edit this statistic or download as text // json
Identifier
Values
=>
0=>1 1=>0 00=>2 01=>1 10=>0 11=>0 000=>3 001=>2 010=>1 011=>1 100=>1 101=>0 110=>0 111=>0 0000=>4 0001=>3 0010=>2 0011=>2 0100=>2 0101=>1 0110=>1 0111=>1 1000=>2 1001=>1 1010=>0 1011=>0 1100=>0 1101=>0 1110=>0 1111=>0 00000=>5 00001=>4 00010=>3 00011=>3 00100=>3 00101=>2 00110=>2 00111=>2 01000=>3 01001=>2 01010=>1 01011=>1 01100=>1 01101=>1 01110=>1 01111=>1 10000=>3 10001=>2 10010=>1 10011=>1 10100=>1 10101=>0 10110=>0 10111=>0 11000=>1 11001=>0 11010=>0 11011=>0 11100=>0 11101=>0 11110=>0 11111=>0 000000=>6 000001=>5 000010=>4 000011=>4 000100=>4 000101=>3 000110=>3 000111=>3 001000=>4 001001=>3 001010=>2 001011=>2 001100=>2 001101=>2 001110=>2 001111=>2 010000=>4 010001=>3 010010=>2 010011=>2 010100=>2 010101=>1 010110=>1 010111=>1 011000=>2 011001=>1 011010=>1 011011=>1 011100=>1 011101=>1 011110=>1 011111=>1 100000=>4 100001=>3 100010=>2 100011=>2 100100=>2 100101=>1 100110=>1 100111=>1 101000=>2 101001=>1 101010=>0 101011=>0 101100=>0 101101=>0 101110=>0 101111=>0 110000=>2 110001=>1 110010=>0 110011=>0 110100=>0 110101=>0 110110=>0 110111=>0 111000=>0 111001=>0 111010=>0 111011=>0 111100=>0 111101=>0 111110=>0 111111=>0 0000000=>7 0000001=>6 0000010=>5 0000011=>5 0000100=>5 0000101=>4 0000110=>4 0000111=>4 0001000=>5 0001001=>4 0001010=>3 0001011=>3 0001100=>3 0001101=>3 0001110=>3 0001111=>3 0010000=>5 0010001=>4 0010010=>3 0010011=>3 0010100=>3 0010101=>2 0010110=>2 0010111=>2 0011000=>3 0011001=>2 0011010=>2 0011011=>2 0011100=>2 0011101=>2 0011110=>2 0011111=>2 0100000=>5 0100001=>4 0100010=>3 0100011=>3 0100100=>3 0100101=>2 0100110=>2 0100111=>2 0101000=>3 0101001=>2 0101010=>1 0101011=>1 0101100=>1 0101101=>1 0101110=>1 0101111=>1 0110000=>3 0110001=>2 0110010=>1 0110011=>1 0110100=>1 0110101=>1 0110110=>1 0110111=>1 0111000=>1 0111001=>1 0111010=>1 0111011=>1 0111100=>1 0111101=>1 0111110=>1 0111111=>1 1000000=>5 1000001=>4 1000010=>3 1000011=>3 1000100=>3 1000101=>2 1000110=>2 1000111=>2 1001000=>3 1001001=>2 1001010=>1 1001011=>1 1001100=>1 1001101=>1 1001110=>1 1001111=>1 1010000=>3 1010001=>2 1010010=>1 1010011=>1 1010100=>1 1010101=>0 1010110=>0 1010111=>0 1011000=>1 1011001=>0 1011010=>0 1011011=>0 1011100=>0 1011101=>0 1011110=>0 1011111=>0 1100000=>3 1100001=>2 1100010=>1 1100011=>1 1100100=>1 1100101=>0 1100110=>0 1100111=>0 1101000=>1 1101001=>0 1101010=>0 1101011=>0 1101100=>0 1101101=>0 1101110=>0 1101111=>0 1110000=>1 1110001=>0 1110010=>0 1110011=>0 1110100=>0 1110101=>0 1110110=>0 1110111=>0 1111000=>0 1111001=>0 1111010=>0 1111011=>0 1111100=>0 1111101=>0 1111110=>0 1111111=>0 00000000=>8 00000001=>7 00000010=>6 00000011=>6 00000100=>6 00000101=>5 00000110=>5 00000111=>5 00001000=>6 00001001=>5 00001010=>4 00001011=>4 00001100=>4 00001101=>4 00001110=>4 00001111=>4 00010000=>6 00010001=>5 00010010=>4 00010011=>4 00010100=>4 00010101=>3 00010110=>3 00010111=>3 00011000=>4 00011001=>3 00011010=>3 00011011=>3 00011100=>3 00011101=>3 00011110=>3 00011111=>3 00100000=>6 00100001=>5 00100010=>4 00100011=>4 00100100=>4 00100101=>3 00100110=>3 00100111=>3 00101000=>4 00101001=>3 00101010=>2 00101011=>2 00101100=>2 00101101=>2 00101110=>2 00101111=>2 00110000=>4 00110001=>3 00110010=>2 00110011=>2 00110100=>2 00110101=>2 00110110=>2 00110111=>2 00111000=>2 00111001=>2 00111010=>2 00111011=>2 00111100=>2 00111101=>2 00111110=>2 00111111=>2 01000000=>6 01000001=>5 01000010=>4 01000011=>4 01000100=>4 01000101=>3 01000110=>3 01000111=>3 01001000=>4 01001001=>3 01001010=>2 01001011=>2 01001100=>2 01001101=>2 01001110=>2 01001111=>2 01010000=>4 01010001=>3 01010010=>2 01010011=>2 01010100=>2 01010101=>1 01010110=>1 01010111=>1 01011000=>2 01011001=>1 01011010=>1 01011011=>1 01011100=>1 01011101=>1 01011110=>1 01011111=>1 