000 => 6
0010101010 => 6
0000011110 => 3
0000001111 => 0
0000000011 => 0
0001010101 => 2
0000000111 => 0
0000000110 => 1
0000001011 => 0
0000011011 => 1
0010011001 => 4
0001011001 => 3
0000111001 => 2
0001101111 => 1
0000110101 => 1
0001111110 => 5
0010001110 => 6
0010001000 => 5
0001000010 => 5
0001100101 => 3
0000100001 => 3
0010000100 => 4
0001000110 => 5
0010100011 => 3
0010000110 => 6
0001000101 => 4
0010001001 => 3
0000001000 => 2
0000100011 => 2
0001001011 => 3
0010000101 => 5
0000100010 => 4
0001100010 => 5
0000001100 => 0
0000110110 => 2
0000010100 => 1
0000111000 => 0
0001110100 => 2
0001111011 => 3
0000110100 => 4
0000100100 => 2
0001010100 => 5
0010010011 => 2
0000100110 => 4
0001001110 => 5
0001000111 => 2
0000011001 => 0
0000110011 => 0
0001000000 => 5
0000100101 => 3
0000101011 => 2
0001000100 => 3
0001001001 => 2
0001001010 => 3
0010010010 => 5
0010010101 => 3
0010010000 => 6
0000010111 => 0
0001011100 => 5
0001111000 => 3
0010101000 => 3
0000011100 => 2
0010101111 => 2
0001110111 => 2
0001010001 => 3
0000010000 => 3
0010000111 => 3
0010000011 => 4
0010010110 => 4
0001010110 => 3
0010010100 => 6
0010001010 => 4
0001001000 => 4
0010011100 => 6
0010110000 => 4
0001110000 => 3
0010011000 => 2
0001011000 => 1
0001001100 => 4
0001010000 => 5
0010010001 => 4
0010100100 => 7
0001001101 => 4
0010101001 => 5
0001110001 => 0
0001101100 => 6
0001100011 => 2
10000000000 => 9
10000000010 => 9
10000000110 => 9
10000001110 => 9
10000011110 => 9
10000111110 => 9
10001111110 => 9
10011111110 => 9
10111111110 => 9
11111111110 => 9
10000000100 => 7
10000001010 => 7
10000010110 => 7
10000101110 => 7
10001011110 => 7
10010111110 => 7
10101111110 => 7
11011111110 => 7
10000010000 => 9
10000100010 => 9
10001000010 => 10
10000100100 => 10
10001001010 => 10
10001000100 => 11
10000101000 => 6
10010001010 => 11
10001010010 => 6
10010000100 => 12
10001001000 => 7
10010010010 => 7
10001010100 => 7
10010101010 => 7
10010001000 => 8
10100010010 => 8
10010100010 => 8
10010010100 => 8
10100101010 => 8
00001000001 => 4
00000000010 => 0
00000000001 => 0
01000000001 => 7
01100000001 => 10
01110000001 => 9
01111000001 => 4
01111100001 => 4
01111110001 => 9
01111111001 => 10
01111111101 => 7
01111111111 => 0
00000000101 => 0
00000001101 => 1
00000011101 => 2
00000111101 => 3
00001111101 => 4
00011111101 => 5
00111111101 => 6
11111111101 => 8
01000000000 => 8
01000000011 => 6
01000000111 => 5
01000001111 => 4
01000011111 => 3
01000111111 => 2
01001111111 => 1
01011111111 => 0
00010100001 => 5
00100100001 => 6
00010010001 => 4
01000001000 => 7
01000100001 => 7
00101010001 => 3
00010000010 => 6
00010001001 => 3
10100001000 => 9
10000100001 => 8
01000010100 => 8
01001010001 => 4
00100000100 => 5
00100010001 => 5
00101000010 => 8
00101001001 => 7
00010000101 => 5
10100010100 => 9
10010100100 => 9
10001010001 => 5
01000100100 => 9
01000010010 => 7
01010000100 => 11
01010010001 => 5
01001000010 => 9
01001001001 => 8
00100001010 => 5
00100100010 => 7
00100101001 => 6
00101000101 => 6
10101010010 => 10
10101001010 => 9
01001001010 => 9
01001010010 => 5
01010001010 => 10
01010010010 => 6
00100010010 => 6
10100100010 => 9
10100100100 => 10
00100101010 => 7
01010101010 => 6
01010100010 => 7
01000101010 => 8
01000100010 => 8
10101000100 => 11
00101010010 => 4
