************************************************************************ * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2013 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. * ************************************************************************ ------------------------------------------------------------------------ Map identifier: Mp00224 ------------------------------------------------------------------------ Map name: runsort ------------------------------------------------------------------------ Domain: Binary words ------------------------------------------------------------------------ Codomain: Binary words ------------------------------------------------------------------------ Description: The word obtained by sorting the weakly increasing runs lexicographically. ------------------------------------------------------------------------ References: [1] Alexandersson, P., Nabawanda, O. Peaks are preserved under run-sorting [[arXiv:2104.04220]] ------------------------------------------------------------------------ Code: def mapping(w): runs = [] last = None run = [] for l in w: if last is not None and last > l: runs.append(run) run = [] run.append(l) last = l runs.append(run) runs.sort() return Words([0,1], len(w))([l for run in runs for l in run]) ------------------------------------------------------------------------ Map images: 0 => 0 1 => 1 00 => 00 01 => 01 10 => 01 11 => 11 000 => 000 001 => 001 010 => 001 011 => 011 100 => 001 101 => 011 110 => 011 111 => 111 0000 => 0000 0001 => 0001 0010 => 0001 0011 => 0011 0100 => 0001 0101 => 0101 0110 => 0011 0111 => 0111 1000 => 0001 1001 => 0011 1010 => 0011 1011 => 0111 1100 => 0011 1101 => 0111 1110 => 0111 1111 => 1111 00000 => 00000 00001 => 00001 00010 => 00001 00011 => 00011 00100 => 00001 00101 => 00101 00110 => 00011 00111 => 00111 01000 => 00001 01001 => 00101 01010 => 00101 01011 => 01011 01100 => 00011 01101 => 01011 01110 => 00111 01111 => 01111 10000 => 00001 10001 => 00011 10010 => 00011 10011 => 00111 10100 => 00011 10101 => 01011 10110 => 00111 10111 => 01111 11000 => 00011 11001 => 00111 11010 => 00111 11011 => 01111 11100 => 00111 11101 => 01111 11110 => 01111 11111 => 11111 000000 => 000000 000001 => 000001 000010 => 000001 000011 => 000011 000100 => 000001 000101 => 000101 000110 => 000011 000111 => 000111 001000 => 000001 001001 => 001001 001010 => 000101 001011 => 001011 001100 => 000011 001101 => 001101 001110 => 000111 001111 => 001111 010000 => 000001 010001 => 000101 010010 => 000101 010011 => 001101 010100 => 000101 010101 => 010101 010110 => 001011 010111 => 010111 011000 => 000011 011001 => 001011 011010 => 001011 011011 => 011011 011100 => 000111 011101 => 010111 011110 => 001111 011111 => 011111 100000 => 000001 100001 => 000011 100010 => 000011 100011 => 000111 100100 => 000011 100101 => 001011 100110 => 000111 100111 => 001111 101000 => 000011 101001 => 001011 101010 => 001011 101011 => 010111 101100 => 000111 101101 => 010111 101110 => 001111 101111 => 011111 110000 => 000011 110001 => 000111 110010 => 000111 110011 => 001111 110100 => 000111 110101 => 010111 110110 => 001111 110111 => 011111 111000 => 000111 111001 => 001111 111010 => 001111 111011 => 011111 111100 => 001111 111101 => 011111 111110 => 011111 111111 => 111111 0000000 => 0000000 0000001 => 0000001 0000010 => 0000001 0000011 => 0000011 0000100 => 0000001 0000101 => 0000101 0000110 => 0000011 0000111 => 0000111 0001000 => 0000001 0001001 => 0001001 0001010 => 0000101 0001011 => 0001011 0001100 => 0000011 0001101 => 0001101 0001110 => 0000111 0001111 => 0001111 0010000 => 0000001 0010001 => 0001001 0010010 => 0001001 0010011 => 0010011 0010100 => 0000101 0010101 => 0010101 0010110 => 0001011 0010111 => 0010111 0011000 => 0000011 0011001 => 0010011 0011010 => 0001101 0011011 => 0011011 0011100 => 0000111 0011101 => 0011101 0011110 => 0001111 0011111 => 0011111 0100000 => 0000001 0100001 => 0000101 0100010 => 0000101 0100011 => 0001101 0100100 => 0000101 0100101 => 0010101 0100110 => 0001101 0100111 => 0011101 0101000 => 0000101 0101001 => 0010101 0101010 => 0010101 0101011 => 0101011 0101100 => 0001011 0101101 => 0101011 0101110 => 0010111 0101111 => 0101111 0110000 => 0000011 0110001 => 0001011 0110010 => 0001011 0110011 => 0011011 0110100 => 0001011 0110101 => 0101011 0110110 => 0011011 0110111 => 0110111 0111000 => 0000111 0111001 => 0010111 0111010 => 0010111 0111011 => 0110111 0111100 => 0001111 0111101 => 0101111 0111110 => 0011111 0111111 => 0111111 1000000 => 0000001 1000001 => 0000011 1000010 => 0000011 1000011 => 0000111 1000100 => 0000011 1000101 => 0001011 1000110 => 0000111 1000111 => 0001111 1001000 => 0000011 1001001 => 0010011 1001010 => 0001011 1001011 => 0010111 1001100 => 0000111 1001101 => 0011011 1001110 => 0001111 1001111 => 0011111 1010000 => 0000011 1010001 => 0001011 1010010 => 0001011 1010011 => 0011011 1010100 => 0001011 1010101 => 0101011 1010110 => 0010111 1010111 => 0101111 1011000 => 0000111 1011001 => 0010111 1011010 => 0010111 1011011 => 0110111 1011100 => 0001111 1011101 => 0101111 1011110 => 0011111 1011111 => 0111111 1100000 => 0000011 1100001 => 0000111 1100010 => 0000111 1100011 => 0001111 1100100 => 0000111 1100101 => 0010111 1100110 => 0001111 1100111 => 0011111 1101000 => 0000111 1101001 => 0010111 1101010 => 0010111 1101011 => 0101111 1101100 => 0001111 1101101 => 0101111 1101110 => 0011111 1101111 => 0111111 1110000 => 0000111 1110001 => 0001111 1110010 => 0001111 1110011 => 0011111 1110100 => 0001111 1110101 => 0101111 1110110 => 0011111 1110111 => 0111111 1111000 => 0001111 1111001 => 0011111 1111010 => 0011111 1111011 => 0111111 1111100 => 0011111 1111101 => 0111111 1111110 => 0111111 1111111 => 1111111 00000000 => 00000000 00000001 => 00000001 00000010 => 00000001 00000011 => 00000011 00000100 => 00000001 00000101 => 00000101 00000110 => 00000011 00000111 => 00000111 00001000 => 00000001 00001001 => 00001001 00001010 => 00000101 00001011 => 00001011 00001100 => 00000011 00001101 => 00001101 00001110 => 00000111 00001111 => 00001111 00010000 => 00000001 00010001 => 00010001 00010010 => 00001001 00010011 => 00010011 00010100 => 00000101 00010101 => 00010101 00010110 => 00001011 00010111 => 00010111 00011000 => 00000011 00011001 => 00011001 00011010 => 00001101 00011011 => 00011011 00011100 => 00000111 00011101 => 00011101 00011110 => 00001111 00011111 => 00011111 00100000 => 00000001 00100001 => 00001001 00100010 => 00001001 00100011 => 00011001 00100100 => 00001001 00100101 => 00100101 00100110 => 00010011 00100111 => 00100111 00101000 => 00000101 00101001 => 00100101 00101010 => 00010101 00101011 => 00101011 00101100 => 00001011 00101101 => 00101011 00101110 => 00010111 00101111 => 00101111 00110000 => 00000011 00110001 => 00010011 00110010 => 00010011 00110011 => 00110011 00110100 => 00001101 00110101 => 00110101 00110110 => 00011011 00110111 => 00110111 00111000 => 00000111 00111001 => 00100111 00111010 => 00011101 00111011 => 00111011 00111100 => 00001111 00111101 => 