01100000=>4 01100001=>3 01100010=>2 01100011=>2 01100100=>2 01100101=>1 01100110=>1 01100111=>1 01101000=>2 01101001=>1 01101010=>1 01101011=>1 01101100=>1 01101101=>1 01101110=>1 01101111=>1 01110000=>2 01110001=>1 01110010=>1 01110011=>1 01110100=>1 01110101=>1 01110110=>1 01110111=>1 01111000=>1 01111001=>1 01111010=>1 01111011=>1 01111100=>1 01111101=>1 01111110=>1 01111111=>1 10000000=>6 10000001=>5 10000010=>4 10000011=>4 10000100=>4 10000101=>3 10000110=>3 10000111=>3 10001000=>4 10001001=>3 10001010=>2 10001011=>2 10001100=>2 10001101=>2 10001110=>2 10001111=>2 10010000=>4 10010001=>3 10010010=>2 10010011=>2 10010100=>2 10010101=>1 10010110=>1 10010111=>1 10011000=>2 10011001=>1 10011010=>1 10011011=>1 10011100=>1 10011101=>1 10011110=>1 10011111=>1 10100000=>4 10100001=>3 10100010=>2 10100011=>2 10100100=>2 10100101=>1 10100110=>1 10100111=>1 10101000=>2 10101001=>1 10101010=>0 10101011=>0 10101100=>0 10101101=>0 10101110=>0 10101111=>0 10110000=>2 10110001=>1 10110010=>0 10110011=>0 10110100=>0 10110101=>0 10110110=>0 10110111=>0 10111000=>0 10111001=>0 10111010=>0 10111011=>0 10111100=>0 10111101=>0 10111110=>0 10111111=>0 11000000=>4 11000001=>3 11000010=>2 11000011=>2 11000100=>2 11000101=>1 11000110=>1 11000111=>1 11001000=>2 11001001=>1 11001010=>0 11001011=>0 11001100=>0 11001101=>0 11001110=>0 11001111=>0 11010000=>2 11010001=>1 11010010=>0 11010011=>0 11010100=>0 11010101=>0 11010110=>0 11010111=>0 11011000=>0 11011001=>0 11011010=>0 11011011=>0 11011100=>0 11011101=>0 11011110=>0 11011111=>0 11100000=>2 11100001=>1 11100010=>0 11100011=>0 11100100=>0 11100101=>0 11100110=>0 11100111=>0 11101000=>0 11101001=>0 11101010=>0 11101011=>0 11101100=>0 11101101=>0 11101110=>0 11101111=>0 11110000=>0 11110001=>0 11110010=>0 11110011=>0 11110100=>0 11110101=>0 11110110=>0 11110111=>0 11111000=>0 11111001=>0 11111010=>0 11111011=>0 11111100=>0 11111101=>0 11111110=>0 11111111=>0 000000000=>9 000000001=>8 000000010=>7 000000011=>7 000000100=>7 000000101=>6 000000110=>6 000000111=>6 000001000=>7 000001001=>6 000001010=>5 000001011=>5 000001100=>5 000001101=>5 000001110=>5 000001111=>5 000010000=>7 000010001=>6 000010010=>5 000010011=>5 000010100=>5 000010101=>4 000010110=>4 000010111=>4 000011000=>5 000011001=>4 000011010=>4 000011011=>4 000011100=>4 000011101=>4 000011110=>4 000011111=>4 000100000=>7 000100001=>6 000100010=>5 000100011=>5 000100100=>5 000100101=>4 000100110=>4 000100111=>4 000101000=>5 000101001=>4 000101010=>3 000101011=>3 000101100=>3 000101101=>3 000101110=>3 000101111=>3 000110000=>5 000110001=>4 000110010=>3 000110011=>3 000110100=>3 000110101=>3 000110110=>3 000110111=>3 000111000=>3 000111001=>3 000111010=>3 000111011=>3 000111100=>3 000111101=>3 000111110=>3 000111111=>3 001000000=>7 001000001=>6 001000010=>5 001000011=>5 001000100=>5 001000101=>4 001000110=>4 001000111=>4 001001000=>5 001001001=>4 001001010=>3 001001011=>3 001001100=>3 001001101=>3 001001110=>3 001001111=>3 001010000=>5 001010001=>4 001010010=>3 001010011=>3 001010100=>3 001010101=>2 001010110=>2 001010111=>2 001011000=>3 001011001=>2 001011010=>2 001011011=>2 001011100=>2 001011101=>2 001011110=>2 001011111=>2 001100000=>5 001100001=>4 001100010=>3 001100011=>3 001100100=>3 001100101=>2 001100110=>2 001100111=>2 001101000=>3 001101001=>2 001101010=>2 001101011=>2 001101100=>2 001101101=>2 001101110=>2 001101111=>2 001110000=>3 001110001=>2 001110010=>2 001110011=>2 001110100=>2 001110101=>2 001110110=>2 001110111=>2 001111000=>2 001111001=>2 001111010=>2 001111011=>2 001111100=>2 001111101=>2 001111110=>2 001111111=>2 010000000=>7 010000001=>6 010000010=>5 010000011=>5 010000100=>5 010000101=>4 010000110=>4 010000111=>4 010001000=>5 010001001=>4 010001010=>3 010001011=>3 010001100=>3 010001101=>3 