************************************************************************ * 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: Mp00234 ------------------------------------------------------------------------ Map name: valleys-to-peaks ------------------------------------------------------------------------ Domain: Binary words ------------------------------------------------------------------------ Codomain: Binary words ------------------------------------------------------------------------ Description: Return the binary word with every valley replaced by a peak. A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak. ------------------------------------------------------------------------ References: [1] Tasoulas, I., Manes, K., Sapounakis, A., Tsikouras, P. Chains with small intervals in the lattice of binary paths [[MathSciNet:4054761]] ------------------------------------------------------------------------ Code: def mapping(w): w = list(w) f = list(w) for i in range(len(w)-1): if w[i:i+2] == [0, 1]: f[i:i+2] = [1, 0] if w[len(w)-1] == 0: f[len(w)-1] = 1 return Words([0,1])(f) ------------------------------------------------------------------------ Map images: 0 => 1 1 => 1 00 => 01 01 => 10 10 => 11 11 => 11 000 => 001 001 => 010 010 => 101 011 => 101 100 => 101 101 => 110 110 => 111 111 => 111 0000 => 0001 0001 => 0010 0010 => 0101 0011 => 0101 0100 => 1001 0101 => 1010 0110 => 1011 0111 => 1011 1000 => 1001 1001 => 1010 1010 => 1101 1011 => 1101 1100 => 1101 1101 => 1110 1110 => 1111 1111 => 1111 00000 => 00001 00001 => 00010 00010 => 00101 00011 => 00101 00100 => 01001 00101 => 01010 00110 => 01011 00111 => 01011 01000 => 10001 01001 => 10010 01010 => 10101 01011 => 10101 01100 => 10101 01101 => 10110 01110 => 10111 01111 => 10111 10000 => 10001 10001 => 10010 10010 => 10101 10011 => 10101 10100 => 11001 10101 => 11010 10110 => 11011 10111 => 11011 11000 => 11001 11001 => 11010 11010 => 11101 11011 => 11101 11100 => 11101 11101 => 11110 11110 => 11111 11111 => 11111 000000 => 000001 000001 => 000010 000010 => 000101 000011 => 000101 000100 => 001001 000101 => 001010 000110 => 001011 000111 => 001011 001000 => 010001 001001 => 010010 001010 => 010101 001011 => 010101 001100 => 010101 001101 => 010110 001110 => 010111 001111 => 010111 010000 => 100001 010001 => 100010 010010 => 100101 010011 => 100101 010100 => 101001 010101 => 101010 010110 => 101011 010111 => 101011 011000 => 101001 011001 => 101010 011010 => 101101 011011 => 101101 011100 => 101101 011101 => 101110 011110 => 101111 011111 => 101111 100000 => 100001 100001 => 100010 100010 => 100101 100011 => 100101 100100 => 101001 100101 => 101010 100110 => 101011 100111 => 101011 101000 => 110001 101001 => 110010 101010 => 110101 101011 => 110101 101100 => 110101 101101 => 110110 101110 => 110111 101111 => 110111 110000 => 110001 110001 => 110010 110010 => 110101 110011 => 110101 110100 => 111001 110101 => 111010 110110 => 111011 110111 => 111011 111000 => 111001 111001 => 111010 111010 => 111101 111011 => 111101 111100 => 111101 111101 => 111110 111110 => 111111 111111 => 111111 0000000 => 0000001 0000001 => 0000010 0000010 => 0000101 0000011 => 0000101 0000100 => 0001001 0000101 => 0001010 0000110 => 0001011 0000111 => 0001011 0001000 => 0010001 0001001 => 0010010 0001010 => 0010101 0001011 => 0010101 0001100 => 0010101 0001101 => 0010110 0001110 => 0010111 0001111 => 0010111 0010000 => 0100001 0010001 => 0100010 0010010 => 0100101 0010011 => 0100101 0010100 => 0101001 0010101 => 0101010 0010110 => 0101011 0010111 => 0101011 0011000 => 0101001 0011001 => 0101010 0011010 => 0101101 0011011 => 0101101 0011100 => 0101101 0011101 => 0101110 0011110 => 0101111 0011111 => 0101111 0100000 => 1000001 0100001 => 1000010 0100010 => 1000101 0100011 => 1000101 0100100 => 1001001 0100101 => 1001010 0100110 => 1001011 0100111 => 1001011 0101000 => 1010001 0101001 => 1010010 0101010 => 1010101 0101011 => 1010101 0101100 => 1010101 0101101 => 1010110 0101110 => 1010111 0101111 => 1010111 0110000 => 1010001 0110001 => 1010010 0110010 => 1010101 0110011 => 1010101 0110100 => 1011001 0110101 => 1011010 0110110 => 1011011 0110111 => 1011011 0111000 => 1011001 0111001 => 1011010 0111010 => 1011101 0111011 => 1011101 0111100 => 1011101 0111101 => 1011110 0111110 => 1011111 0111111 => 1011111 1000000 => 1000001 1000001 => 1000010 1000010 => 1000101 1000011 => 1000101 1000100 => 1001001 1000101 => 1001010 1000110 => 1001011 1000111 => 1001011 1001000 => 1010001 1001001 => 1010010 1001010 => 1010101 1001011 => 1010101 1001100 => 1010101 1001101 => 1010110 1001110 => 1010111 1001111 => 1010111 1010000 => 1100001 1010001 => 1100010 1010010 => 1100101 1010011 => 1100101 1010100 => 1101001 1010101 => 1101010 1010110 => 1101011 1010111 => 1101011 1011000 => 1101001 1011001 => 1101010 1011010 => 1101101 1011011 => 1101101 1011100 => 1101101 1011101 => 1101110 1011110 => 1101111 1011111 => 1101111 1100000 => 1100001 1100001 => 1100010 1100010 => 1100101 1100011 => 1100101 1100100 => 1101001 1100101 => 1101010 1100110 => 1101011 1100111 => 1101011 1101000 => 1110001 1101001 => 1110010 1101010 => 1110101 1101011 => 1110101 1101100 => 1110101 1101101 => 1110110 1101110 => 1110111 1101111 => 1110111 1110000 => 1110001 1110001 => 1110010 1110010 => 1110101 1110011 => 1110101 1110100 => 1111001 1110101 => 1111010 1110110 => 1111011 1110111 => 1111011 1111000 => 1111001 1111001 => 1111010 1111010 => 1111101 1111011 => 1111101 1111100 => 1111101 1111101 => 1111110 1111110 => 1111111 1111111 => 1111111 00000000 => 00000001 00000001 => 00000010 00000010 => 00000101 00000011 => 00000101 00000100 => 00001001 00000101 => 00001010 00000110 => 00001011 00000111 => 00001011 00001000 => 00010001 00001001 => 00010010 00001010 => 00010101 00001011 => 00010101 00001100 => 00010101 00001101 => 00010110 00001110 => 00010111 00001111 => 00010111 00010000 => 00100001 00010001 => 00100010 00010010 => 00100101 00010011 => 00100101 00010100 => 00101001 00010101 => 00101010 00010110 => 00101011 00010111 => 00101011 00011000 => 00101001 00011001 => 00101010 00011010 => 00101101 00011011 => 00101101 00011100 => 00101101 00011101 => 00101110 00011110 => 00101111 00011111 => 00101111 00100000 => 01000001 00100001 => 01000010 00100010 => 01000101 00100011 => 01000101 00100100 => 01001001 00100101 => 01001010 00100110 => 01001011 00100111 => 01001011 00101000 => 01010001 00101001 => 01010010 00101010 => 01010101 00101011 => 01010101 00101100 => 01010101 00101101 => 01010110 00101110 => 01010111 00101111 => 01010111 00110000 => 01010001 00110001 => 01010010 00110010 => 01010101 00110011 => 01010101 00110100 => 01011001 00110101 => 01011010 00110110 => 01011011 00110111 => 01011011 00111000 => 01011001 00111001 => 01011010 00111010 => 01011101 00111011 => 01011101 00111100 => 01011101 00111101 => 01011110 00111110 => 01011111 00111111 => 01011111 01000000 => 10000001 01000001 => 10000010 01000010 => 10000101 01000011 => 10000101 01000100 => 10001001 01000101 => 10001010 01000110 => 10001011 01000111 => 10001011 01001000 => 10010001 01001001 => 10010010 01001010 => 10010101 01001011 => 10010101 01001100 => 10010101 01001101 => 10010110 01001110 => 10010111 01001111 => 10010111 01010000 => 10100001 01010001 => 10100010 01010010 => 10100101 01010011 => 10100101 01010100 => 10101001 