00111101 00111110 => 00011111 00111111 => 00111111 01000000 => 00000001 01000001 => 00000101 01000010 => 00000101 01000011 => 00001101 01000100 => 00000101 01000101 => 00010101 01000110 => 00001101 01000111 => 00011101 01001000 => 00000101 01001001 => 00100101 01001010 => 00010101 01001011 => 00101011 01001100 => 00001101 01001101 => 00110101 01001110 => 00011101 01001111 => 00111101 01010000 => 00000101 01010001 => 00010101 01010010 => 00010101 01010011 => 00110101 01010100 => 00010101 01010101 => 01010101 01010110 => 00101011 01010111 => 01010111 01011000 => 00001011 01011001 => 00101011 01011010 => 00101011 01011011 => 01011011 01011100 => 00010111 01011101 => 01010111 01011110 => 00101111 01011111 => 01011111 01100000 => 00000011 01100001 => 00001011 01100010 => 00001011 01100011 => 00011011 01100100 => 00001011 01100101 => 00101011 01100110 => 00011011 01100111 => 00111011 01101000 => 00001011 01101001 => 00101011 01101010 => 00101011 01101011 => 01011011 01101100 => 00011011 01101101 => 01011011 01101110 => 00110111 01101111 => 01101111 01110000 => 00000111 01110001 => 00010111 01110010 => 00010111 01110011 => 00110111 01110100 => 00010111 01110101 => 01010111 01110110 => 00110111 01110111 => 01110111 01111000 => 00001111 01111001 => 00101111 01111010 => 00101111 01111011 => 01101111 01111100 => 00011111 01111101 => 01011111 01111110 => 00111111 01111111 => 01111111 10000000 => 00000001 10000001 => 00000011 10000010 => 00000011 10000011 => 00000111 10000100 => 00000011 10000101 => 00001011 10000110 => 00000111 10000111 => 00001111 10001000 => 00000011 10001001 => 00010011 10001010 => 00001011 10001011 => 00010111 10001100 => 00000111 10001101 => 00011011 10001110 => 00001111 10001111 => 00011111 10010000 => 00000011 10010001 => 00010011 10010010 => 00010011 10010011 => 00100111 10010100 => 00001011 10010101 => 00101011 10010110 => 00010111 10010111 => 00101111 10011000 => 00000111 10011001 => 00100111 10011010 => 00011011 10011011 => 00110111 10011100 => 00001111 10011101 => 00111011 10011110 => 00011111 10011111 => 00111111 10100000 => 00000011 10100001 => 00001011 10100010 => 00001011 10100011 => 00011011 10100100 => 00001011 10100101 => 00101011 10100110 => 00011011 10100111 => 00111011 10101000 => 00001011 10101001 => 00101011 10101010 => 00101011 10101011 => 01010111 10101100 => 00010111 10101101 => 01010111 10101110 => 00101111 10101111 => 01011111 10110000 => 00000111 10110001 => 00010111 10110010 => 00010111 10110011 => 00110111 10110100 => 00010111 10110101 => 01010111 10110110 => 00110111 10110111 => 01101111 10111000 => 00001111 10111001 => 00101111 10111010 => 00101111 10111011 => 01101111 10111100 => 00011111 10111101 => 01011111 10111110 => 00111111 10111111 => 01111111 11000000 => 00000011 11000001 => 00000111 11000010 => 00000111 11000011 => 00001111 11000100 => 00000111 11000101 => 00010111 11000110 => 00001111 11000111 => 00011111 11001000 => 00000111 11001001 => 00100111 11001010 => 00010111 11001011 => 00101111 11001100 => 00001111 11001101 => 00110111 11001110 => 00011111 11001111 => 00111111 11010000 => 00000111 11010001 => 00010111 11010010 => 00010111 11010011 => 00110111 11010100 => 00010111 11010101 => 01010111 11010110 => 00101111 11010111 => 01011111 11011000 => 00001111 11011001 => 00101111 11011010 => 00101111 11011011 => 01101111 11011100 => 00011111 11011101 => 01011111 11011110 => 00111111 11011111 => 01111111 11100000 => 00000111 11100001 => 00001111 11100010 => 00001111 11100011 => 00011111 11100100 => 00001111 