***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000290 ----------------------------------------------------------------------------- Collection: Binary words ----------------------------------------------------------------------------- Description: The major index of a binary word. This is the sum of the positions of descents, i.e., a one followed by a zero. For words of length \$n\$ with \$a\$ zeros, the generating function for the major index is the \$q\$-binomial coefficient \$\binom{n}{a}_q\$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(x): return x.major_index() ----------------------------------------------------------------------------- Statistic values: 0 => 0 1 => 0 00 => 0 01 => 0 10 => 1 11 => 0 000 => 0 001 => 0 010 => 2 011 => 0 100 => 1 101 => 1 110 => 2 111 => 0 0000 => 0 0001 => 0 0010 => 3 0011 => 0 0100 => 2 0101 => 2 0110 => 3 0111 => 0 1000 => 1 1001 => 1 1010 => 4 1011 => 1 1100 => 2 1101 => 2 1110 => 3 1111 => 0 00000 => 0 00001 => 0 00010 => 4 00011 => 0 00100 => 3 00101 => 3 00110 => 4 00111 => 0 01000 => 2 01001 => 2 01010 => 6 01011 => 2 01100 => 3 01101 => 3 01110 => 4 01111 => 0 10000 => 1 10001 => 1 10010 => 5 10011 => 1 10100 => 4 10101 => 4 10110 => 5 10111 => 1 11000 => 2 11001 => 2 11010 => 6 11011 => 2 11100 => 3 11101 => 3 11110 => 4 11111 => 0 000000 => 0 000001 => 0 000010 => 5 000011 => 0 000100 => 4 000101 => 4 000110 => 5 000111 => 0 001000 => 3 001001 => 3 001010 => 8 001011 => 3 001100 => 4 001101 => 4 001110 => 5 001111 => 0 010000 => 2 010001 => 2 010010 => 7 010011 => 2 010100 => 6 010101 => 6 010110 => 7 010111 => 2 011000 => 3 011001 => 3 011010 => 8 011011 => 3 011100 => 4 011101 => 4 011110 => 5 011111 => 0 100000 => 1 100001 => 1 100010 => 6 100011 => 1 100100 => 5 100101 => 5 100110 => 6 100111 => 1 101000 => 4 101001 => 4 101010 => 9 101011 => 4 101100 => 5 101101 => 5 101110 => 6 101111 => 1 110000 => 2 110001 => 2 110010 => 7 110011 => 2 110100 => 6 110101 => 6 110110 => 7 110111 => 2 111000 => 3 111001 => 3 111010 => 8 111011 => 3 111100 => 4 111101 => 4 111110 => 5 111111 => 0 0000000 => 0 0000001 => 0 0000010 => 6 0000011 => 0 0000100 => 5 0000101 => 5 0000110 => 6 0000111 => 0 0001000 => 4 0001001 => 4 0001010 => 10 0001011 => 4 0001100 => 5 0001101 => 5 0001110 => 6 0001111 => 0 0010000 => 3 0010001 => 3 0010010 => 9 0010011 => 3 0010100 => 8 0010101 => 8 0010110 => 9 0010111 => 3 0011000 => 4 0011001 => 4 0011010 => 10 0011011 => 4 0011100 => 5 0011101 => 5 0011110 => 6 0011111 => 0 0100000 => 2 0100001 => 2 0100010 => 8 0100011 => 2 0100100 => 7 0100101 => 7 0100110 => 8 0100111 => 2 0101000 => 6 0101001 => 6 0101010 => 12 0101011 => 6 0101100 => 7 0101101 => 7 0101110 => 8 0101111 => 2 0110000 => 3 0110001 => 3 0110010 => 9 0110011 => 3 0110100 => 8 0110101 => 8 0110110 => 9 0110111 => 3 0111000 => 4 0111001 => 4 0111010 => 10 0111011 => 4 0111100 => 5 0111101 => 5 0111110 => 6 0111111 => 0 1000000 => 1 1000001 => 1 1000010 => 7 1000011 => 1 1000100 => 6 1000101 => 6 1000110 => 7 1000111 => 1 1001000 => 5 1001001 => 5 1001010 => 11 1001011 => 5 1001100 => 6 1001101 => 6 1001110 => 7 1001111 => 1 1010000 => 4 1010001 => 4 1010010 => 10 1010011 => 4 1010100 => 9 1010101 => 9 1010110 => 10 1010111 => 4 1011000 => 5 1011001 => 5 1011010 => 11 1011011 => 5 1011100 => 6 1011101 => 6 1011110 => 7 1011111 => 1 1100000 => 2 1100001 => 2 1100010 => 8 1100011 => 2 1100100 => 7 1100101 => 7 1100110 => 8 1100111 => 2 1101000 => 6 1101001 => 6 1101010 => 12 1101011 => 6 1101100 => 7 1101101 => 7 1101110 => 8 1101111 => 2 1110000 => 3 1110001 => 3 1110010 => 9 1110011 => 3 1110100 => 8 1110101 => 8 1110110 => 9 1110111 => 3 1111000 => 4 1111001 => 4 1111010 => 10 1111011 => 4 1111100 => 5 1111101 => 5 1111110 => 6 1111111 => 0 00000000 => 0 00000001 => 0 00000010 => 7 00000011 => 0 00000100 => 6 00000101 => 6 00000110 => 7 00000111 => 0 00001000 => 5 00001001 => 5 00001010 => 12 00001011 => 5 00001100 => 6 00001101 => 6 00001110 => 7 00001111 => 0 00010000 => 4 00010001 => 4 00010010 => 11 00010011 => 4 00010100 => 10 00010101 => 10 00010110 => 11 00010111 => 4 00011000 => 5 00011001 => 5 00011010 => 12 00011011 => 5 00011100 => 6 00011101 => 6 00011110 => 7 00011111 => 0 00100000 => 3 00100001 => 3 00100010 => 10 00100011 => 3 00100100 => 9 00100101 => 9 00100110 => 10 00100111 => 3 00101000 => 8 00101001 => 8 00101010 => 15 00101011 => 8 00101100 => 9 00101101 => 9 00101110 => 10 00101111 => 3 00110000 => 4 00110001 => 4 00110010 => 11 00110011 => 4 00110100 => 10 00110101 => 10 00110110 => 11 00110111 => 4 00111000 => 5 00111001 => 5 00111010 => 12 00111011 => 5 00111100 => 6 00111101 => 6 00111110 => 7 00111111 => 0 01000000 => 2 01000001 => 2 01000010 => 9 01000011 => 2 01000100 => 8 01000101 => 8 01000110 => 9 01000111 => 2 01001000 => 7 01001001 => 7 01001010 => 14 01001011 => 7 01001100 => 8 01001101 => 8 01001110 => 9 01001111 => 2 01010000 => 6 01010001 => 6 01010010 => 13 01010011 => 6 01010100 => 12 01010101 => 12 01010110 => 13 01010111 => 6 01011000 => 7 01011001 => 7 01011010 => 14 01011011 => 7 01011100 => 8 01011101 => 8 01011110 => 9 01011111 => 2 01100000 => 3 01100001 => 3 01100010 => 10 01100011 => 3 01100100 => 9 01100101 => 9 01100110 => 10 01100111 => 3 01101000 => 8 01101001 => 8 01101010 => 15 01101011 => 8 01101100 => 9 01101101 => 9 01101110 => 10 01101111 => 3 01110000 => 4 01110001 => 4 01110010 => 11 01110011 => 4 01110100 => 10 01110101 => 10 01110110 => 11 01110111 => 4 01111000 => 5 01111001 => 5 01111010 => 12 01111011 => 5 01111100 => 6 01111101 => 6 01111110 => 7 01111111 => 0 10000000 => 1 10000001 => 1 10000010 => 8 10000011 => 1 10000100 => 7 10000101 => 7 10000110 => 8 10000111 => 1 10001000 => 6 10001001 => 6 10001010 => 13 10001011 => 6 10001100 => 7 10001101 => 7 10001110 => 8 10001111 => 1 10010000 => 5 10010001 => 5 10010010 => 12 10010011 => 5 10010100 => 11 10010101 => 11 10010110 => 12 10010111 => 5 10011000 => 6 10011001 => 6 10011010 => 13 10011011 => 6 10011100 => 7 10011101 => 7 10011110 => 8 10011111 => 1 10100000 => 4 10100001 => 4 10100010 => 11 10100011 => 4 10100100 => 10 10100101 => 10 10100110 => 11 10100111 => 4 10101000 => 9 10101001 => 9 10101010 => 16 10101011 => 9 10101100 => 10 10101101 => 10 10101110 => 11 10101111 => 4 10110000 => 5 10110001 => 5 10110010 => 12 10110011 => 5 10110100 => 11 10110101 => 11 10110110 => 12 10110111 => 5 10111000 => 6 10111001 => 6 10111010 => 13 10111011 => 6 10111100 => 7 10111101 => 7 10111110 => 8 10111111 => 1 11000000 => 2 11000001 => 2 11000010 => 9 11000011 => 2 11000100 => 8 11000101 => 8 11000110 => 9 11000111 => 2 11001000 => 7 11001001 => 7 11001010 => 14 11001011 => 7 11001100 => 8 11001101 => 8 11001110 => 9 11001111 => 2 11010000 => 6 11010001 => 6 11010010 => 13 11010011 => 6 11010100 => 12 11010101 => 12 11010110 => 13 11010111 => 6 11011000 => 7 11011001 => 7 11011010 => 14 11011011 => 7 11011100 => 8 11011101 => 8 11011110 => 9 11011111 => 2 11100000 => 3 11100001 => 3 11100010 => 10 11100011 => 3 11100100 => 9 11100101 => 9 11100110 => 10 11100111 => 3 11101000 => 8 11101001 => 8 11101010 => 15 11101011 => 8 11101100 => 9 11101101 => 9 11101110 => 10 11101111 => 3 11110000 => 4 11110001 => 4 11110010 => 11 11110011 => 4 11110100 => 10 11110101 => 10 11110110 => 11 11110111 => 4 11111000 => 5 11111001 => 5 11111010 => 12 11111011 => 5 11111100 => 6 11111101 => 6 11111110 => 7 11111111 => 0 000000000 => 0 000000001 => 0 000000010 => 8 000000011 => 0 000000100 => 7 000000101 => 7 000000110 => 8 000000111 => 0 000001000 => 6 000001001 => 6 000001010 => 14 000001011 => 6 000001100 => 7 000001101 => 7 000001110 => 8 000001111 => 0 000010000 => 5 000010001 => 5 000010010 => 13 000010011 => 5 000010100 => 12 000010101 => 12 000010110 => 13 000010111 => 5 000011000 => 6 000011001 => 6 000011010 => 14 000011011 => 6 000011100 => 7 000011101 => 7 000011110 => 8 000011111 => 0 000100000 => 4 000100001 => 4 000100010 => 12 000100011 => 4 000100100 => 11 000100101 => 11 000100110 => 12 000100111 => 4 000101000 => 10 000101001 => 10 000101010 => 18 000101011 => 10 000101100 => 11 000101101 => 11 000101110 => 12 000101111 => 4 000110000 => 5 000110001 => 5 000110010 => 13 000110011 => 5 000110100 => 12 000110101 => 12 000110110 => 13 000110111 => 5 000111000 => 6 000111001 => 6 000111010 => 14 000111011 => 6 000111100 => 7 000111101 => 7 000111110 => 8 000111111 => 0 001000000 => 3 001000001 => 3 001000010 => 11 001000011 => 3 001000100 => 10 001000101 => 10 001000110 => 11 001000111 => 3 001001000 => 9 001001001 => 9 001001010 => 17 001001011 => 9 001001100 => 10 001001101 => 10 001001110 => 11 001001111 => 3 001010000 => 8 001010001 => 8 001010010 => 16 001010011 => 8 001010100 => 15 001010101 => 15 001010110 => 16 001010111 => 8 001011000 => 9 001011001 => 9 001011010 => 17 001011011 => 9 001011100 => 10 001011101 => 10 001011110 => 11 001011111 => 3 001100000 => 4 001100001 => 4 001100010 => 12 001100011 => 4 001100100 => 11 001100101 => 11 001100110 => 12 001100111 => 4 001101000 => 10 001101001 => 10 001101010 => 18 001101011 => 10 001101100 => 11 001101101 => 11 001101110 => 12 001101111 => 4 001110000 => 5 001110001 => 5 001110010 => 13 