00101001010 => 8
01001000100 => 10
00100010101 => 4
01001000101 => 7
10001000101 => 8
01000010001 => 6
10100010001 => 7
00101010100 => 5
00101000100 => 9
00100100100 => 8
01010100100 => 8
10010010001 => 6
00010010100 => 6
00100010100 => 7
00010010010 => 5
00010001010 => 4
00100001001 => 4
10010001001 => 10
01001010101 => 7
01010010100 => 7
01000100101 => 6
01010010101 => 8
01010001000 => 7
01010101001 => 5
01001010100 => 6
01000101001 => 7
01010100101 => 4
01001001000 => 6
01010001001 => 9
01000101000 => 5
00101001000 => 5
10010100101 => 5
10100101001 => 7
10010010101 => 9
10100100101 => 6
10101001001 => 8
10101010101 => 6
00001000010 => 5
00010100010 => 6
00010000100 => 4
00001000100 => 3
00010100100 => 7
00100100101 => 5
10001001001 => 9
00001001000 => 4
00001010000 => 5
00010001000 => 5
00100101000 => 4
00010101000 => 3
00100010000 => 7
00000100000 => 4
00010010000 => 6
01000010000 => 8
00100001000 => 6
10010101001 => 6
101010101010 => 12
101010101100 => 13
101010110010 => 13
101010110100 => 14
101010111000 => 15
101011001010 => 6
101011001100 => 7
101011010010 => 7
101011010100 => 8
101011011000 => 9
101011100010 => 8
101011100100 => 9
101011101000 => 10
101011110000 => 11
101100101010 => 13
101100101100 => 14
101100110010 => 14
101100110100 => 15
101100111000 => 16
101101001010 => 7
101101001100 => 8
101101010010 => 8
101101010100 => 9
101101011000 => 10
101101100010 => 9
101101100100 => 10
101101101000 => 11
101101110000 => 12
101110001010 => 8
101110001100 => 9
101110010010 => 9
101110010100 => 10
101110011000 => 11
101110100010 => 10
101110100100 => 11
101110101000 => 12
101110110000 => 13
101111000010 => 2
101111000100 => 3
101111001000 => 4
101111010000 => 5
101111100000 => 6
110010101010 => 13
110010101100 => 14
110010110010 => 14
110010110100 => 15
110010111000 => 16
110011001010 => 7
110011001100 => 8
110011010010 => 8
110011010100 => 9
110011011000 => 10
110011100010 => 9
110011100100 => 10
110011101000 => 11
110011110000 => 12
110100101010 => 14
110100101100 => 15
110100110010 => 15
110100110100 => 16
110100111000 => 17
110101001010 => 8
110101001100 => 9
110101010010 => 9
110101010100 => 10
110101011000 => 11
110101100010 => 10
110101100100 => 11
110101101000 => 12
110101110000 => 13
110110001010 => 9
110110001100 => 10
110110010010 => 10
110110010100 => 11
110110011000 => 12
110110100010 => 11
110110100100 => 12
110110101000 => 13
110110110000 => 14
110111000010 => 3
110111000100 => 4
110111001000 => 5
110111010000 => 6
110111100000 => 7
111000101010 => 15
111000101100 => 16
111000110010 => 16
111000110100 => 17
111000111000 => 18
111001001010 => 9
111001001100 => 10
111001010010 => 10
111001010100 => 11
111001011000 => 12
111001100010 => 11
111001100100 => 12
111001101000 => 13
111001110000 => 14
111010001010 => 10
111010001100 => 11
111010010010 => 11
111010010100 => 12
111010011000 => 13
111010100010 => 12
111010100100 => 13
111010101000 => 14
111010110000 => 15
111011000010 => 4
111011000100 => 5
111011001000 => 6
111011010000 => 7
111011100000 => 8
111100001010 => 11
111100001100 => 12
111100010010 => 12
111100010100 => 13
111100011000 => 14
111100100010 => 13
111100100100 => 14
111100101000 => 15
111100110000 => 16
111101000010 => 5
111101000100 => 6
111101001000 => 7
111101010000 => 8
111101100000 => 9
