edit this statistic or download as text // json
Identifier
Values
=>
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 1111111111=>0 1111111110=>8 1111111101=>7 1111111100=>12 1111111001=>10 1111110000=>8 1111101110=>9 1111101101=>8 1111101011=>7 1111101000=>7 1111100111=>6 1111100100=>6 1111100010=>5 1111100001=>4 1111011000=>6 1111010100=>5 1111010010=>4 1111010001=>3 1111001110=>6 1111001100=>4 1111001010=>3 1111001001=>2 1111000101=>1 1111000011=>0 1111000001=>4 1111000000=>8 1110111111=>2 1110111110=>7 1110111101=>6 1110111000=>12 1110110111=>4 1110110100=>11 1110110010=>10 1110110001=>9 1110101100=>10 1110101011=>3 1110101010=>9 1110101001=>8 1110100101=>7 1110100011=>6 1110100001=>3 1110011111=>2 1110011110=>4 1110011001=>7 1110010101=>6 1110010011=>5 1110010001=>9 1110001101=>5 1110001001=>8 1110000111=>3 1110000110=>8 1110000101=>7 1110000011=>6 1110000001=>9 1101111111=>1 1101111110=>6 1101111011=>4 1101110001=>8 1101101011=>7 1101101001=>7 1101100101=>6 1101100011=>5 1101100001=>2 1101011111=>1 1101011110=>8 1101011011=>6 1101011001=>6 1101010111=>5 1101010110=>6 1101010101=>5 1101010011=>4 1101010001=>8 1101001111=>4 1101001110=>5 1101001101=>4 1101001011=>3 1101001001=>7 1101001000=>11 1101000111=>2 1101000101=>6 1101000100=>10 1101000011=>5 1100111111=>0 1100111110=>7 1100111001=>10 1100110101=>9 1100110011=>8 1100110001=>7 1100101110=>9 1100101011=>7 1100101001=>6 1100101000=>10 1100100110=>6 1100100101=>5 1100100010=>8 1100011110=>8 1100011101=>7 1100011100=>12 1100011010=>11 1100011001=>10 1100010110=>10 1100010101=>9 1100010100=>8 1100010010=>7 1100001111=>4 1100001110=>9 1100001011=>7 1100001010=>11 1100001000=>8 1100000111=>6 1100000110=>10 1100000100=>12 1100000010=>11 1100000000=>12 1011111111=>0 1011111110=>8 1011111101=>7 1011110111=>5 1011110001=>7 1011100101=>5 1011100001=>1 1011100000=>5 1011011111=>3 1011011001=>5 1011010101=>4 1011010001=>7 1011010000=>4 1011001101=>3 1011001001=>6 1011001000=>10 1011000111=>1 1011000110=>6 1011000101=>5 1011000100=>9 1011000010=>8 1011000001=>7 1010111111=>2 1010111110=>6 1010110101=>8 1010110001=>6 1010110000=>3 1010101111=>2 1010101011=>6 1010101001=>5 1010101000=>9 1010100110=>5 1010100101=>4 1010100100=>8 1010100010=>7 1010011110=>7 1010011101=>6 1010011100=>11 1010011010=>10 1010011001=>9 1010011000=>8 1010010111=>4 1010010110=>9 1010010101=>8 1010010100=>7 1010010010=>6 1010010001=>5 1010001110=>8 1010001100=>11 1010001010=>10 1010001001=>9 1010000101=>8 1001111111=>1 1001111110=>8 1001111001=>8 1001111000=>8 1001110100=>7 1001110010=>6 1001110001=>5 1001110000=>2 1001101101=>6 1001101100=>6 1001101010=>5 1001101001=>4 1001101000=>8 1001100111=>4 1001100110=>4 1001100101=>3 1001100100=>7 1001100010=>6 1001100001=>5 1001011111=>3 1001011110=>6 1001011010=>9 1001011001=>8 1001011000=>7 1001010111=>3 1001010110=>8 1001010101=>7 1001010100=>6 1001010010=>5 1001010001=>4 1001001110=>7 1001001100=>10 1001001010=>9 1001000110=>8 1001000101=>7 1000111110=>8 1000111101=>7 1000111100=>9 1000111010=>8 1000111000=>6 1000110111=>5 1000110110=>7 1000110101=>6 1000110100=>5 1000110010=>4 1000110001=>3 1000110000=>6 1000101111=>4 1000101110=>6 1000101100=>9 1000101011=>4 1000101010=>8 1000101001=>7 1000100110=>7 1000100101=>6 1000100000=>9 1000011111=>3 1000011110=>8 1000011001=>6 1000010111=>5 1000010110=>6 1000010101=>5 1000010010=>7 1000001110=>8 1000001101=>7 1000001100=>7 1000001011=>6 1000001010=>6 1000001001=>5 1000001000=>7 1000000111=>5 1000000110=>8 1000000101=>7 1000000100=>6 1000000011=>6 1000000010=>8 1000000001=>7 