010001110=>3 010001111=>3 010010000=>5 010010001=>4 010010010=>3 010010011=>3 010010100=>3 010010101=>2 010010110=>2 010010111=>2 010011000=>3 010011001=>2 010011010=>2 010011011=>2 010011100=>2 010011101=>2 010011110=>2 010011111=>2 010100000=>5 010100001=>4 010100010=>3 010100011=>3 010100100=>3 010100101=>2 010100110=>2 010100111=>2 010101000=>3 010101001=>2 010101010=>1 010101011=>1 010101100=>1 010101101=>1 010101110=>1 010101111=>1 010110000=>3 010110001=>2 010110010=>1 010110011=>1 010110100=>1 010110101=>1 010110110=>1 010110111=>1 010111000=>1 010111001=>1 010111010=>1 010111011=>1 010111100=>1 010111101=>1 010111110=>1 010111111=>1 011000000=>5 011000001=>4 011000010=>3 011000011=>3 011000100=>3 011000101=>2 011000110=>2 011000111=>2 011001000=>3 011001001=>2 011001010=>1 011001011=>1 011001100=>1 011001101=>1 011001110=>1 011001111=>1 011010000=>3 011010001=>2 011010010=>1 011010011=>1 011010100=>1 011010101=>1 011010110=>1 011010111=>1 011011000=>1 011011001=>1 011011010=>1 011011011=>1 011011100=>1 011011101=>1 011011110=>1 011011111=>1 011100000=>3 011100001=>2 011100010=>1 011100011=>1 011100100=>1 011100101=>1 011100110=>1 011100111=>1 011101000=>1 011101001=>1 011101010=>1 011101011=>1 011101100=>1 011101101=>1 011101110=>1 011101111=>1 011110000=>1 011110001=>1 011110010=>1 011110011=>1 011110100=>1 011110101=>1 011110110=>1 011110111=>1 011111000=>1 011111001=>1 011111010=>1 011111011=>1 011111100=>1 011111101=>1 011111110=>1 011111111=>1 100000000=>7 100000001=>6 100000010=>5 100000011=>5 100000100=>5 100000101=>4 100000110=>4 100000111=>4 100001000=>5 100001001=>4 100001010=>3 100001011=>3 100001100=>3 100001101=>3 100001110=>3 100001111=>3 100010000=>5 100010001=>4 100010010=>3 100010011=>3 100010100=>3 100010101=>2 100010110=>2 100010111=>2 100011000=>3 100011001=>2 100011010=>2 100011011=>2 100011100=>2 100011101=>2 100011110=>2 100011111=>2 100100000=>5 100100001=>4 100100010=>3 100100011=>3 100100100=>3 100100101=>2 100100110=>2 100100111=>2 100101000=>3 100101001=>2 100101010=>1 100101011=>1 100101100=>1 100101101=>1 100101110=>1 100101111=>1 100110000=>3 100110001=>2 100110010=>1 100110011=>1 100110100=>1 100110101=>1 100110110=>1 100110111=>1 100111000=>1 100111001=>1 100111010=>1 100111011=>1 100111100=>1 100111101=>1 100111110=>1 100111111=>1 101000000=>5 101000001=>4 101000010=>3 101000011=>3 101000100=>3 101000101=>2 101000110=>2 101000111=>2 101001000=>3 101001001=>2 101001010=>1 101001011=>1 101001100=>1 101001101=>1 101001110=>1 101001111=>1 101010000=>3 101010001=>2 101010010=>1 101010011=>1 101010100=>1 101010101=>0 101010110=>0 101010111=>0 101011000=>1 101011001=>0 101011010=>0 101011011=>0 101011100=>0 101011101=>0 101011110=>0 101011111=>0 101100000=>3 101100001=>2 101100010=>1 101100011=>1 101100100=>1 101100101=>0 101100110=>0 101100111=>0 101101000=>1 101101001=>0 101101010=>0 101101011=>0 101101100=>0 101101101=>0 101101110=>0 101101111=>0 101110000=>1 101110001=>0 101110010=>0 101110011=>0 101110100=>0 101110101=>0 101110110=>0 101110111=>0 101111000=>0 101111001=>0 101111010=>0 101111011=>0 101111100=>0 101111101=>0 101111110=>0 101111111=>0 110000000=>5 110000001=>4 110000010=>3 110000011=>3 110000100=>3 110000101=>2 110000110=>2 110000111=>2 110001000=>3 110001001=>2 110001010=>1 110001011=>1 110001100=>1 110001101=>1 110001110=>1 110001111=>1 110010000=>3 110010001=>2 110010010=>1 110010011=>1 110010100=>1 110010101=>0 110010110=>0 110010111=>0 110011000=>1 110011001=>0 110011010=>0 110011011=>0 110011100=>0 110011101=>0 110011110=>0 110011111=>0 110100000=>3 110100001=>2 110100010=>1 110100011=>1 110100100=>1 110100101=>0 110100110=>0 110100111=>0 110101000=>1 110101001=>0 110101010=>0 110101011=>0 110101100=>0 110101101=>0 110101110=>0 110101111=>0 