11100101 => 00101111 11100110 => 00011111 11100111 => 00111111 11101000 => 00001111 11101001 => 00101111 11101010 => 00101111 11101011 => 01011111 11101100 => 00011111 11101101 => 01011111 11101110 => 00111111 11101111 => 01111111 11110000 => 00001111 11110001 => 00011111 11110010 => 00011111 11110011 => 00111111 11110100 => 00011111 11110101 => 01011111 11110110 => 00111111 11110111 => 01111111 11111000 => 00011111 11111001 => 00111111 11111010 => 00111111 11111011 => 01111111 11111100 => 00111111 11111101 => 01111111 11111110 => 01111111 11111111 => 11111111 000000000 => 000000000 000000001 => 000000001 000000010 => 000000001 000000011 => 000000011 000000100 => 000000001 000000101 => 000000101 000000110 => 000000011 000000111 => 000000111 000001000 => 000000001 000001001 => 000001001 000001010 => 000000101 000001011 => 000001011 000001100 => 000000011 000001101 => 000001101 000001110 => 000000111 000001111 => 000001111 000010000 => 000000001 000010001 => 000010001 000010010 => 000001001 000010011 => 000010011 000010100 => 000000101 000010101 => 000010101 000010110 => 000001011 000010111 => 000010111 000011000 => 000000011 000011001 => 000011001 000011010 => 000001101 000011011 => 000011011 000011100 => 000000111 000011101 => 000011101 000011110 => 000001111 000011111 => 000011111 000100000 => 000000001 000100001 => 000010001 000100010 => 000010001 000100011 => 000100011 000100100 => 000001001 000100101 => 000100101 000100110 => 000010011 000100111 => 000100111 000101000 => 000000101 000101001 => 000100101 000101010 => 000010101 000101011 => 000101011 000101100 => 000001011 000101101 => 000101011 000101110 => 000010111 000101111 => 000101111 000110000 => 000000011 000110001 => 000100011 000110010 => 000011001 000110011 => 000110011 000110100 => 000001101 000110101 => 000110101 000110110 => 000011011 000110111 => 000110111 000111000 => 000000111 000111001 => 000111001 000111010 => 000011101 000111011 => 000111011 000111100 => 000001111 000111101 => 000111101 000111110 => 000011111 000111111 => 000111111 001000000 => 000000001 001000001 => 000001001 001000010 => 000001001 001000011 => 000011001 001000100 => 000001001 001000101 => 000100101 001000110 => 000011001 001000111 => 000111001 001001000 => 000001001 001001001 => 001001001 001001010 => 000100101 001001011 => 001001011 001001100 => 000010011 001001101 => 001001101 001001110 => 000100111 001001111 => 001001111 001010000 => 000000101 001010001 => 000100101 001010010 => 000100101 001010011 => 001001101 001010100 => 000010101 001010101 => 001010101 001010110 => 000101011 001010111 => 001010111 001011000 => 000001011 001011001 => 001001011 001011010 => 000101011 001011011 => 001011011 001011100 => 000010111 001011101 => 001010111 001011110 => 000101111 001011111 => 001011111 001100000 => 000000011 001100001 => 000010011 001100010 => 000010011 001100011 => 000110011 001100100 => 000010011 001100101 => 001001101 001100110 => 000110011 001100111 => 001100111 001101000 => 000001101 001101001 => 001001101 001101010 => 000110101 001101011 => 001101011 001101100 => 000011011 001101101 => 001101011 001101110 => 000110111 001101111 => 001101111 001110000 => 000000111 001110001 => 000100111 001110010 => 000100111 001110011 => 001100111 001110100 => 000011101 001110101 => 001110101 001110110 => 000111011 001110111 => 001110111 001111000 => 000001111 001111001 => 001001111 001111010 => 000111101 001111011 => 001111011 001111100 => 000011111 001111101 => 001111101 001111110 => 000111111 001111111 => 001111111 