1000000000=>8 0111111111=>0 0111111101=>6 0111111001=>8 0111110001=>6 0111100001=>0 0111000001=>6 0110000001=>8 0100000001=>6 0000000001=>0 0111111011=>5 0111110101=>7 0111101001=>5 0111010001=>6 0110100001=>5 0101000001=>7 0010000001=>5 0101010101=>6 0101010011=>5 0101001101=>5 0101001011=>4 0101000111=>3 0100110101=>5 0100110011=>4 0100101101=>4 0100101011=>3 0100100111=>2 0100011101=>6 0100011011=>5 0100010111=>4 0100001111=>3 0011010101=>5 0011010011=>4 0011001101=>4 0011001011=>3 0011000111=>2 0010110101=>4 0010110011=>3 0010101101=>3 0010101011=>2 0010100111=>1 0010011101=>5 0010011011=>4 0010010111=>3 0010001111=>2 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011110110000=>12 011111000001=>0 011111000100=>2 011111010000=>4 001111000110=>2 001111001010=>3 100111001100=>6 001111001100=>4 001011010110=>5 001111010010=>4 100111010100=>7 001111010100=>5 000111010110=>4 001011011010=>6 100111011000=>8 001111011000=>6 100011011100=>9 010011011100=>8 001011011100=>7 000111011100=>6 000011011110=>4 001101100110=>7 001101101010=>8 100101101100=>11 001101101100=>9 001011100110=>6 001111100010=>5 100111100100=>8 001111100100=>6 010011101010=>8 001011101010=>7 100111101000=>9 001111101000=>7 000111101010=>6 100011101100=>10 010011101100=>9 001011101100=>8 000111101100=>7 000011101110=>5 101001110100=>13 001001110110=>8 001101110010=>9 100101110100=>12 001101110100=>10 000101110110=>7 001011110010=>8 100111110000=>10 001111110000=>8 100011110100=>11 010011110100=>10 001011110100=>9 000111110100=>8 000011110110=>6 110001111000=>15 101001111000=>14 001001111010=>9 100101111000=>13 001101111000=>11 100011111000=>12 001011111000=>10 000011111010=>7 010001111100=>11 001001111100=>10 000101111100=>9 000011111100=>8 100101010101=>7 100101011001=>8 100101100101=>8 100101101001=>9 100101110001=>10 100110010101=>8 100110101001=>10 100111000101=>3 100111001001=>4 100111010001=>5 101001010101=>8 101001101001=>10 101010011001=>10 101010100101=>10 101010101001=>11 101010110001=>12 101011001001=>5 101011100001=>7 101100010101=>10 101100101001=>12 101101000101=>5 101101001001=>6 101101010001=>7 101110001001=>7 101110100001=>9 110001010101=>9 110001011001=>10 110001100101=>10 110001101001=>11 110001110001=>12 110010010101=>10 110010011001=>11 110010100101=>11 110010101001=>12 110010110001=>13 110011000101=>5 110011001001=>6 110011010001=>7 110011100001=>8 110100010101=>11 110100011001=>12 110100100101=>12 110100101001=>13 110100110001=>14 110101000101=>6 110101001001=>7 110101010001=>8 110101100001=>9 110110000101=>7 110110001001=>8 110110010001=>9 110110100001=>10 110111000001=>2 111000010101=>12 111000101001=>14 111001000101=>7 111001001001=>8 111001010001=>9 111010001001=>9 111010100001=>11 111100000101=>9 111100001001=>10 111100010001=>11 111100100001=>12 111101000001=>4 110101000011=>5 110100011100=>14 110100000111=>8 110011000011=>4 110110000011=>6 110001110100=>14 110000111100=>16 110000001111=>8 011101000011=>3 011100000111=>6 111001000011=>6 111010000011=>7 111000011100=>15 001111010001=>3 001111000011=>0 011110000011=>4 111100000011=>8 000111110001=>6 001111100001=>4 110101010101=>11 110101010011=>10 110101001101=>10 110101011001=>12 110101000111=>8 110100110101=>10 110100110011=>9 110101100101=>12 110101101001=>13 110101100011=>11 110100011101=>8 110100111001=>11 110101110001=>14 110100001111=>5 110011010101=>10 110011010011=>9 110011001101=>9 110011011001=>11 110011000111=>7 110110010101=>5 110110010011=>4 110110100101=>6 110110101001=>7 110110100011=>5 110110001101=>4 