110110000=>1 110110001=>0 110110010=>0 110110011=>0 110110100=>0 110110101=>0 110110110=>0 110110111=>0 110111000=>0 110111001=>0 110111010=>0 110111011=>0 110111100=>0 110111101=>0 110111110=>0 110111111=>0 111000000=>3 111000001=>2 111000010=>1 111000011=>1 111000100=>1 111000101=>0 111000110=>0 111000111=>0 111001000=>1 111001001=>0 111001010=>0 111001011=>0 111001100=>0 111001101=>0 111001110=>0 111001111=>0 111010000=>1 111010001=>0 111010010=>0 111010011=>0 111010100=>0 111010101=>0 111010110=>0 111010111=>0 111011000=>0 111011001=>0 111011010=>0 111011011=>0 111011100=>0 111011101=>0 111011110=>0 111011111=>0 111100000=>1 111100001=>0 111100010=>0 111100011=>0 111100100=>0 111100101=>0 111100110=>0 111100111=>0 111101000=>0 111101001=>0 111101010=>0 111101011=>0 111101100=>0 111101101=>0 111101110=>0 111101111=>0 111110000=>0 111110001=>0 111110010=>0 111110011=>0 111110100=>0 111110101=>0 111110110=>0 111110111=>0 111111000=>0 111111001=>0 111111010=>0 111111011=>0 111111100=>0 111111101=>0 111111110=>0 111111111=>0 1010101010=>0 1010101100=>0 1010110010=>0 1010110100=>0 1010111000=>0 1011001010=>0 1011001100=>0 1011010010=>0 1011010100=>0 1011011000=>0 1011100010=>0 1011100100=>0 1011101000=>0 1011110000=>0 1100101010=>0 1100101100=>0 1100110010=>0 1100110100=>0 1100111000=>0 1101001010=>0 1101001100=>0 1101010010=>0 1101010100=>0 1101011000=>0 1101100010=>0 1101100100=>0 1101101000=>0 1101110000=>0 1110001010=>0 1110001100=>0 1110010010=>0 1110010100=>0 1110011000=>0 1110100010=>0 1110100100=>0 1110101000=>0 1110110000=>0 1111000010=>0 1111000100=>0 1111001000=>0 1111010000=>0 1111100000=>0 1111111110=>0 1111111101=>0 1111000001=>1 1110111110=>0 1110100001=>1 1110011110=>0 1110010001=>1 1110001001=>1 1110000101=>1 1101111110=>0 1101100001=>1 1101010001=>1 1101001110=>0 1101001001=>1 1101000101=>1 1100110001=>1 1100101001=>1 1100100110=>1 1100100101=>1 1100011001=>1 1100010101=>1 1100010010=>2 1100001000=>4 1011111110=>0 1011111101=>0 1011100001=>1 1011010001=>1 1011001001=>1 1011000101=>1 1010111110=>0 1010110001=>1 1010101001=>1 1010100110=>1 1010100101=>1 1010011010=>1 1010011001=>1 1010010110=>1 1010010101=>1 1010001110=>2 1001111110=>1 1001111000=>1 1001110100=>1 1001110001=>1 1001101100=>1 1001101010=>1 1001101001=>1 1001100110=>1 1001100101=>1 1001011110=>1 1001011010=>1 1001011001=>1 1001010110=>1 1001010101=>1 1001001110=>2 1000111110=>2 1000111100=>2 1000111010=>2 1000110110=>2 1000101110=>2 1000011110=>3 1000010110=>3 1000001110=>4 1000001010=>4 1000000110=>5 1000000100=>6 1000000010=>6 1000000000=>8 0111111111=>1 0111111101=>1 0111111001=>1 0111110001=>1 0111100001=>1 0111000001=>3 0110000001=>5 0100000001=>7 0000000001=>9 0111111011=>1 0111110101=>1 0111101001=>1 0111010001=>1 0110100001=>3 0101000001=>5 0010000001=>7 0101010101=>1 0101010011=>2 0101001101=>2 0101001011=>2 0101000111=>3 0100110101=>2 0100110011=>2 0100101101=>2 0100101011=>2 0100100111=>3 0100011101=>3 0100011011=>3 0100010111=>3 0100001111=>4 0011010101=>2 0011010011=>2 0011001101=>2 0011001011=>2 0011000111=>3 0010110101=>2 0010110011=>2 0010101101=>2 0010101011=>2 0010100111=>3 0010011101=>3 0010011011=>3 0010010111=>3 0010001111=>4 0001110101=>3 0001110011=>3 0001101101=>3 0001101011=>3 0001100111=>3 0001011101=>3 0001011011=>3 0001010111=>3 0001001111=>4 0000111101=>4 0000111011=>4 0000110111=>4 0000101111=>4 0000011111=>5 0000000000=>10 0000000110=>7 0000011000=>6 0000011110=>5 0000010010=>6 0001100000=>6 0001100110=>3 0001111000=>3 0001111110=>3 0001110010=>3 0001001000=>6 0001001110=>4 0001000010=>6 0001011010=>3 0100000010=>6 0010101010=>2 0010101000=>4 0010101100=>2 0010100100=>4 0010010100=>4 0001010100=>4 0010101110=>2 0010100000=>6 0010111100=>2 0010000100=>6 0011110100=>2 0000010100=>6 0111010100=>1 