001110011 => 5 001110100 => 12 001110101 => 12 001110110 => 13 001110111 => 5 001111000 => 6 001111001 => 6 001111010 => 14 001111011 => 6 001111100 => 7 001111101 => 7 001111110 => 8 001111111 => 0 010000000 => 2 010000001 => 2 010000010 => 10 010000011 => 2 010000100 => 9 010000101 => 9 010000110 => 10 010000111 => 2 010001000 => 8 010001001 => 8 010001010 => 16 010001011 => 8 010001100 => 9 010001101 => 9 010001110 => 10 010001111 => 2 010010000 => 7 010010001 => 7 010010010 => 15 010010011 => 7 010010100 => 14 010010101 => 14 010010110 => 15 010010111 => 7 010011000 => 8 010011001 => 8 010011010 => 16 010011011 => 8 010011100 => 9 010011101 => 9 010011110 => 10 010011111 => 2 010100000 => 6 010100001 => 6 010100010 => 14 010100011 => 6 010100100 => 13 010100101 => 13 010100110 => 14 010100111 => 6 010101000 => 12 010101001 => 12 010101010 => 20 010101011 => 12 010101100 => 13 010101101 => 13 010101110 => 14 010101111 => 6 010110000 => 7 010110001 => 7 010110010 => 15 010110011 => 7 010110100 => 14 010110101 => 14 010110110 => 15 010110111 => 7 010111000 => 8 010111001 => 8 010111010 => 16 010111011 => 8 010111100 => 9 010111101 => 9 010111110 => 10 010111111 => 2 011000000 => 3 011000001 => 3 011000010 => 11 011000011 => 3 011000100 => 10 011000101 => 10 011000110 => 11 011000111 => 3 011001000 => 9 011001001 => 9 011001010 => 17 011001011 => 9 011001100 => 10 011001101 => 10 011001110 => 11 011001111 => 3 011010000 => 8 011010001 => 8 011010010 => 16 011010011 => 8 011010100 => 15 011010101 => 15 011010110 => 16 011010111 => 8 011011000 => 9 011011001 => 9 011011010 => 17 011011011 => 9 011011100 => 10 011011101 => 10 011011110 => 11 011011111 => 3 011100000 => 4 011100001 => 4 011100010 => 12 011100011 => 4 011100100 => 11 011100101 => 11 011100110 => 12 011100111 => 4 011101000 => 10 011101001 => 10 011101010 => 18 011101011 => 10 011101100 => 11 011101101 => 11 011101110 => 12 011101111 => 4 011110000 => 5 011110001 => 5 011110010 => 13 011110011 => 5 011110100 => 12 011110101 => 12 011110110 => 13 011110111 => 5 011111000 => 6 011111001 => 6 011111010 => 14 011111011 => 6 011111100 => 7 011111101 => 7 011111110 => 8 011111111 => 0 100000000 => 1 100000001 => 1 100000010 => 9 100000011 => 1 100000100 => 8 100000101 => 8 100000110 => 9 100000111 => 1 100001000 => 7 100001001 => 7 100001010 => 15 100001011 => 7 100001100 => 8 100001101 => 8 100001110 => 9 100001111 => 1 100010000 => 6 100010001 => 6 100010010 => 14 100010011 => 6 100010100 => 13 100010101 => 13 100010110 => 14 100010111 => 6 100011000 => 7 100011001 => 7 100011010 => 15 100011011 => 7 100011100 => 8 100011101 => 8 100011110 => 9 100011111 => 1 100100000 => 5 100100001 => 5 100100010 => 13 100100011 => 5 100100100 => 12 100100101 => 12 100100110 => 13 100100111 => 5 100101000 => 11 100101001 => 11 100101010 => 19 100101011 => 11 100101100 => 12 100101101 => 12 100101110 => 13 100101111 => 5 100110000 => 6 100110001 => 6 100110010 => 14 100110011 => 6 100110100 => 13 100110101 => 13 100110110 => 14 100110111 => 6 100111000 => 7 100111001 => 7 100111010 => 15 100111011 => 7 100111100 => 8 100111101 => 8 100111110 => 9 100111111 => 1 101000000 => 4 101000001 => 4 101000010 => 12 101000011 => 4 101000100 => 11 101000101 => 11 101000110 => 12 101000111 => 4 101001000 => 10 101001001 => 10 101001010 => 18 101001011 => 10 101001100 => 11 101001101 => 11 101001110 => 12 101001111 => 4 101010000 => 9 101010001 => 9 101010010 => 17 101010011 => 9 101010100 => 16 101010101 => 16 101010110 => 17 101010111 => 9 101011000 => 10 101011001 => 10 101011010 => 18 101011011 => 10 101011100 => 11 101011101 => 11 101011110 => 12 101011111 => 4 101100000 => 5 101100001 => 5 101100010 => 13 101100011 => 5 101100100 => 12 101100101 => 12 101100110 => 13 101100111 => 5 101101000 => 11 101101001 => 11 101101010 => 19 101101011 => 11 101101100 => 12 101101101 => 12 101101110 => 13 101101111 => 5 101110000 => 6 101110001 => 6 101110010 => 14 101110011 => 6 101110100 => 13 101110101 => 13 101110110 => 14 101110111 => 6 101111000 => 7 101111001 => 7 101111010 => 15 101111011 => 7 101111100 => 8 101111101 => 8 101111110 => 9 101111111 => 1 110000000 => 2 110000001 => 2 110000010 => 10 110000011 => 2 110000100 => 9 110000101 => 9 110000110 => 10 110000111 => 2 110001000 => 8 110001001 => 8 110001010 => 16 110001011 => 8 110001100 => 9 110001101 => 9 110001110 => 10 110001111 => 2 110010000 => 7 110010001 => 7 110010010 => 15 110010011 => 7 110010100 => 14 110010101 => 14 110010110 => 15 110010111 => 7 110011000 => 8 110011001 => 8 110011010 => 16 110011011 => 8 110011100 => 9 110011101 => 9 110011110 => 10 110011111 => 2 110100000 => 6 110100001 => 6 110100010 => 14 110100011 => 6 110100100 => 13 110100101 => 13 110100110 => 14 110100111 => 6 110101000 => 12 110101001 => 12 110101010 => 20 110101011 => 12 110101100 => 13 110101101 => 13 110101110 => 14 110101111 => 6 110110000 => 7 110110001 => 7 110110010 => 15 110110011 => 7 110110100 => 14 110110101 => 14 110110110 => 15 110110111 => 7 110111000 => 8 110111001 => 8 110111010 => 16 110111011 => 8 110111100 => 9 110111101 => 9 110111110 => 10 110111111 => 2 111000000 => 3 111000001 => 3 111000010 => 11 111000011 => 3 111000100 => 10 111000101 => 10 111000110 => 11 111000111 => 3 111001000 => 9 111001001 => 9 111001010 => 17 111001011 => 9 111001100 => 10 111001101 => 10 111001110 => 11 111001111 => 3 111010000 => 8 111010001 => 8 111010010 => 16 111010011 => 8 111010100 => 15 111010101 => 15 111010110 => 16 111010111 => 8 111011000 => 9 111011001 => 9 111011010 => 17 111011011 => 9 111011100 => 10 111011101 => 10 111011110 => 11 111011111 => 3 111100000 => 4 111100001 => 4 111100010 => 12 111100011 => 4 111100100 => 11 111100101 => 11 111100110 => 12 111100111 => 4 111101000 => 10 111101001 => 10 111101010 => 18 111101011 => 10 111101100 => 11 111101101 => 11 111101110 => 12 111101111 => 4 111110000 => 5 111110001 => 5 111110010 => 13 111110011 => 5 111110100 => 12 111110101 => 12 111110110 => 13 111110111 => 5 111111000 => 6 111111001 => 6 111111010 => 14 111111011 => 6 111111100 => 7 111111101 => 7 111111110 => 8 111111111 => 0 1010101010 => 25 1010101100 => 17 1010110010 => 19 1010110100 => 18 1010111000 => 11 1011001010 => 21 1011001100 => 13 1011010010 => 20 1011010100 => 19 1011011000 => 12 1011100010 => 15 1011100100 => 14 1011101000 => 13 1011110000 => 7 1100101010 => 23 1100101100 => 15 1100110010 => 17 1100110100 => 16 1100111000 => 9 1101001010 => 22 1101001100 => 14 1101010010 => 21 1101010100 => 20 1101011000 => 13 1101100010 => 16 1101100100 => 15 1101101000 => 14 1101110000 => 8 1110001010 => 19 1110001100 => 11 1110010010 => 18 1110010100 => 17 1110011000 => 10 1110100010 => 17 1110100100 => 16 1110101000 => 15 1110110000 => 9 1111000010 => 13 1111000100 => 12 1111001000 => 11 1111010000 => 10 1111100000 => 5 1111111110 => 9 1111111101 => 8 1111000001 => 4 1110111110 => 12 1110100001 => 8 1110011110 => 12 1110010001 => 9 1110001001 => 10 1110000101 => 11 1101111110 => 11 1101100001 => 7 1101010001 => 12 1101001110 => 15 1101001001 => 13 1101000101 => 14 1100110001 => 8 1100101001 => 14 1100100110 => 16 1100100101 => 15 1100011001 => 9 1100010101 => 16 1100010010 => 17 1100001000 => 9 1011111110 => 10 1011111101 => 9 1011100001 => 6 1011010001 => 11 1011001001 => 12 1011000101 => 13 1010111110 => 13 1010110001 => 10 1010101001 => 16 1010100110 => 18 1010100101 => 17 1010011010 => 20 1010011001 => 11 1010010110 => 19 1010010101 => 18 1010001110 => 13 1001111110 => 10 1001111000 => 8 1001110100 => 15 1001110001 => 7 1001101100 => 14 1001101010 => 22 1001101001 => 13 1001100110 => 15 1001100101 => 14 1001011110 => 14 1001011010 => 21 1001011001 => 12 1001010110 => 20 1001010101 => 19 1001001110 => 14 1000111110 => 10 1000111100 => 9 1000111010 => 17 1000110110 => 16 1000101110 => 15 1000011110 => 10 1000010110 => 16 1000001110 => 10 1000001010 => 17 1000000110 => 10 1000000100 => 9 1000000010 => 10 1000000000 => 1 0111111111 => 0 0111111101 => 8 0111111001 => 7 0111110001 => 6 0111100001 => 5 0111000001 => 4 0110000001 => 3 0100000001 => 2 0000000001 => 0 0111111011 => 7 0111110101 => 14 0111101001 => 12 0111010001 => 10 0110100001 => 8 0101000001 => 6 0010000001 => 3 0101010101 => 20 0101010011 => 12 0101001101 => 14 0101001011 => 13 0101000111 => 6 0100110101 => 16 0100110011 => 8 0100101101 => 15 0100101011 => 14 0100100111 => 7 0100011101 => 10 0100011011 => 9 0100010111 => 8 0100001111 => 2 0011010101 => 18 0011010011 => 10 0011001101 => 12 0011001011 => 11 0011000111 => 4 0010110101 => 17 0010110011 => 9 0010101101 => 16 0010101011 => 15 0010100111 => 8 0010011101 => 11 0010011011 => 10 0010010111 => 9 0010001111 => 3 0001110101 => 14 0001110011 => 6 0001101101 => 13 0001101011 => 12 0001100111 => 5 0001011101 => 12 0001011011 => 11 0001010111 => 10 0001001111 => 4 0000111101 => 8 0000111011 => 7 0000110111 => 6 0000101111 => 5 0000011111 => 0 0000000000 => 0 0000000110 => 9 0000011000 => 7 0000011110 => 9 0000010010 => 15 0001100000 => 5 0001100110 => 14 0001111000 => 7 0001111110 => 9 0001110010 => 15 0001001000 => 11 0001001110 => 13 0001000010 => 13 0001011010 => 20 0100000010 => 11 0010101010 => 24 