110110011001=>6 110110110001=>8 110110000111=>2 110001110101=>13 110001110011=>12 110011100101=>11 110011101001=>12 110011100011=>10 110111000101=>7 110111001001=>8 110111010001=>9 110111000011=>6 110000111101=>10 110001111001=>14 110011110001=>13 110111100001=>10 110000011111=>6 011101010101=>9 011101010011=>8 011101001101=>8 011101011001=>10 011101000111=>6 011100110101=>8 011100110011=>7 011101100101=>10 011101101001=>11 011101100011=>9 011100011101=>6 011100111001=>9 011101110001=>12 011100001111=>3 111001010101=>12 111001010011=>11 111001001101=>11 111001011001=>13 111001000111=>9 111010010101=>6 111010010011=>5 111010100101=>7 111010101001=>8 111010100011=>6 111010001101=>5 111010011001=>7 111010110001=>9 111010000111=>3 111000110101=>11 111000110011=>10 111001100101=>13 111001101001=>14 111001100011=>12 111011000101=>8 111011001001=>9 111011010001=>10 111011000011=>7 111000011101=>9 111000111001=>12 111001110001=>15 111011100001=>11 111000001111=>6 001111010101=>6 001111010011=>5 001111001101=>5 001111011001=>7 001111000111=>3 011110010101=>3 011110010011=>2 011110100101=>4 011110101001=>5 011110100011=>3 011110001101=>2 011110011001=>4 011110110001=>6 011110000111=>0 111100010101=>7 111100010011=>6 111100100101=>8 111100101001=>9 111100100011=>7 111101000101=>9 111101001001=>10 111101010001=>11 111101000011=>8 111100001101=>6 111100011001=>8 111100110001=>10 111101100001=>12 111100000111=>4 000111110101=>7 000111110011=>6 001111100101=>7 001111101001=>8 001111100011=>6 011111000101=>5 011111001001=>6 011111010001=>7 011111000011=>4 111110000101=>1 111110001001=>2 111110010001=>3 111110100001=>4 111110000011=>0 000011111101=>5 000111111001=>8 001111110001=>9 011111100001=>8 111111000001=>5 000001111111=>0 101110011001=>5 100100011001=>12 101000011001=>13 100110111001=>8 101110111001=>10 100100111001=>12 101100111001=>10 101000111001=>13 100101111001=>12 101001111001=>13 101011111001=>13 100110010001=>11 100100010001=>8 101100010001=>13 101110110001=>7 100100110001=>9 101000110001=>10 101101110001=>13 101011110001=>12 100110100001=>5 100100100001=>9 101100100001=>7 101000100001=>10 100101100001=>4 101001100001=>5 100101000001=>10 101101000001=>8 101011000001=>7 101010000001=>12 100110011011=>4 101110011011=>6 100100011011=>8 101100011011=>6 101000011011=>9 100110111011=>7 101110111011=>8 100100111011=>7 101100111011=>4 101000111011=>8 100101111011=>6 101101111011=>7 101001111011=>7 101011111011=>6 100110010011=>7 101110010011=>3 100100010011=>10 101100010011=>9 101000010011=>11 100110110011=>6 101110110011=>8 100100110011=>10 101100110011=>8 101000110011=>11 100101110011=>10 101101110011=>7 101001110011=>11 101011110011=>11 100110100011=>8 101110100011=>4 100100100011=>6 101100100011=>10 101000100011=>7 100101100011=>7 101101100011=>10 101001100011=>8 101011100011=>9 100101000011=>7 101101000011=>4 101001000011=>8 101011000011=>3 101010000011=>9 100110010111=>3 100100010111=>7 101100010111=>5 101110110111=>7 100100110111=>6 101000110111=>7 100101110111=>5 101101110111=>6 101011110111=>5 100110100111=>4 101110100111=>6 100100100111=>8 101100100111=>6 101000100111=>9 100101100111=>8 101001100111=>9 101011100111=>9 100101000111=>4 101101000111=>7 101011000111=>6 101010000111=>6 100110101111=>5 101110101111=>6 100100101111=>5 101100101111=>2 101000101111=>6 100101101111=>4 101101101111=>5 101001101111=>5 101011101111=>4 100101001111=>6 101101001111=>3 101001001111=>7 101011001111=>7 101010001111=>3 100101011111=>3 101101011111=>4 101011011111=>3 101010011111=>5 101010111111=>2 