0000000010=>8 0000001110=>6 0000111110=>4 0000000100=>8 0000001010=>6 0000010110=>5 0000101110=>4 0001011110=>3 0100000000=>8 0100000011=>6 0100000111=>5 0100011111=>3 0100111111=>2 0101111111=>1 0100000101=>5 0100001011=>4 0100101111=>2 0101011111=>1 0110111111=>1 0101010110=>1 0101011001=>1 0101011010=>1 0101011100=>1 0101100101=>1 0101100110=>1 0101101001=>1 0101101010=>1 0101101100=>1 0101110001=>1 0101110010=>1 0101110100=>1 0101111000=>1 0110010101=>1 0110010110=>1 0110011001=>1 0110011010=>1 0110011100=>1 0110100101=>1 0110100110=>1 0110101001=>1 0110101010=>1 0110101100=>1 0110110001=>1 0110110010=>1 0110110100=>1 0110111000=>1 0111000101=>1 0111000110=>1 0111001001=>1 0111001010=>1 0111001100=>1 0111010010=>1 0111011000=>1 0111100010=>1 0111100100=>1 0111101000=>1 0111110000=>1 0100000100=>6 0011100110=>2 0011101010=>2 0011101100=>2 0001101110=>3 0010110110=>2 0011110010=>2 0001110110=>3 0100111010=>2 0010111010=>2 0011111000=>2 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0001000101=>5 0000100011=>6 0000100100=>6 0000100010=>6 0010110000=>4 0000011100=>5 0000001000=>8 0000101100=>4 0010101111=>2 0000101000=>6 0010001000=>6 0001001100=>4 0001000110=>5 0001100100=>4 0001100010=>4 0000100110=>5 0000110010=>4 0010010000=>6 0001010010=>4 0001000000=>8 0001011001=>3 0001100101=>3 0001110001=>3 0010011001=>3 0010100101=>3 0010101001=>3 0010011111=>3 0000111001=>4 0010001101=>4 0001001101=>4 0001010001=>5 0001010011=>4 0001111011=>3 0010011000=>4 0001011000=>4 0000100000=>8 0010001011=>4 0010000111=>5 0000010011=>6 0010001100=>4 0010000110=>5 0000110000=>6 0000100001=>7 0010100011=>4 0010100001=>5 0000111000=>4 0001101000=>4 0000010000=>8 0000101001=>5 0010100010=>4 0010001001=>5 0010000011=>6 0010001010=>4 0001110000=>4 10000000000=>9 10000000010=>7 10000000110=>6 10000001110=>5 10000011110=>4 10000111110=>3 10001111110=>2 10011111110=>1 10111111110=>0 11111111110=>0 10000000100=>7 10000001010=>5 10000010110=>4 10000101110=>3 10001011110=>2 10010111110=>1 10101111110=>0 11011111110=>0 10000010000=>7 10000100010=>5 10001000010=>5 10000100100=>5 10001001010=>3 10001000100=>5 10000101000=>5 10010001010=>3 10001010010=>3 10010000100=>5 10001001000=>5 10010010010=>3 10001010100=>3 10010101010=>1 10010001000=>5 10100010010=>3 10010100010=>3 10010010100=>3 10100101010=>1 01111111111=>1 01111111101=>1 01111111001=>1 01111110001=>1 01111100001=>1 01111000001=>2 01110000001=>4 01100000001=>6 01000000001=>8 00000000001=>10 00000000010=>9 10101010101=>0 10101010010=>1 10101001001=>2 10101001010=>1 10101000100=>3 10100100101=>2 10100100010=>3 10100101001=>2 10100100100=>3 10100010001=>4 10100010100=>3 10100001000=>5 10010010101=>2 10010001001=>4 10010100101=>2 10010101001=>2 10010100100=>3 10010010001=>4 10001000101=>4 10001001001=>4 10001010001=>4 10000100001=>6 01001010101=>2 01001010010=>3 01001001001=>4 01001001010=>3 01001000100=>5 01000100101=>4 01000100010=>5 01000101001=>4 01000101010=>3 01000100100=>5 01000010001=>6 01000010010=>5 01000010100=>5 01000001000=>7 01010010101=>2 01010010010=>3 01010001001=>4 01010001010=>3 01010000100=>5 01010100101=>2 01010100010=>3 01010101001=>2 01010101010=>1 01010100100=>3 01010010001=>4 01010010100=>3 01010001000=>5 01001000101=>4 01001000010=>5 01001010001=>4 01001010100=>3 01001001000=>5 01000100001=>6 01000101000=>5 01000010000=>7 00100010101=>4 00100010010=>5 00100001001=>6 00100001010=>5 00100000100=>7 00100100101=>4 00100100010=>5 00100101001=>4 00100101010=>3 00100100100=>5 00100010001=>6 00100010100=>5 00100001000=>7 00101000101=>4 00101000010=>5 00101001001=>4 00101001010=>3 00101000100=>5 00101010001=>4 00101010010=>3 00101010100=>3 00101001000=>5 00100100001=>6 00100101000=>5 00100010000=>7 00010000101=>6 00010000010=>7 00010001001=>6 00010001010=>5 