01010101 => 10101010 01010110 => 10101011 01010111 => 10101011 01011000 => 10101001 01011001 => 10101010 01011010 => 10101101 01011011 => 10101101 01011100 => 10101101 01011101 => 10101110 01011110 => 10101111 01011111 => 10101111 01100000 => 10100001 01100001 => 10100010 01100010 => 10100101 01100011 => 10100101 01100100 => 10101001 01100101 => 10101010 01100110 => 10101011 01100111 => 10101011 01101000 => 10110001 01101001 => 10110010 01101010 => 10110101 01101011 => 10110101 01101100 => 10110101 01101101 => 10110110 01101110 => 10110111 01101111 => 10110111 01110000 => 10110001 01110001 => 10110010 01110010 => 10110101 01110011 => 10110101 01110100 => 10111001 01110101 => 10111010 01110110 => 10111011 01110111 => 10111011 01111000 => 10111001 01111001 => 10111010 01111010 => 10111101 01111011 => 10111101 01111100 => 10111101 01111101 => 10111110 01111110 => 10111111 01111111 => 10111111 10000000 => 10000001 10000001 => 10000010 10000010 => 10000101 10000011 => 10000101 10000100 => 10001001 10000101 => 10001010 10000110 => 10001011 10000111 => 10001011 10001000 => 10010001 10001001 => 10010010 10001010 => 10010101 10001011 => 10010101 10001100 => 10010101 10001101 => 10010110 10001110 => 10010111 10001111 => 10010111 10010000 => 10100001 10010001 => 10100010 10010010 => 10100101 10010011 => 10100101 10010100 => 10101001 10010101 => 10101010 10010110 => 10101011 10010111 => 10101011 10011000 => 10101001 10011001 => 10101010 10011010 => 10101101 10011011 => 10101101 10011100 => 10101101 10011101 => 10101110 10011110 => 10101111 10011111 => 10101111 10100000 => 11000001 10100001 => 11000010 10100010 => 11000101 10100011 => 11000101 10100100 => 11001001 10100101 => 11001010 10100110 => 11001011 10100111 => 11001011 10101000 => 11010001 10101001 => 11010010 10101010 => 11010101 10101011 => 11010101 10101100 => 11010101 10101101 => 11010110 10101110 => 11010111 10101111 => 11010111 10110000 => 11010001 10110001 => 11010010 10110010 => 11010101 10110011 => 11010101 10110100 => 11011001 10110101 => 11011010 10110110 => 11011011 10110111 => 11011011 10111000 => 11011001 10111001 => 11011010 10111010 => 11011101 10111011 => 11011101 10111100 => 11011101 10111101 => 11011110 10111110 => 11011111 10111111 => 11011111 11000000 => 11000001 11000001 => 11000010 11000010 => 11000101 11000011 => 11000101 11000100 => 11001001 11000101 => 11001010 11000110 => 11001011 11000111 => 11001011 11001000 => 11010001 11001001 => 11010010 11001010 => 11010101 11001011 => 11010101 11001100 => 11010101 11001101 => 11010110 11001110 => 11010111 11001111 => 11010111 11010000 => 11100001 11010001 => 11100010 11010010 => 11100101 11010011 => 11100101 11010100 => 11101001 11010101 => 11101010 11010110 => 11101011 11010111 => 11101011 11011000 => 11101001 11011001 => 11101010 11011010 => 11101101 11011011 => 11101101 11011100 => 11101101 11011101 => 11101110 11011110 => 11101111 11011111 => 11101111 11100000 => 11100001 11100001 => 11100010 11100010 => 11100101 11100011 => 11100101 11100100 => 11101001 11100101 => 11101010 11100110 => 11101011 11100111 => 11101011 11101000 => 11110001 11101001 => 11110010 11101010 => 11110101 11101011 => 11110101 11101100 => 11110101 11101101 => 11110110 11101110 => 11110111 11101111 => 11110111 11110000 => 11110001 11110001 => 11110010 11110010 => 11110101 11110011 => 11110101 11110100 => 11111001 11110101 => 11111010 11110110 => 11111011 11110111 => 11111011 11111000 => 11111001 11111001 => 11111010 11111010 => 11111101 11111011 => 11111101 11111100 => 11111101 11111101 => 11111110 11111110 => 11111111 11111111 => 11111111 000000000 => 000000001 000000001 => 000000010 000000010 => 000000101 