100110011010=>10 101001100110=>10 011100010011=>8 011010001011=>6 011000101011=>9 011000010111=>7 010100000000=>13 000101000000=>9 010001000000=>11 011011000000=>10 000001010000=>5 010101010000=>6 000100010000=>7 010000010000=>9 011010010000=>8 000110110000=>2 010010110000=>4 011000110000=>6 000000010100=>1 010100010100=>9 000101010100=>5 010001010100=>7 000001000100=>3 010101000100=>11 000100000100=>5 010000000100=>7 011010000100=>13 000110100100=>7 010010100100=>9 011000100100=>11 000001101100=>6 000100101100=>8 010000101100=>10 000110001100=>10 010010001100=>12 011000001100=>14 011110111100=>11 000000000101=>0 010100000101=>10 000101000101=>6 010001000101=>8 000001010101=>2 000100010101=>4 010000010101=>6 011000110101=>11 011101110101=>7 000000010001=>2 010100010001=>7 000101010001=>3 010001010001=>5 000001000001=>4 010101000001=>9 000100000001=>6 010000000001=>8 011010000001=>11 000110100001=>5 010010100001=>7 011000100001=>9 000001101001=>4 000100101001=>6 010000101001=>8 000110001001=>8 010010001001=>10 011000001001=>12 000111011001=>4 010011011001=>6 011110111001=>9 000000011011=>1 011011011011=>8 000001001011=>3 000100001011=>5 010000001011=>7 011101101011=>5 000001100011=>2 010101100011=>6 000100100011=>4 010000100011=>6 011010100011=>8 000110000011=>6 010010000011=>8 011000000011=>10 011001010011=>6 011110110011=>7 010101110111=>4 011010110111=>6 011101010111=>3 011001000111=>4 011110100111=>5 000111101111=>3 010011101111=>5 011001101111=>4 011100101111=>1 011110001111=>3 011111011111=>4 100111100010=>7 101001110010=>12 100011110010=>10 110001010110=>10 101100011010=>12 100110111000=>14 101001101100=>12 110001011100=>12 100101011100=>10 101000111100=>15 111010000110=>9 101110000110=>7 100110110010=>12 110010011010=>12 101100100110=>12 110000111010=>15 111000100110=>14 110100010110=>12 101100001110=>10 110010001110=>10 111111100000=>10 100010101100=>9 100010110010=>9 100010111000=>11 100011001010=>9 100011001100=>10 100011100010=>4 100011110000=>7 111010101010=>9 111010101100=>10 111010110010=>10 111010110100=>11 111010111000=>12 111011001010=>10 111011001100=>11 111011010010=>11 111011010100=>12 111011011000=>13 111011100010=>12 111011100100=>13 111011101000=>14 111011110000=>15 111100101010=>10 111100101100=>11 111100110010=>11 111100110100=>12 111100111000=>13 111101001010=>11 111101001100=>12 111101010010=>12 111101010100=>13 111101011000=>14 111101100010=>13 111101100100=>14 111101101000=>15 111101110000=>16 111110001010=>3 111110001100=>4 111110010010=>4 111110010100=>5 111110011000=>6 111110100010=>5 111110100100=>6 111110101000=>7 111110110000=>8 111111000010=>6 111111000100=>7 111111001000=>8 111111010000=>9 100010110100=>10 100011010010=>10 100011010100=>11 100011011000=>12 100011100100=>5 100011101000=>6 100100101010=>9 100100101100=>10 100100110010=>10 100100110100=>11 100100111000=>12 100101001010=>10 100101001100=>11 100101010010=>11 100101010100=>12 100101011000=>13 100101100010=>5 100101100100=>6 100101101000=>7 100101110000=>8 100110001010=>11 100110001100=>12 100110010010=>12 100110010100=>13 100110011000=>14 100110100010=>6 100110100100=>7 100110101000=>8 100110110000=>9 100111000010=>7 100111000100=>8 100111001000=>9 100111010000=>10 100111100000=>2 101000101010=>10 101000101100=>11 101000110010=>11 101000110100=>12 101000111000=>13 101001001010=>11 101001001100=>12 101001010010=>12 101001010100=>13 101001011000=>14 101001100010=>6 101001100100=>7 101001101000=>8 101001110000=>9 101010001010=>12 101010001100=>13 101010010010=>13 101010010100=>14 101010011000=>15 