00010000100=>7 00010010001=>6 00010010010=>5 00010010100=>5 00010001000=>7 00010100001=>6 00010100010=>5 00010100100=>5 00010101000=>5 00010010000=>7 00001000001=>8 00001000010=>7 00001000100=>7 00001001000=>7 00001010000=>7 00000100000=>9 01000000000=>9 01000000011=>7 01000000111=>6 01000001111=>5 01000011111=>4 01000111111=>3 01001111111=>2 01011111111=>1 00000000101=>8 00000001101=>7 00000011101=>6 00000111101=>5 00001111101=>4 00011111101=>3 00111111101=>2 11111111101=>0 101010101010=>0 101010101100=>0 101010110010=>0 101010110100=>0 101010111000=>0 101011001010=>0 101011001100=>0 101011010010=>0 101011010100=>0 101011011000=>0 101011100010=>0 101011100100=>0 101011101000=>0 101011110000=>0 101100101010=>0 101100101100=>0 101100110010=>0 101100110100=>0 101100111000=>0 101101001010=>0 101101001100=>0 101101010010=>0 101101010100=>0 101101011000=>0 101101100010=>0 101101100100=>0 101101101000=>0 101101110000=>0 101110001010=>0 101110001100=>0 101110010010=>0 101110010100=>0 101110011000=>0 101110100010=>0 101110100100=>0 101110101000=>0 101110110000=>0 101111000010=>0 101111000100=>0 101111001000=>0 101111010000=>0 101111100000=>0 110010101010=>0 110010101100=>0 110010110010=>0 110010110100=>0 110010111000=>0 110011001010=>0 110011001100=>0 110011010010=>0 110011010100=>0 110011011000=>0 110011100010=>0 110011100100=>0 110011101000=>0 110011110000=>0 110100101010=>0 110100101100=>0 110100110010=>0 110100110100=>0 110100111000=>0 110101001010=>0 110101001100=>0 110101010010=>0 110101010100=>0 110101011000=>0 110101100010=>0 110101100100=>0 110101101000=>0 110101110000=>0 110110001010=>0 110110001100=>0 110110010010=>0 110110010100=>0 110110011000=>0 110110100010=>0 110110100100=>0 110110101000=>0 110110110000=>0 110111000010=>0 110111000100=>0 110111001000=>0 110111010000=>0 110111100000=>0 111000101010=>0 111000101100=>0 111000110010=>0 111000110100=>0 111000111000=>0 111001001010=>0 111001001100=>0 111001010010=>0 111001010100=>0 111001011000=>0 111001100010=>0 111001100100=>0 111001101000=>0 111001110000=>0 111010001010=>0 111010001100=>0 111010010010=>0 111010010100=>0 111010011000=>0 111010100010=>0 111010100100=>0 111010101000=>0 111010110000=>0 111011000010=>0 111011000100=>0 111011001000=>0 111011010000=>0 111011100000=>0 111100001010=>0 111100001100=>0 111100010010=>0 111100010100=>0 111100011000=>0 111100100010=>0 111100100100=>0 111100101000=>0 111100110000=>0 111101000010=>0 111101000100=>0 111101001000=>0 111101010000=>0 111101100000=>0 111110000010=>0 111110000100=>0 111110001000=>0 111110010000=>0 111110100000=>0 111111000000=>0 100001111100=>3 010101010101=>1 010101010011=>2 010101001101=>2 010101001011=>2 010101000111=>3 010100110101=>2 010100110011=>2 010100101101=>2 010100101011=>2 010100100111=>3 010100011101=>3 010100011011=>3 010100010111=>3 010100001111=>4 010011010101=>2 010011010011=>2 010011001101=>2 010011001011=>2 010011000111=>3 010010110101=>2 010010110011=>2 010010101101=>2 010010101011=>2 010010100111=>3 010010011101=>3 010010011011=>3 010010010111=>3 010010001111=>4 010001110101=>3 010001110011=>3 010001101101=>3 010001101011=>3 010001100111=>3 010001011101=>3 010001011011=>3 010001010111=>3 010001001111=>4 010000111101=>4 010000111011=>4 010000110111=>4 010000101111=>4 010000011111=>5 001101010101=>2 001101010011=>2 001101001101=>2 001101001011=>2 001101000111=>3 001100110101=>2 001100110011=>2 001100101101=>2 001100101011=>2 001100100111=>3 001100011101=>3 001100011011=>3 001100010111=>3 001100001111=>4 001011010101=>2 001011010011=>2 001011001101=>2 001011001011=>2 001011000111=>3 001010110101=>2 001010110011=>2 001010101101=>2 001010101011=>2 001010100111=>3 001010011101=>3 001010011011=>3 001010010111=>3 001010001111=>4 001001110101=>3 001001110011=>3 001001101101=>3 