111110000010 => 6
111110000100 => 7
111110001000 => 8
111110010000 => 9
111110100000 => 10
111111000000 => 0
100001111100 => 12
000011011110 => 4
010000011111 => 4
000001111101 => 4
111100000101 => 9
011111000001 => 0
010111110000 => 9
000111011100 => 6
100011111000 => 12
000111011010 => 5
001011011100 => 7
100011110100 => 11
100101111000 => 13
000111010110 => 4
001111011000 => 6
010011011100 => 8
000101101110 => 6
100011101100 => 10
100111110000 => 10
010001111010 => 10
101001111000 => 14
000111001110 => 3
001111010100 => 5
001011011010 => 6
010111011000 => 7
100011011100 => 9
001101101100 => 9
100111101000 => 9
001001110110 => 8
100101110100 => 12
010011110010 => 9
110001111000 => 15
001111001100 => 4
001111010010 => 4
010111010100 => 6
011011011000 => 8
100111011000 => 8
001101101010 => 8
010101101100 => 10
001011100110 => 6
100111100100 => 8
010011101010 => 8
011001110100 => 12
010101110010 => 10
000010111101 => 5
010000101111 => 5
000011011101 => 3
000100111101 => 6
010000110111 => 6
010001001111 => 3
000011101101 => 4
000101011101 => 4
001000111101 => 7
000011110011 => 4
010000111011 => 7
010001010111 => 4
001100001111 => 4
010010001111 => 4
000011110101 => 5
000101101101 => 5
000110011101 => 5
001001011101 => 5
010000111101 => 8
000101110011 => 5
010001011011 => 5
000111000111 => 0
010001100111 => 5
001100010111 => 5
010010010111 => 5
010100001111 => 5
000101110101 => 6
000110101101 => 6
001001101101 => 6
001010011101 => 6
010001011101 => 6
000110110011 => 6
001001110011 => 6
000111001011 => 1
010001101011 => 6
001100011011 => 6
010010011011 => 6
001011000111 => 1
001100100111 => 6
010010100111 => 6
010100010111 => 6
011110100001 => 8
111010000101 => 8
011101100001 => 7
011110010001 => 7
110110000101 => 7
111001000101 => 7
011011100001 => 6
011101010001 => 6
011110001001 => 6
100111100001 => 6
101110000101 => 6
110101000101 => 6
111000011001 => 13
111000100101 => 13
010111100001 => 5
011011010001 => 5
011100110001 => 12
011101001001 => 5
011110000101 => 5
100111010001 => 5
101101000101 => 5
110001110001 => 12
110011000101 => 5
110100011001 => 12
110100100101 => 12
111000010101 => 12
010111010001 => 4
011010110001 => 11
011011001001 => 4
011100101001 => 11
011101000101 => 4
100110110001 => 11
100111001001 => 4
101001110001 => 11
101011000101 => 4
101100011001 => 11
101100100101 => 11
110001101001 => 11
110010011001 => 11
110010100101 => 11
110100010101 => 11
010111101000 => 8
010111100100 => 7
010110111000 => 13
010111100010 => 6
011001111000 => 13
011110000110 => 6
010101111000 => 12
010110110100 => 12
010111001100 => 5
010111010010 => 5
011100011100 => 12
011101000110 => 5
010101110100 => 11
010110101100 => 11
010110110010 => 11
010111001010 => 4
011001101100 => 11
011001110010 => 11
011010011100 => 11
011011000110 => 4
011100011010 => 11
011100100110 => 11
011111000100 => 2
011111000010 => 1
011101100100 => 9
011101100010 => 8
011011100100 => 8
011011010100 => 7
011011100010 => 7
011011010010 => 6
011111010000 => 4
011111001000 => 3
001111001010 => 3
011101110000 => 11
011111100000 => 5
011101101000 => 10
010101101010 => 9
001111000110 => 2
010011110100 => 10
010011101100 => 9
011011110000 => 10
011011101000 => 9
010011011010 => 7
001101100110 => 7
001011010101 => 4
001101010101 => 5
001011010011 => 3
001101010011 => 4
001011001011 => 2