0010101000 => 15 0010101100 => 16 0010100100 => 16 0010010100 => 17 0001010100 => 18 0010101110 => 17 0010100000 => 8 0010111100 => 11 0010000100 => 11 0011110100 => 14 0000010100 => 14 0111010100 => 18 0000000010 => 9 0000001110 => 9 0000111110 => 9 0000000100 => 8 0000001010 => 16 0000010110 => 15 0000101110 => 14 0001011110 => 13 0100000000 => 2 0100000011 => 2 0100000111 => 2 0100011111 => 2 0100111111 => 2 0101111111 => 2 0100000101 => 10 0100001011 => 9 0100101111 => 7 0101011111 => 6 0110111111 => 3 0101010110 => 21 0101011001 => 13 0101011010 => 22 0101011100 => 14 0101100101 => 15 0101100110 => 16 0101101001 => 14 0101101010 => 23 0101101100 => 15 0101110001 => 8 0101110010 => 17 0101110100 => 16 0101111000 => 9 0110010101 => 17 0110010110 => 18 0110011001 => 10 0110011010 => 19 0110011100 => 11 0110100101 => 16 0110100110 => 17 0110101001 => 15 0110101010 => 24 0110101100 => 16 0110110001 => 9 0110110010 => 18 0110110100 => 17 0110111000 => 10 0111000101 => 12 0111000110 => 13 0111001001 => 11 0111001010 => 20 0111001100 => 12 0111010010 => 19 0111011000 => 11 0111100010 => 14 0111100100 => 13 0111101000 => 12 0111110000 => 6 0100000100 => 10 0011100110 => 14 0011101010 => 21 0011101100 => 13 0001101110 => 14 0010110110 => 18 0011110010 => 15 0001110110 => 15 0100111010 => 18 0010111010 => 19 0011111000 => 7 0001111010 => 16 0100111100 => 10 0001111100 => 8 0000000101 => 8 0000001101 => 8 0000011101 => 8 0001111101 => 8 0011111101 => 8 0000001001 => 7 0000010101 => 14 0000101101 => 13 0010111101 => 11 0101111101 => 10 0010110001 => 9 0001100001 => 5 0001000001 => 4 0000111111 => 0 0001110100 => 14 0001101100 => 13 0010011100 => 11 0001011100 => 12 0000111100 => 8 0001101010 => 21 0010011010 => 19 0000111010 => 16 0010100110 => 17 0010010110 => 18 0001010110 => 19 0000110110 => 15 0010001110 => 12 0001101001 => 12 0000110001 => 6 0000010001 => 6 0000001100 => 8 0000011001 => 7 0000110011 => 6 0000110100 => 14 0000000011 => 0 0000011011 => 7 0001101111 => 5 0000110101 => 14 0010000010 => 12 0001000011 => 4 0010011110 => 12 0001010000 => 10 0001000100 => 12 0001010101 => 18 0001001011 => 11 0001100011 => 5 0001110111 => 6 0010000000 => 3 0000000111 => 0 0000001111 => 0 0001111111 => 0 0000001011 => 7 0000010111 => 6 0001011111 => 4 0001111001 => 7 0000011010 => 16 0000101010 => 21 0000100101 => 13 0010010001 => 9 0010000101 => 11 0010010101 => 17 0010010011 => 9 0000101011 => 12 0001000111 => 4 0000100111 => 5 0010010010 => 18 0001001010 => 20 0001001001 => 11 0001000101 => 12 0000100011 => 5 0000100100 => 13 0000100010 => 14 0010110000 => 9 0000011100 => 8 0000001000 => 7 0000101100 => 13 0010101111 => 8 0000101000 => 12 0010001000 => 10 0001001100 => 12 0001000110 => 13 0001100100 => 13 0001100010 => 14 0000100110 => 14 0000110010 => 15 0010010000 => 9 0001010010 => 19 0001000000 => 4 0001011001 => 11 0001100101 => 13 0001110001 => 6 0010011001 => 10 0010100101 => 16 0010101001 => 15 0010011111 => 3 0000111001 => 7 0010001101 => 11 0001001101 => 12 0001010001 => 10 0001010011 => 10 0001111011 => 7 0010011000 => 10 0001011000 => 11 0000100000 => 5 0010001011 => 10 0010000111 => 3 0000010011 => 6 0010001100 => 11 0010000110 => 12 0000110000 => 6 0000100001 => 5 0010100011 => 8 0010100001 => 8 0000111000 => 7 0001101000 => 12 0000010000 => 6 0000101001 => 12 0010100010 => 17 0010001001 => 10 0010000011 => 3 0010001010 => 19 0001110000 => 6 10000000000 => 1 10000000010 => 11 10000000110 => 11 10000001110 => 11 10000011110 => 11 10000111110 => 11 10001111110 => 11 10011111110 => 11 10111111110 => 11 11111111110 => 10 10000000100 => 10 10000001010 => 19 10000010110 => 18 10000101110 => 17 10001011110 => 16 10010111110 => 15 10101111110 => 14 11011111110 => 12 10000010000 => 8 10000100010 => 17 10001000010 => 16 10000100100 => 16 10001001010 => 24 10001000100 => 15 10000101000 => 15 10010001010 => 23 10001010010 => 23 10010000100 => 14 10001001000 => 14 10010010010 => 22 10001010100 => 22 10010101010 => 29 10010001000 => 13 10100010010 => 21 10010100010 => 21 10010010100 => 21 10100101010 => 28 01111111111 => 0 01111111101 => 9 01111111001 => 8 01111110001 => 7 01111100001 => 6 01111000001 => 5 01110000001 => 4 01100000001 => 3 01000000001 => 2 00000000001 => 0 00000000010 => 10 10101010101 => 25 10101010010 => 26 10101001001 => 17 10101001010 => 27 10101000100 => 18 10100100101 => 19 10100100010 => 20 10100101001 => 18 10100100100 => 19 10100010001 => 11 10100010100 => 20 10100001000 => 12 10010010101 => 21 10010001001 => 13 10010100101 => 20 10010101001 => 19 10010100100 => 20 10010010001 => 12 10001000101 => 15 10001001001 => 14 10001010001 => 13 10000100001 => 7 01001010101 => 23 01001010010 => 24 01001001001 => 15 01001001010 => 25 01001000100 => 16 01000100101 => 17 01000100010 => 18 01000101001 => 16 01000101010 => 26 01000100100 => 17 01000010001 => 9 01000010010 => 19 01000010100 => 18 01000001000 => 10 01010010101 => 22 01010010010 => 23 01010001001 => 14 01010001010 => 24 01010000100 => 15 01010100101 => 21 01010100010 => 22 01010101001 => 20 01010101010 => 30 01010100100 => 21 01010010001 => 13 01010010100 => 22 01010001000 => 14 01001000101 => 16 01001000010 => 17 01001010001 => 14 01001010100 => 23 01001001000 => 15 01000100001 => 8 01000101000 => 16 01000010000 => 9 00100010101 => 19 00100010010 => 20 00100001001 => 11 00100001010 => 21 00100000100 => 12 00100100101 => 18 00100100010 => 19 00100101001 => 17 00100101010 => 27 00100100100 => 18 00100010001 => 10 00100010100 => 19 00100001000 => 11 00101000101 => 17 00101000010 => 18 00101001001 => 16 00101001010 => 26 00101000100 => 17 00101010001 => 15 00101010010 => 25 00101010100 => 24 00101001000 => 16 00100100001 => 9 00100101000 => 17 00100010000 => 10 00010000101 => 13 00010000010 => 14 00010001001 => 12 00010001010 => 22 00010000100 => 13 00010010001 => 11 00010010010 => 21 00010010100 => 20 00010001000 => 12 00010100001 => 10 00010100010 => 20 00010100100 => 19 00010101000 => 18 00010010000 => 11 00001000001 => 5 00001000010 => 15 00001000100 => 14 00001001000 => 13 00001010000 => 12 00000100000 => 6 01000000000 => 2 01000000011 => 2 01000000111 => 2 01000001111 => 2 01000011111 => 2 01000111111 => 2 01001111111 => 2 01011111111 => 2 00000000101 => 9 00000001101 => 9 00000011101 => 9 00000111101 => 9 00001111101 => 9 00011111101 => 9 00111111101 => 9 11111111101 => 9 101010101010 => 36 101010101100 => 26 101010110010 => 28 101010110100 => 27 101010111000 => 18 101011001010 => 30 101011001100 => 20 101011010010 => 29 101011010100 => 28 101011011000 => 19 101011100010 => 22 101011100100 => 21 101011101000 => 20 101011110000 => 12 101100101010 => 32 101100101100 => 22 101100110010 => 24 101100110100 => 23 101100111000 => 14 101101001010 => 31 101101001100 => 21 101101010010 => 30 101101010100 => 29 101101011000 => 20 101101100010 => 23 101101100100 => 22 101101101000 => 21 101101110000 => 13 101110001010 => 26 101110001100 => 16 101110010010 => 25 101110010100 => 24 101110011000 => 15 101110100010 => 24 101110100100 => 23 101110101000 => 22 101110110000 => 14 101111000010 => 18 101111000100 => 17 101111001000 => 16 101111010000 => 15 101111100000 => 8 110010101010 => 34 110010101100 => 24 110010110010 => 26 110010110100 => 25 110010111000 => 16 110011001010 => 28 110011001100 => 18 110011010010 => 27 110011010100 => 26 110011011000 => 17 110011100010 => 20 110011100100 => 19 110011101000 => 18 110011110000 => 10 110100101010 => 33 110100101100 => 23 110100110010 => 25 110100110100 => 24 110100111000 => 15 110101001010 => 32 110101001100 => 22 110101010010 => 31 110101010100 => 30 110101011000 => 21 110101100010 => 24 110101100100 => 23 110101101000 => 22 110101110000 => 14 110110001010 => 27 110110001100 => 17 110110010010 => 26 110110010100 => 25 110110011000 => 16 110110100010 => 25 110110100100 => 24 110110101000 => 23 110110110000 => 15 110111000010 => 19 110111000100 => 18 110111001000 => 17 110111010000 => 16 110111100000 => 9 111000101010 => 30 111000101100 => 20 111000110010 => 22 111000110100 => 21 111000111000 => 12 111001001010 => 29 111001001100 => 19 111001010010 => 28 111001010100 => 27 111001011000 => 18 111001100010 => 21 111001100100 => 20 111001101000 => 19 111001110000 => 11 111010001010 => 28 111010001100 => 18 111010010010 => 27 111010010100 => 26 111010011000 => 17 111010100010 => 26 111010100100 => 25 111010101000 => 24 111010110000 => 16 111011000010 => 20 111011000100 => 19 111011001000 => 18 111011010000 => 17 111011100000 => 10 111100001010 => 24 111100001100 => 14 111100010010 => 23 111100010100 => 22 111100011000 => 13 111100100010 => 22 111100100100 => 21 111100101000 => 20 111100110000 => 12 111101000010 => 21 111101000100 => 20 111101001000 => 19 111101010000 => 18 111101100000 => 11 111110000010 => 16 111110000100 => 15 111110001000 => 14 111110010000 => 13 111110100000 => 12 111111000000 => 6 100001111100 => 11 010101010101 => 30 010101010011 => 20 010101001101 => 22 010101001011 => 21 010101000111 => 12 010100110101 => 24 010100110011 => 14 010100101101 => 23 010100101011 => 22 010100100111 => 13 010100011101 => 16 010100011011 => 15 010100010111 => 14 010100001111 => 6 010011010101 => 26 010011010011 => 16 