010000000 => 000000001 010000001 => 000000101 010000010 => 000000101 010000011 => 000001101 010000100 => 000000101 010000101 => 000010101 010000110 => 000001101 010000111 => 000011101 010001000 => 000000101 010001001 => 000100101 010001010 => 000010101 010001011 => 000101011 010001100 => 000001101 010001101 => 000110101 010001110 => 000011101 010001111 => 000111101 010010000 => 000000101 010010001 => 000100101 010010010 => 000100101 010010011 => 001001101 010010100 => 000010101 010010101 => 001010101 010010110 => 000101011 010010111 => 001010111 010011000 => 000001101 010011001 => 001001101 010011010 => 000110101 010011011 => 001101011 010011100 => 000011101 010011101 => 001110101 010011110 => 000111101 010011111 => 001111101 010100000 => 000000101 010100001 => 000010101 010100010 => 000010101 010100011 => 000110101 010100100 => 000010101 010100101 => 001010101 010100110 => 000110101 010100111 => 001110101 010101000 => 000010101 010101001 => 001010101 010101010 => 001010101 010101011 => 010101011 010101100 => 000101011 010101101 => 010101011 010101110 => 001010111 010101111 => 010101111 010110000 => 000001011 010110001 => 000101011 010110010 => 000101011 010110011 => 001101011 010110100 => 000101011 010110101 => 010101011 010110110 => 001011011 010110111 => 010110111 010111000 => 000010111 010111001 => 001010111 010111010 => 001010111 010111011 => 010110111 010111100 => 000101111 010111101 => 010101111 010111110 => 001011111 010111111 => 010111111 011000000 => 000000011 011000001 => 000001011 011000010 => 000001011 011000011 => 000011011 011000100 => 000001011 011000101 => 000101011 011000110 => 000011011 011000111 => 000111011 011001000 => 000001011 011001001 => 001001011 011001010 => 000101011 011001011 => 001011011 011001100 => 000011011 011001101 => 001101011 011001110 => 000111011 011001111 => 001111011 011010000 => 000001011 011010001 => 000101011 011010010 => 000101011 011010011 => 001101011 011010100 => 000101011 011010101 => 010101011 011010110 => 001011011 011010111 => 010110111 011011000 => 000011011 011011001 => 001011011 011011010 => 001011011 011011011 => 011011011 011011100 => 000110111 011011101 => 010110111 011011110 => 001101111 011011111 => 011011111 011100000 => 000000111 011100001 => 000010111 011100010 => 000010111 011100011 => 000110111 011100100 => 000010111 011100101 => 001010111 011100110 => 000110111 011100111 => 001110111 011101000 => 000010111 011101001 => 001010111 011101010 => 001010111 011101011 => 010110111 011101100 => 000110111 011101101 => 010110111 011101110 => 001110111 011101111 => 011101111 011110000 => 000001111 011110001 => 000101111 011110010 => 000101111 011110011 => 001101111 011110100 => 000101111 011110101 => 010101111 011110110 => 001101111 011110111 => 011101111 011111000 => 000011111 011111001 => 001011111 011111010 => 001011111 011111011 => 011011111 011111100 => 000111111 011111101 => 010111111 011111110 => 001111111 011111111 => 011111111 100000000 => 000000001 100000001 => 000000011 100000010 => 000000011 100000011 => 000000111 100000100 => 000000011 100000101 => 000001011 100000110 => 000000111 100000111 => 000001111 100001000 => 000000011 100001001 => 000010011 100001010 => 000001011 100001011 => 000010111 100001100 => 000000111 100001101 => 000011011 100001110 => 000001111 100001111 => 000011111 100010000 => 000000011 100010001 => 000100011 100010010 => 000010011 100010011 => 000100111 100010100 => 000001011 100010101 => 000101011 100010110 => 000010111 100010111 => 000101111 100011000 => 000000111 100011001 => 000110011 100011010 => 000011011 100011011 => 000110111 100011100 => 000001111 100011101 => 000111011 100011110 => 000011111 100011111 => 000111111 100100000 => 000000011 100100001 => 000010011 100100010 => 000010011 100100011 => 000110011 100100100 => 000010011 100100101 => 001001011 100100110 => 000100111 100100111 => 001001111 100101000 => 000001011 100101001 => 001001011 100101010 => 000101011 100101011 => 001010111 100101100 => 000010111 100101101 => 001010111 100101110 => 000101111 100101111 => 001011111 100110000 => 000000111 100110001 => 000100111 100110010 => 000100111 100110011 => 001100111 100110100 => 000011011 100110101 => 001101011 100110110 => 000110111 100110111 => 001101111 100111000 => 000001111 100111001 => 001001111 100111010 => 000111011 100111011 => 001110111 100111100 => 000011111 100111101 => 001111011 100111110 => 000111111 100111111 => 001111111 101000000 => 000000011 101000001 => 000001011 101000010 => 000001011 101000011 => 000011011 101000100 => 000001011 101000101 => 000101011 101000110 => 000011011 101000111 => 000111011 101001000 => 000001011 101001001 => 001001011 101001010 => 000101011 101001011 => 001010111 101001100 => 000011011 101001101 => 001101011 101001110 => 000111011 101001111 => 001111011 101010000 => 000001011 101010001 => 000101011 101010010 => 000101011 101010011 => 001101011 101010100 => 000101011 101010101 => 010101011 101010110 => 001010111 101010111 => 010101111 101011000 => 000010111 101011001 => 001010111 101011010 => 001010111 101011011 => 010110111 101011100 => 000101111 101011101 => 010101111 101011110 => 001011111 101011111 => 010111111 101100000 => 000000111 101100001 => 000010111 101100010 => 000010111 101100011 => 000110111 101100100 => 000010111 101100101 => 001010111 101100110 => 000110111 101100111 => 001110111 101101000 => 000010111 101101001 => 001010111 101101010 => 001010111 101101011 => 010110111 101101100 => 000110111 101101101 => 010110111 101101110 => 001101111 101101111 => 011011111 101110000 => 000001111 101110001 => 000101111 101110010 => 000101111 101110011 => 001101111 101110100 => 000101111 101110101 => 010101111 101110110 => 001101111 101110111 => 011101111 101111000 => 000011111 101111001 => 001011111 101111010 => 001011111 101111011 => 011011111 101111100 => 000111111 101111101 => 010111111 101111110 => 001111111 101111111 => 011111111 110000000 => 000000011 110000001 => 000000111 110000010 => 000000111 110000011 => 000001111 110000100 => 000000111 110000101 => 000010111 110000110 => 000001111 110000111 => 000011111 110001000 => 000000111 110001001 => 000100111 110001010 => 000010111 110001011 => 000101111 110001100 => 000001111 110001101 => 000110111 110001110 => 000011111 110001111 => 000111111 110010000 => 000000111 110010001 => 000100111 110010010 => 000100111 110010011 => 001001111 110010100 => 000010111 110010101 => 001010111 110010110 => 000101111 110010111 => 001011111 110011000 => 000001111 110011001 => 001001111 110011010 => 000110111 110011011 => 001101111 110011100 => 000011111 110011101 => 001110111 110011110 => 000111111 110011111 => 001111111 110100000 => 000000111 110100001 => 000010111 110100010 => 000010111 110100011 => 000110111 110100100 => 000010111 110100101 => 001010111 110100110 => 000110111 110100111 => 001110111 110101000 => 000010111 110101001 => 001010111 110101010 => 001010111 110101011 => 010101111 110101100 => 000101111 110101101 => 010101111 110101110 => 001011111 110101111 => 010111111 110110000 => 000001111 