001011001101 => 3
001101001011 => 3
001101001101 => 4
001001110101 => 7
001010101101 => 7
001100101101 => 8
001101000111 => 2
001010110101 => 8
001100110101 => 9
001001100111 => 4
001001101011 => 5
000110110101 => 7
001010100111 => 5
001010101011 => 6
001100101011 => 7
001010110011 => 7
001100110011 => 8
000111010101 => 3
001000110111 => 5
001000111011 => 6
001001010111 => 3
001001011011 => 4
001010010111 => 4
001010011011 => 5
001100011101 => 7
000111010011 => 2
010101001011 => 4
010101010011 => 5
010011001011 => 3
010011010011 => 4
010100011011 => 7
010010101011 => 7
010010110011 => 8
010100101011 => 8
010100110011 => 9
000110011011 => 4
010100100111 => 7
000110101011 => 5
010101000111 => 3
000100111011 => 5
000101011011 => 3
000101101011 => 4
010001110011 => 7
010101101001 => 8
010101011001 => 7
100101101001 => 9
100101011001 => 8
101001101001 => 10
011001101001 => 9
101001011001 => 9
011001011001 => 8
010111001001 => 3
011010101001 => 10
011010011001 => 9
110001011001 => 10
010110101001 => 9
010110011001 => 8
110011001001 => 6
101011001001 => 5
010110110001 => 10
110010101001 => 12
101010101001 => 11
101010011001 => 10
100110101001 => 10
100110011001 => 9
010101110001 => 9
110110001001 => 8
101110001001 => 7
110101001001 => 7
101101001001 => 6
110100101001 => 13
101100101001 => 12
011100011001 => 10
100101110001 => 10
010101011010 => 8
010101010110 => 7
011001011010 => 9
011001010110 => 8
011010011010 => 10
010110011010 => 9
011010010110 => 9
010110010110 => 8
010110101010 => 10
010110100110 => 9
011100010110 => 10
010101100110 => 8
011100110010 => 13
011010110010 => 12
011100101010 => 12
011010101010 => 11
011010100110 => 10
011001101010 => 10
011001100110 => 9
010101011100 => 9
011101010010 => 7
011101001010 => 6
011011001010 => 5
010111000110 => 3
011001011100 => 10
100101101100 => 11
100111001100 => 6
001111110000 => 8
001011110010 => 8
001101110010 => 9
001111100010 => 5
100111010100 => 7
001101111000 => 11
001101110100 => 10
001011101010 => 7
001011010110 => 5
010100011101 => 8
010001110101 => 8
000101010111 => 2
000110010111 => 3
000110100111 => 4
010001101101 => 7
000101001111 => 1
000101100111 => 3
001001001111 => 2
001010001111 => 3
000111001101 => 2
010010011101 => 7
000011010111 => 1
000011011011 => 2
000011101011 => 3
010011000111 => 2
110001010101 => 9
101100010101 => 10
011100010101 => 9
100111000101 => 3
010111000101 => 2
110101010001 => 8
110100110001 => 14
110010110001 => 13
101010110001 => 12
011011000101 => 3
111001010001 => 9
110011010001 => 7
111001001001 => 8
101100110001 => 13
111000101001 => 14
011001110001 => 10
011101010100 => 8
011101001100 => 7
011100101100 => 13
011010101100 => 12
011110010100 => 9
011100110100 => 14
011110010010 => 8
011011001100 => 6
011110001010 => 7
010110011100 => 10
101001110100 => 13
010011001101 => 4
110001100101 => 10
011001100101 => 8
001111100100 => 6
000111100110 => 5
001111101000 => 7
000111101010 => 6
001011101100 => 8
000111101100 => 7
000111110010 => 7
000010111011 => 4
001000101111 => 4
100101010101 => 7
100101100101 => 8
101011010001 => 6
100110010101 => 8
101001010101 => 8
101011100001 => 7
101010100101 => 10
101101010001 => 7
100110100101 => 9
101010010101 => 9
101101100001 => 8
101001100101 => 9
101110010001 => 8
101110100001 => 9
110101100001 => 9