101010100010=>7 101010100100=>8 101010101000=>9 101010110000=>10 101011000010=>8 101011000100=>9 101011001000=>10 101011010000=>11 101011100000=>3 101100001010=>13 101100001100=>14 101100010010=>14 101100010100=>15 101100011000=>16 101100100010=>8 101100100100=>9 101100101000=>10 101100110000=>11 101101000010=>9 101101000100=>10 101101001000=>11 101101010000=>12 101101100000=>4 101110000010=>10 101110000100=>11 101110001000=>12 101110010000=>13 101110100000=>5 101111000000=>6 110000000000=>16 1000000000000=>11 1000011111100=>14 1000000110000=>9 10101010101010=>12 10101010101100=>13 10101010110010=>13 10101010110100=>14 10101010111000=>15 10101011001010=>13 10101011001100=>14 10101011010100=>15 10101011100010=>15 10101011100100=>16 10101011101000=>17 10101011110000=>18 10101100101010=>13 10101100101100=>14 10101100110010=>14 10101100111000=>16 10101101010100=>16 10101110001010=>6 10101110001100=>7 10101110010100=>8 10101110100100=>9 10101110101000=>10 10101110110000=>11 10101111000010=>9 10101111000100=>10 10101111010000=>12 10101111100000=>13 10110010101010=>13 10110010101100=>14 10110010110010=>14 10110010111000=>16 10110011001010=>14 10110011001100=>15 10110011100010=>16 10110011110000=>19 10110101010100=>17 10110111100000=>14 10111000101010=>15 10111000101100=>16 10111000110010=>16 10111000111000=>18 10111001010100=>18 10111010010100=>10 10111010100100=>11 10111011000100=>12 10111011010000=>14 10111011100000=>15 10111100001010=>9 10111100001100=>10 10111100010100=>11 10111100110000=>14 10111101000100=>13 10111101001000=>14 10111101010000=>15 10111101100000=>16 10111110000010=>2 10111110000100=>3 10111110001000=>4 10111110010000=>5 10111110100000=>6 10111111000000=>7 11001010101010=>13 11001010101100=>14 11001010110010=>14 11001010111000=>16 11001011001010=>14 11001011001100=>15 11001011100010=>16 11001011110000=>19 11001100101010=>14 11001100101100=>15 11001100110010=>15 11001100111000=>17 11001110001010=>7 11001110001100=>8 11001111000010=>10 11001111100000=>14 11010101010100=>18 11010101011000=>19 11010101100100=>19 11010101101000=>20 11010101110000=>21 11010110010100=>10 11010110011000=>11 11010110100100=>11 11010110101000=>12 11010110110000=>13 11010111000100=>12 11010111001000=>13 11010111010000=>14 11010111100000=>15 11011001010100=>19 11011001011000=>20 11011001100100=>20 11011001101000=>21 11011001110000=>22 11011010010100=>11 11011010011000=>12 11011010100100=>12 11011010101000=>13 11011010110000=>14 11011011000100=>13 11011011001000=>14 11011011010000=>15 11011011100000=>16 11011100010100=>12 11011100011000=>13 11011100100100=>13 11011100101000=>14 11011100110000=>15 11011101000100=>14 11011101001000=>15 11011101010000=>16 11011101100000=>17 11011110000010=>3 11011110000100=>4 11011110001000=>5 11011110010000=>6 11011110100000=>7 11011111000000=>8 11100010101010=>15 11100010101100=>16 11100010110010=>16 11100010111000=>18 11100011001010=>16 11100011001100=>17 11100011100010=>18 11100011110000=>21 11100101010100=>19 11100101011000=>20 11100101100100=>20 11100101101000=>21 11100101110000=>22 11100110010100=>11 11100110011000=>12 11100110100100=>12 11100110101000=>13 11100110110000=>14 11100111000100=>13 11100111001000=>14 11100111010000=>15 11100111100000=>16 11101001010100=>20 11101001011000=>21 11101001100100=>21 11101001101000=>22 11101001110000=>23 11101010010100=>12 11101010011000=>13 11101010100100=>13 11101010101000=>14 11101010110000=>15 11101011000100=>14 11101011001000=>15 11101011010000=>16 11101011100000=>17 11101100010100=>13 11101100011000=>14 