010011001101 => 18 010011001011 => 17 010011000111 => 8 010010110101 => 25 010010110011 => 15 010010101101 => 24 010010101011 => 23 010010100111 => 14 010010011101 => 17 010010011011 => 16 010010010111 => 15 010010001111 => 7 010001110101 => 20 010001110011 => 10 010001101101 => 19 010001101011 => 18 010001100111 => 9 010001011101 => 18 010001011011 => 17 010001010111 => 16 010001001111 => 8 010000111101 => 12 010000111011 => 11 010000110111 => 10 010000101111 => 9 010000011111 => 2 001101010101 => 28 001101010011 => 18 001101001101 => 20 001101001011 => 19 001101000111 => 10 001100110101 => 22 001100110011 => 12 001100101101 => 21 001100101011 => 20 001100100111 => 11 001100011101 => 14 001100011011 => 13 001100010111 => 12 001100001111 => 4 001011010101 => 27 001011010011 => 17 001011001101 => 19 001011001011 => 18 001011000111 => 9 001010110101 => 26 001010110011 => 16 001010101101 => 25 001010101011 => 24 001010100111 => 15 001010011101 => 18 001010011011 => 17 001010010111 => 16 001010001111 => 8 001001110101 => 21 001001110011 => 11 001001101101 => 20 001001101011 => 19 001001100111 => 10 001001011101 => 19 001001011011 => 18 001001010111 => 17 001001001111 => 9 001000111101 => 13 001000111011 => 12 001000110111 => 11 001000101111 => 10 001000011111 => 3 000111010101 => 24 000111010011 => 14 000111001101 => 16 000111001011 => 15 000111000111 => 6 000110110101 => 23 000110110011 => 13 000110101101 => 22 000110101011 => 21 000110100111 => 12 000110011101 => 15 000110011011 => 14 000110010111 => 13 000110001111 => 5 000101110101 => 22 000101110011 => 12 000101101101 => 21 000101101011 => 20 000101100111 => 11 000101011101 => 20 000101011011 => 19 000101010111 => 18 000101001111 => 10 000100111101 => 14 000100111011 => 13 000100110111 => 12 000100101111 => 11 000100011111 => 4 000011110101 => 18 000011110011 => 8 000011101101 => 17 000011101011 => 16 000011100111 => 7 000011011101 => 16 000011011011 => 15 000011010111 => 14 000011001111 => 6 000010111101 => 15 000010111011 => 14 000010110111 => 13 000010101111 => 12 000010011111 => 5 000001111101 => 10 000001111011 => 9 000001110111 => 8 000001101111 => 7 000001011111 => 6 000000111111 => 0 111110000001 => 5 111001100001 => 10 111000011001 => 12 111000110001 => 11 111000100101 => 20 111011000001 => 9 111010010001 => 16 111010000101 => 18 100111100001 => 8 100110011001 => 15 100110110001 => 14 100110100101 => 23 101101100001 => 12 101100011001 => 14 101100110001 => 13 101100100101 => 22 101111000001 => 7 101110010001 => 14 101110000101 => 16 101001011001 => 19 101001110001 => 12 101001100101 => 21 101011010001 => 18 101011000101 => 20 101010010101 => 27 000001111110 => 11 000111100110 => 18 000111111000 => 9 000111110010 => 19 000111001110 => 17 000111011010 => 26 000101101110 => 22 000101111010 => 24 011001100110 => 21 011001111000 => 12 011001110010 => 22 011001011010 => 29 011110000110 => 16 011110011000 => 14 011110010010 => 24 011111100000 => 7 011111001000 => 15 011111000010 => 17 011100100110 => 22 011100111000 => 13 011100110010 => 23 011100011010 => 24 011101101000 => 20 011101100010 => 22 011101001010 => 30 010011111000 => 11 010011110010 => 21 010011011010 => 28 010001111010 => 22 010110100110 => 25 010110111000 => 16 010110110010 => 26 010110011010 => 27 010111101000 => 18 010111100010 => 20 010111001010 => 28 010101101010 => 33 010101010110 => 31 010101011001 => 21 010101011010 => 32 010101011100 => 22 010101100101 => 23 010101100110 => 24 010101101001 => 22 010101101100 => 23 010101110001 => 14 010101110010 => 25 010101110100 => 24 010101111000 => 15 010110010101 => 25 010110010110 => 26 010110011001 => 16 010110011100 => 17 010110100101 => 24 010110101001 => 23 010110101010 => 34 010110101100 => 24 010110110001 => 15 010110110100 => 25 010111000101 => 18 010111000110 => 19 010111001001 => 17 010111001100 => 18 010111010001 => 16 010111010010 => 27 010111010100 => 26 010111011000 => 17 010111100001 => 9 010111100100 => 19 010111110000 => 10 011001010101 => 27 011001010110 => 28 011001011001 => 18 011001011100 => 19 011001100101 => 20 011001101001 => 19 011001101010 => 30 011001101100 => 20 011001110001 => 11 011001110100 => 21 011010010101 => 26 011010010110 => 27 011010011001 => 17 011010011010 => 28 011010011100 => 18 011010100101 => 25 011010100110 => 26 011010101001 => 24 011010101010 => 35 011010101100 => 25 011010110001 => 16 011010110010 => 27 011010110100 => 26 011010111000 => 17 011011000101 => 19 011011000110 => 20 011011001001 => 18 011011001010 => 29 011011001100 => 19 011011010001 => 17 011011010010 => 28 011011010100 => 27 