011001010101 => 7
011010110100 => 13
011010010101 => 8
011010111000 => 14
011010100101 => 9
011101011000 => 9
010100101101 => 9
010010110101 => 9
010101001101 => 5
010100110101 => 10
010011010101 => 5
010101010101 => 6
010110100101 => 8
010110010101 => 7
010101100101 => 7
010001111100 => 11
010011111000 => 11
001001111010 => 9
001001111100 => 10
001011111000 => 10
001000011111 => 3
000110001111 => 2
000100011111 => 2
000100101111 => 3
000001111011 => 3
000011100111 => 2
000001110111 => 2
000010110111 => 3
111100001001 => 10
111010001001 => 9
111000110001 => 15
111100010001 => 11
111010010001 => 10
011110100010 => 9
011110001100 => 8
011110100100 => 10
110010010101 => 10
011100100101 => 10
000101111100 => 9
000011111100 => 8
001011110100 => 9
000101111010 => 8
000111110100 => 8
000111111000 => 9
000010011111 => 1
000001011111 => 0
000100110111 => 4
000011001111 => 0
000010101111 => 2
000001101111 => 1
111100100001 => 12
111101000001 => 4
110110010001 => 9
111001100001 => 10
110110100001 => 10
111010100001 => 11
011110011000 => 10
011110101000 => 11
000011110110 => 6
000001111110 => 5
000011111010 => 7
000000111111 => 0
110111000001 => 2
111110000001 => 5
111011000001 => 3
011110110000 => 12
000011101110 => 5
000101110110 => 7
101111000001 => 1
110011100001 => 8
011100111000 => 15
010010101101 => 8
10110111100000 => 14
10111011010000 => 14
10111011100000 => 15
10111100110000 => 14
10111101001000 => 14
10111101010000 => 15
10111101100000 => 16
10111110000100 => 3
10111110001000 => 4
10111110010000 => 5
10111110100000 => 6
10111111000000 => 7
11001111100000 => 14
11011110000010 => 3
11101101000010 => 14
11101110000010 => 4
11110011000010 => 14
11110100100010 => 14
11110101000010 => 15
11110110000010 => 5
11111000001100 => 14
11111000010010 => 14
11111000100010 => 15
11111001000010 => 16
11111010000010 => 6
11111100000010 => 7
1011110111000000 => 18
1011111010100000 => 18
1011111011000000 => 19
1011111100010000 => 5
1011111100100000 => 6
1011111101000000 => 7
1011111110000000 => 8
1111011100000010 => 5
1111101010000010 => 18
1111101100000010 => 6
1111110001000010 => 18
1111110010000010 => 19
1111110100000010 => 7
1111111000000010 => 8
111111110000000010 => 9
101111111100000000 => 9
111111101000000010 => 8
101111111010000000 => 8
111111100100000010 => 22
111111011000000010 => 7
101111111001000000 => 7
101111110110000000 => 22
11111111100000000010 => 10
10111111111000000000 => 10
11111111010000000010 => 9
10111111110100000000 => 9
1111111111000000000010 => 11
1011111111110000000000 => 11
click to show generating function       
Description
The number of internal inversions of a binary word.
Let $\bar w$ be the non-decreasing rearrangement of $w$, that is, $\bar w$ is sorted.
An internal inversion is a pair $i < j$ such that $w_i > w_j$ and $\bar w_i = \bar w_j$. For example, the word $110$ has two inversions, but only the second is internal.
References
[1] Foata, D., Han, G.-N. Inverses of words MathSciNet:1611988
[2] Hohlweg, C., Reutenauer, C. Inverses of words and the parabolic structure of the symmetric group MathSciNet:1861050
Code
def statistic(w):
    w_bar = sorted(w)
    return len([(i,j) for (i, j) in w.inversions() if w_bar[i] == w_bar[j]])
Created
Aug 01, 2017 at 08:16 by Martin Rubey
Updated
Apr 19, 2019 at 22:18 by Martin Rubey