001001101011=>3 001001100111=>3 001001011101=>3 001001011011=>3 001001010111=>3 001001001111=>4 001000111101=>4 001000111011=>4 001000110111=>4 001000101111=>4 001000011111=>5 000111010101=>3 000111010011=>3 000111001101=>3 000111001011=>3 000111000111=>3 000110110101=>3 000110110011=>3 000110101101=>3 000110101011=>3 000110100111=>3 000110011101=>3 000110011011=>3 000110010111=>3 000110001111=>4 000101110101=>3 000101110011=>3 000101101101=>3 000101101011=>3 000101100111=>3 000101011101=>3 000101011011=>3 000101010111=>3 000101001111=>4 000100111101=>4 000100111011=>4 000100110111=>4 000100101111=>4 000100011111=>5 000011110101=>4 000011110011=>4 000011101101=>4 000011101011=>4 000011100111=>4 000011011101=>4 000011011011=>4 000011010111=>4 000011001111=>4 000010111101=>4 000010111011=>4 000010110111=>4 000010101111=>4 000010011111=>5 000001111101=>5 000001111011=>5 000001110111=>5 000001101111=>5 000001011111=>5 000000111111=>6 111110000001=>1 111001100001=>1 111000011001=>1 111000110001=>1 111000100101=>1 111011000001=>1 111010010001=>1 111010000101=>1 100111100001=>1 100110011001=>1 100110110001=>1 100110100101=>1 101101100001=>1 101100011001=>1 101100110001=>1 101100100101=>1 101111000001=>1 101110010001=>1 101110000101=>1 101001011001=>1 101001110001=>1 101001100101=>1 101011010001=>1 101011000101=>1 101010010101=>1 000001111110=>5 000111100110=>3 000111111000=>3 000111110010=>3 000111001110=>3 000111011010=>3 000101101110=>3 000101111010=>3 011001100110=>1 011001111000=>1 011001110010=>1 011001011010=>1 011110000110=>1 011110011000=>1 011110010010=>1 011111100000=>1 011111001000=>1 011111000010=>1 011100100110=>1 011100111000=>1 011100110010=>1 011100011010=>1 011101101000=>1 011101100010=>1 011101001010=>1 010011111000=>2 010011110010=>2 010011011010=>2 010001111010=>3 010110100110=>1 010110111000=>1 010110110010=>1 010110011010=>1 010111101000=>1 010111100010=>1 010111001010=>1 010101101010=>1 010101010110=>1 010101011001=>1 010101011010=>1 010101011100=>1 010101100101=>1 010101100110=>1 010101101001=>1 010101101100=>1 010101110001=>1 010101110010=>1 010101110100=>1 010101111000=>1 010110010101=>1 010110010110=>1 010110011001=>1 010110011100=>1 010110100101=>1 010110101001=>1 010110101010=>1 010110101100=>1 010110110001=>1 010110110100=>1 010111000101=>1 010111000110=>1 010111001001=>1 010111001100=>1 010111010001=>1 010111010010=>1 010111010100=>1 010111011000=>1 010111100001=>1 010111100100=>1 010111110000=>1 011001010101=>1 011001010110=>1 011001011001=>1 011001011100=>1 011001100101=>1 011001101001=>1 011001101010=>1 011001101100=>1 011001110001=>1 011001110100=>1 011010010101=>1 011010010110=>1 011010011001=>1 011010011010=>1 011010011100=>1 011010100101=>1 011010100110=>1 011010101001=>1 011010101010=>1 011010101100=>1 011010110001=>1 011010110010=>1 011010110100=>1 011010111000=>1 011011000101=>1 011011000110=>1 011011001001=>1 011011001010=>1 011011001100=>1 011011010001=>1 011011010010=>1 011011010100=>1 011011011000=>1 011011100001=>1 011011100010=>1 011011100100=>1 011011101000=>1 011011110000=>1 011100010101=>1 011100010110=>1 011100011001=>1 011100011100=>1 011100100101=>1 011100101001=>1 011100101010=>1 011100101100=>1 011100110001=>1 011100110100=>1 011101000101=>1 011101000110=>1 011101001001=>1 011101001100=>1 011101010001=>1 011101010010=>1 011101010100=>1 011101011000=>1 011101100001=>1 011101100100=>1 011101110000=>1 011110000101=>1 011110001001=>1 011110001010=>1 011110001100=>1 011110010001=>1 011110010100=>1 011110100001=>1 011110100010=>1 011110100100=>1 011110101000=>1 011110110000=>1 011111000001=>1 011111000100=>1 011111010000=>1 001111000110=>2 001111001010=>2 100111001100=>1 001111001100=>2 001011010110=>2 001111010010=>2 100111010100=>1 001111010100=>2 