011011011000 => 18 011011100001 => 10 011011100010 => 21 011011100100 => 20 011011101000 => 19 011011110000 => 11 011100010101 => 22 011100010110 => 23 011100011001 => 13 011100011100 => 14 011100100101 => 21 011100101001 => 20 011100101010 => 31 011100101100 => 21 011100110001 => 12 011100110100 => 22 011101000101 => 20 011101000110 => 21 011101001001 => 19 011101001100 => 20 011101010001 => 18 011101010010 => 29 011101010100 => 28 011101011000 => 19 011101100001 => 11 011101100100 => 21 011101110000 => 12 011110000101 => 15 011110001001 => 14 011110001010 => 25 011110001100 => 15 011110010001 => 13 011110010100 => 23 011110100001 => 12 011110100010 => 23 011110100100 => 22 011110101000 => 21 011110110000 => 13 011111000001 => 6 011111000100 => 16 011111010000 => 14 001111000110 => 17 001111001010 => 26 100111001100 => 17 001111001100 => 16 001011010110 => 28 001111010010 => 25 100111010100 => 25 001111010100 => 24 000111010110 => 25 001011011010 => 29 100111011000 => 16 001111011000 => 15 100011011100 => 17 010011011100 => 18 001011011100 => 19 000111011100 => 16 000011011110 => 17 001101100110 => 22 001101101010 => 31 100101101100 => 22 001101101100 => 21 001011100110 => 21 001111100010 => 18 100111100100 => 18 001111100100 => 17 010011101010 => 29 001011101010 => 30 100111101000 => 17 001111101000 => 16 000111101010 => 27 100011101100 => 18 010011101100 => 19 001011101100 => 20 000111101100 => 17 000011101110 => 18 101001110100 => 22 001001110110 => 22 001101110010 => 23 100101110100 => 23 001101110100 => 22 000101110110 => 23 001011110010 => 22 100111110000 => 9 001111110000 => 8 100011110100 => 19 010011110100 => 20 001011110100 => 21 000111110100 => 18 000011110110 => 19 110001111000 => 11 101001111000 => 13 001001111010 => 23 100101111000 => 14 001101111000 => 13 100011111000 => 10 001011111000 => 12 000011111010 => 20 010001111100 => 12 001001111100 => 13 000101111100 => 14 000011111100 => 10 100101010101 => 29 100101011001 => 20 100101100101 => 22 100101101001 => 21 100101110001 => 13 100110010101 => 24 100110101001 => 22 100111000101 => 17 100111001001 => 16 100111010001 => 15 101001010101 => 28 101001101001 => 20 101010011001 => 18 101010100101 => 26 101010101001 => 25 101010110001 => 17 101011001001 => 19 101011100001 => 11 101100010101 => 23 101100101001 => 21 101101000101 => 21 101101001001 => 20 101101010001 => 19 101110001001 => 15 101110100001 => 13 110001010101 => 26 110001011001 => 17 110001100101 => 19 110001101001 => 18 110001110001 => 10 110010010101 => 25 110010011001 => 16 110010100101 => 24 110010101001 => 23 110010110001 => 15 110011000101 => 18 110011001001 => 17 110011010001 => 16 110011100001 => 9 110100010101 => 24 110100011001 => 15 110100100101 => 23 110100101001 => 22 110100110001 => 14 110101000101 => 22 110101001001 => 21 110101010001 => 20 110101100001 => 13 110110000101 => 17 110110001001 => 16 110110010001 => 15 110110100001 => 14 110111000001 => 8 111000010101 => 21 111000101001 => 19 111001000101 => 19 111001001001 => 18 111001010001 => 17 111010001001 => 17 111010100001 => 15 111100000101 => 14 111100001001 => 13 111100010001 => 12 111100100001 => 11 111101000001 => 10 10110111100000 => 14 10111011010000 => 24 10111011100000 => 15 10111100110000 => 17 10111101001000 => 26 10111101010000 => 25 10111101100000 => 16 10111110000100 => 20 10111110001000 => 19 10111110010000 => 18 10111110100000 => 17 10111111000000 => 9 11001111100000 => 11 11011110000010 => 22 11101101000010 => 30 11101110000010 => 23 11110011000010 => 25 11110100100010 => 32 11110101000010 => 31 11110110000010 => 24 11111000001100 => 17 11111000010010 => 28 11111000100010 => 27 11111001000010 => 26 11111010000010 => 25 11111100000010 => 19 1011110111000000 => 17 1011111010100000 => 28 1011111011000000 => 18 1011111100010000 => 21 1011111100100000 => 20 1011111101000000 => 19 1011111110000000 => 10 1111011100000010 => 27 1111101010000010 => 36 1111101100000010 => 28 1111110001000010 => 31 1111110010000010 => 30 1111110100000010 => 29 1111111000000010 => 22 111111110000000010 => 25 101111111100000000 => 11 111111101000000010 => 33 101111111010000000 => 21 111111100100000010 => 34 111111011000000010 => 32 101111111001000000 => 22 101111110110000000 => 20 11111111100000000010 => 28 10111111111000000000 => 12 11111111010000000010 => 37 10111111110100000000 => 23 1111111111000000000010 => 31 1011111111110000000000 => 13 ----------------------------------------------------------------------------- Created: Nov 19, 2015 at 11:57 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 17, 2019 at 18:31 by Martin Rubey