11101100100100=>14 11101100101000=>15 11101100110000=>16 11101101000010=>14 11101101000100=>15 11101101001000=>16 11101101010000=>17 11101101100000=>18 11101110000010=>4 11101110000100=>5 11101110001000=>6 11101110010000=>7 11101110100000=>8 11101111000000=>9 11110000101010=>18 11110000101100=>19 11110000110010=>19 11110000111000=>21 11110001010100=>21 11110001011000=>22 11110001100100=>22 11110001101000=>23 11110001110000=>24 11110010010100=>13 11110010011000=>14 11110010100100=>14 11110010101000=>15 11110010110000=>16 11110011000010=>14 11110011000100=>15 11110011001000=>16 11110011010000=>17 11110011100000=>18 11110100010100=>14 11110100011000=>15 11110100100010=>14 11110100100100=>15 11110100101000=>16 11110100110000=>17 11110101000010=>15 11110101000100=>16 11110101001000=>17 11110101010000=>18 11110101100000=>19 11110110000010=>5 11110110000100=>6 11110110001000=>7 11110110010000=>8 11110110100000=>9 11110111000000=>10 11111000001010=>13 11111000001100=>14 11111000010010=>14 11111000010100=>15 11111000011000=>16 11111000100010=>15 11111000100100=>16 11111000101000=>17 11111000110000=>18 11111001000010=>16 11111001000100=>17 11111001001000=>18 11111001010000=>19 11111001100000=>20 11111010000010=>6 11111010000100=>7 11111010001000=>8 11111010010000=>9 11111010100000=>10 11111011000000=>11 11111100000010=>7 11111100000100=>8 11111100001000=>9 11111100010000=>10 11111100100000=>11 11111101000000=>12 11111110000000=>0 10000000000000=>12 10000000010000=>12 11110000000000=>24 100000000000000=>13 1010101010101010=>20 1010101010101100=>21 1010101010110100=>22 1010101010111000=>23 1010101011010100=>23 1010101011100100=>24 1010101011101000=>25 1010101011110000=>26 1010101101010100=>15 1010101110010100=>16 1010101110100100=>17 1010101111000100=>18 1010110101010100=>16 1010111001010100=>17 1010111010010100=>18 1010111100010100=>8 1011010101010100=>17 1011100101010100=>18 1011101001010100=>19 1011110001010100=>20 1011110111000000=>18 1011111010100000=>18 1011111011000000=>19 1011111100010000=>5 1011111100100000=>6 1011111101000000=>7 1011111110000000=>8 1101010101010100=>18 1110010101010100=>19 1110100101010100=>20 1111000101010100=>21 1111011100000010=>5 1111101010000010=>18 1111101100000010=>6 1111110001000010=>18 1111110010000010=>19 1111110100000010=>7 1111111000000010=>8 1000000000000000=>14 11111111111100000=>35 11000000000000000=>26 101010101010101010=>20 101010101010101100=>21 101010101010110100=>22 101010101011010100=>23 101010101101010100=>24 101010110101010100=>25 101011010101010100=>26 101101010101010100=>27 110101010101010100=>28 101010101010111000=>23 101010101011100100=>24 101010101110010100=>25 101010111001010100=>15 101011100101010100=>27 101110010101010100=>28 111001010101010100=>29 111111110000000010=>9 101111111100000000=>9 111111101000000010=>8 101111111010000000=>8 111111100100000010=>22 111111011000000010=>7 101111111001000000=>7 101111110110000000=>22 111111111111111100=>28 100000000001100000=>16 10101010101010101010=>30 10101010101010101100=>31 10101010101010110100=>32 10101010101011010100=>33 10101010101101010100=>34 10101010110101010100=>24 10101011010101010100=>25 10101101010101010100=>26 10110101010101010100=>27 11010101010101010100=>28 11111111100000000010=>10 10111111111000000000=>10 11111111010000000010=>9 10111111110100000000=>9 1111111111000000000010=>11 1011111111110000000000=>11 11111111111111111111111100000=>95
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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
Sep 01, 2025 at 16:52 by Martin Rubey