000111010110=>3 001011011010=>2 100111011000=>1 001111011000=>2 100011011100=>2 010011011100=>2 001011011100=>2 000111011100=>3 000011011110=>4 001101100110=>2 001101101010=>2 100101101100=>1 001101101100=>2 001011100110=>2 001111100010=>2 100111100100=>1 001111100100=>2 010011101010=>2 001011101010=>2 100111101000=>1 001111101000=>2 000111101010=>3 100011101100=>2 010011101100=>2 001011101100=>2 000111101100=>3 000011101110=>4 101001110100=>1 001001110110=>3 001101110010=>2 100101110100=>1 001101110100=>2 000101110110=>3 001011110010=>2 100111110000=>1 001111110000=>2 100011110100=>2 010011110100=>2 001011110100=>2 000111110100=>3 000011110110=>4 110001111000=>1 101001111000=>1 001001111010=>3 100101111000=>1 001101111000=>2 100011111000=>2 001011111000=>2 000011111010=>4 010001111100=>3 001001111100=>3 000101111100=>3 000011111100=>4 100101010101=>1 100101011001=>1 100101100101=>1 100101101001=>1 100101110001=>1 100110010101=>1 100110101001=>1 100111000101=>1 100111001001=>1 100111010001=>1 101001010101=>1 101001101001=>1 101010011001=>1 101010100101=>1 101010101001=>1 101010110001=>1 101011001001=>1 101011100001=>1 101100010101=>1 101100101001=>1 101101000101=>1 101101001001=>1 101101010001=>1 101110001001=>1 101110100001=>1 110001010101=>1 110001011001=>1 110001100101=>1 110001101001=>1 110001110001=>1 110010010101=>1 110010011001=>1 110010100101=>1 110010101001=>1 110010110001=>1 110011000101=>1 110011001001=>1 110011010001=>1 110011100001=>1 110100010101=>1 110100011001=>1 110100100101=>1 110100101001=>1 110100110001=>1 110101000101=>1 110101001001=>1 110101010001=>1 110101100001=>1 110110000101=>1 110110001001=>1 110110010001=>1 110110100001=>1 110111000001=>1 111000010101=>1 111000101001=>1 111001000101=>1 111001001001=>1 111001010001=>1 111010001001=>1 111010100001=>1 111100000101=>1 111100001001=>1 111100010001=>1 111100100001=>1 111101000001=>1 10110111100000=>0 10111011010000=>0 10111011100000=>0 10111100110000=>0 10111101001000=>0 10111101010000=>0 10111101100000=>0 10111110000100=>0 10111110001000=>0 10111110010000=>0 10111110100000=>0 10111111000000=>0 11001111100000=>0 11011110000010=>0 11101101000010=>0 11101110000010=>0 11110011000010=>0 11110100100010=>0 11110101000010=>0 11110110000010=>0 11111000001100=>0 11111000010010=>0 11111000100010=>0 11111001000010=>0 11111010000010=>0 11111100000010=>0 1011110111000000=>0 1011111010100000=>0 1011111011000000=>0 1011111100010000=>0 1011111100100000=>0 1011111101000000=>0 1011111110000000=>0 1111011100000010=>0 1111101010000010=>0 1111101100000010=>0 1111110001000010=>0 1111110010000010=>0 1111110100000010=>0 1111111000000010=>0 111111110000000010=>0 101111111100000000=>0 111111101000000010=>0 101111111010000000=>0 111111100100000010=>0 111111011000000010=>0 101111111001000000=>0 101111110110000000=>0 11111111100000000010=>0 10111111111000000000=>0 11111111010000000010=>0 10111111110100000000=>0 1111111111000000000010=>0 1011111111110000000000=>0
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Description
The depth of the binary word interpreted as a path.
This is the maximal value of the number of zeros minus the number of ones occurring in a prefix of the binary word, see [1, sec.9.1.2].
The number of binary words of length $n$ with depth $k$ is $\binom{n}{\lfloor\frac{(n+1) - (-1)^{n-k}(k+1)}{2}\rfloor}$, see [2].
References
[1] Lothaire, M. Applied combinatorics on words MathSciNet:2165687
[2] Square table read by antidiagonals: a(n,k) = binomial(n+k, floor(k/2)). OEIS:A061554
Code
def statistic(w):
    h = m = 0
    for i, s in enumerate(w):
        if s == 1:
            h += 1
        else:
            h -= 1
        m = min(h, m)
    return -m

Created
Jul 03, 2017 at 08:07 by Martin Rubey
Updated
Dec 19, 2017 at 18:24 by Martin Rubey