110110001 => 000101111 110110010 => 000101111 110110011 => 001101111 110110100 => 000101111 110110101 => 010101111 110110110 => 001101111 110110111 => 011011111 110111000 => 000011111 110111001 => 001011111 110111010 => 001011111 110111011 => 011011111 110111100 => 000111111 110111101 => 010111111 110111110 => 001111111 110111111 => 011111111 111000000 => 000000111 111000001 => 000001111 111000010 => 000001111 111000011 => 000011111 111000100 => 000001111 111000101 => 000101111 111000110 => 000011111 111000111 => 000111111 111001000 => 000001111 111001001 => 001001111 111001010 => 000101111 111001011 => 001011111 111001100 => 000011111 111001101 => 001101111 111001110 => 000111111 111001111 => 001111111 111010000 => 000001111 111010001 => 000101111 111010010 => 000101111 111010011 => 001101111 111010100 => 000101111 111010101 => 010101111 111010110 => 001011111 111010111 => 010111111 111011000 => 000011111 111011001 => 001011111 111011010 => 001011111 111011011 => 011011111 111011100 => 000111111 111011101 => 010111111 111011110 => 001111111 111011111 => 011111111 111100000 => 000001111 111100001 => 000011111 111100010 => 000011111 111100011 => 000111111 111100100 => 000011111 111100101 => 001011111 111100110 => 000111111 111100111 => 001111111 111101000 => 000011111 111101001 => 001011111 111101010 => 001011111 111101011 => 010111111 111101100 => 000111111 111101101 => 010111111 111101110 => 001111111 111101111 => 011111111 111110000 => 000011111 111110001 => 000111111 111110010 => 000111111 111110011 => 001111111 111110100 => 000111111 111110101 => 010111111 111110110 => 001111111 111110111 => 011111111 111111000 => 000111111 111111001 => 001111111 111111010 => 001111111 111111011 => 011111111 111111100 => 001111111 111111101 => 011111111 111111110 => 011111111 111111111 => 111111111 1010101010 => 0010101011 1010101100 => 0001010111 1010110010 => 0001010111 1010110100 => 0001010111 1010111000 => 0000101111 1011001010 => 0001010111 1011001100 => 0000110111 1011010010 => 0001010111 1011010100 => 0001010111 1011011000 => 0000110111 1011100010 => 0000101111 1011100100 => 0000101111 1011101000 => 0000101111 1011110000 => 0000011111 1100101010 => 0001010111 1100101100 => 0000101111 1100110010 => 0001001111 1100110100 => 0000110111 1100111000 => 0000011111 1101001010 => 0001010111 1101001100 => 0000110111 1101010010 => 0001010111 1101010100 => 0001010111 1101011000 => 0000101111 1101100010 => 0000101111 1101100100 => 0000101111 1101101000 => 0000101111 1101110000 => 0000011111 1110001010 => 0000101111 1110001100 => 0000011111 1110010010 => 0001001111 1110010100 => 0000101111 1110011000 => 0000011111 1110100010 => 0000101111 1110100100 => 0000101111 1110101000 => 0000101111 1110110000 => 0000011111 1111000010 => 0000011111 1111000100 => 0000011111 1111001000 => 0000011111 1111010000 => 0000011111 1111100000 => 0000011111 101010101010 => 001010101011 101010101100 => 000101010111 101010110010 => 000101010111 101010110100 => 000101010111 101010111000 => 000010101111 101011001010 => 000101010111 101011001100 => 000011010111 101011010010 => 000101010111 101011010100 => 000101010111 101011011000 => 000010110111 101011100010 => 000010101111 101011100100 => 000010101111 101011101000 => 000010101111 101011110000 => 000001011111 101100101010 => 000101010111 101100101100 => 000010110111 101100110010 => 000100110111 101100110100 => 000011010111 101100111000 => 000001110111 101101001010 => 000101010111 101101001100 => 000011010111 101101010010 => 000101010111 101101010100 => 000101010111 101101011000 => 000010110111 101101100010 => 000010110111 101101100100 => 000010110111 101101101000 => 000010110111 101101110000 => 000001101111 101110001010 => 000010101111 101110001100 => 000001101111 101110010010 => 000100101111 101110010100 => 000010101111 101110011000 => 000001101111 101110100010 => 000010101111 101110100100 => 000010101111 101110101000 => 000010101111 101110110000 => 000001101111 101111000010 => 000001011111 101111000100 => 000001011111 101111001000 => 000001011111 101111010000 => 000001011111 101111100000 => 000000111111 110010101010 => 000101010111 110010101100 => 000010101111 110010110010 => 000100101111 110010110100 => 000010101111 110010111000 => 000001011111 110011001010 => 000100110111 110011001100 => 000011001111 110011010010 => 000100110111 110011010100 => 000011010111 110011011000 => 000001101111 110011100010 => 000010011111 110011100100 => 000010011111 110011101000 => 000001110111 110011110000 => 000000111111 110100101010 => 000101010111 110100101100 => 000010101111 110100110010 => 000100110111 110100110100 => 000011010111 110100111000 => 000001110111 110101001010 => 000101010111 110101001100 => 000011010111 110101010010 => 000101010111 110101010100 => 000101010111 110101011000 => 000010101111 110101100010 => 000010101111 110101100100 => 000010101111 110101101000 => 000010101111 110101110000 => 000001011111 110110001010 => 000010101111 110110001100 => 000001101111 110110010010 => 000100101111 110110010100 => 000010101111 110110011000 => 000001101111 110110100010 => 000010101111 110110100100 => 000010101111 110110101000 => 000010101111 110110110000 => 000001101111 110111000010 => 000001011111 110111000100 => 000001011111 110111001000 => 000001011111 110111010000 => 000001011111 110111100000 => 000000111111 111000101010 => 000010101111 111000101100 => 000001011111 111000110010 => 000011001111 111000110100 => 000001101111 111000111000 => 000000111111 111001001010 => 000100101111 111001001100 => 000010011111 111001010010 => 000100101111 111001010100 => 000010101111 111001011000 => 000001011111 111001100010 => 000010011111 111001100100 => 000010011111 111001101000 => 000001101111 111001110000 => 000000111111 111010001010 => 000010101111 111010001100 => 000001101111 111010010010 => 000100101111 111010010100 => 000010101111 111010011000 => 000001101111 111010100010 => 000010101111 111010100100 => 000010101111 111010101000 => 000010101111 111010110000 => 000001011111 111011000010 => 000001011111 111011000100 => 000001011111 111011001000 => 000001011111 111011010000 => 000001011111 111011100000 => 000000111111 111100001010 => 000001011111 111100001100 => 000000111111 111100010010 => 000010011111 111100010100 => 000001011111 111100011000 => 000000111111 111100100010 => 000010011111 111100100100 => 000010011111 111100101000 => 000001011111 111100110000 => 000000111111 111101000010 => 000001011111 111101000100 => 000001011111 111101001000 => 000001011111 111101010000 => 000001011111 111101100000 => 000000111111 111110000010 => 000000111111 111110000100 => 000000111111 111110001000 => 000000111111 111110010000 => 000000111111 111110100000 => 000000111111 111111000000 => 000000111111 10101010101010 => 00101010101011 10101010101100 => 00010101010111 10101010110100 => 00010101010111 10101010111000 => 00001010101111 ----------------------------------------------------------------------------- Created: Apr 12, 2021 at 17:42 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 12, 2021 at 17:42 by Martin Rubey