000000011 => 000000101 000000100 => 000001001 000000101 => 000001010 000000110 => 000001011 000000111 => 000001011 000001000 => 000010001 000001001 => 000010010 000001010 => 000010101 000001011 => 000010101 000001100 => 000010101 000001101 => 000010110 000001110 => 000010111 000001111 => 000010111 000010000 => 000100001 000010001 => 000100010 000010010 => 000100101 000010011 => 000100101 000010100 => 000101001 000010101 => 000101010 000010110 => 000101011 000010111 => 000101011 000011000 => 000101001 000011001 => 000101010 000011010 => 000101101 000011011 => 000101101 000011100 => 000101101 000011101 => 000101110 000011110 => 000101111 000011111 => 000101111 000100000 => 001000001 000100001 => 001000010 000100010 => 001000101 000100011 => 001000101 000100100 => 001001001 000100101 => 001001010 000100110 => 001001011 000100111 => 001001011 000101000 => 001010001 000101001 => 001010010 000101010 => 001010101 000101011 => 001010101 000101100 => 001010101 000101101 => 001010110 000101110 => 001010111 000101111 => 001010111 000110000 => 001010001 000110001 => 001010010 000110010 => 001010101 000110011 => 001010101 000110100 => 001011001 000110101 => 001011010 000110110 => 001011011 000110111 => 001011011 000111000 => 001011001 000111001 => 001011010 000111010 => 001011101 000111011 => 001011101 000111100 => 001011101 000111101 => 001011110 000111110 => 001011111 000111111 => 001011111 001000000 => 010000001 001000001 => 010000010 001000010 => 010000101 001000011 => 010000101 001000100 => 010001001 001000101 => 010001010 001000110 => 010001011 001000111 => 010001011 001001000 => 010010001 001001001 => 010010010 001001010 => 010010101 001001011 => 010010101 001001100 => 010010101 001001101 => 010010110 001001110 => 010010111 001001111 => 010010111 001010000 => 010100001 001010001 => 010100010 001010010 => 010100101 001010011 => 010100101 001010100 => 010101001 001010101 => 010101010 001010110 => 010101011 001010111 => 010101011 001011000 => 010101001 001011001 => 010101010 001011010 => 010101101 001011011 => 010101101 001011100 => 010101101 001011101 => 010101110 001011110 => 010101111 001011111 => 010101111 001100000 => 010100001 001100001 => 010100010 001100010 => 010100101 001100011 => 010100101 001100100 => 010101001 001100101 => 010101010 001100110 => 010101011 001100111 => 010101011 001101000 => 010110001 001101001 => 010110010 001101010 => 010110101 001101011 => 010110101 001101100 => 010110101 001101101 => 010110110 001101110 => 010110111 001101111 => 010110111 001110000 => 010110001 001110001 => 010110010 001110010 => 010110101 001110011 => 010110101 001110100 => 010111001 001110101 => 010111010 001110110 => 010111011 001110111 => 010111011 001111000 => 010111001 001111001 => 010111010 001111010 => 010111101 001111011 => 010111101 001111100 => 010111101 001111101 => 010111110 001111110 => 010111111 001111111 => 010111111 010000000 => 100000001 010000001 => 100000010 010000010 => 100000101 010000011 => 100000101 010000100 => 100001001 010000101 => 100001010 010000110 => 100001011 010000111 => 100001011 010001000 => 100010001 010001001 => 100010010 010001010 => 100010101 010001011 => 100010101 010001100 => 100010101 010001101 => 100010110 010001110 => 100010111 010001111 => 100010111 010010000 => 100100001 010010001 => 100100010 010010010 => 100100101 010010011 => 100100101 010010100 => 100101001 010010101 => 100101010 010010110 => 100101011 010010111 => 100101011 010011000 => 100101001 010011001 => 100101010 010011010 => 100101101 010011011 => 100101101 010011100 => 100101101 010011101 => 100101110 010011110 => 100101111 010011111 => 100101111 010100000 => 101000001 010100001 => 101000010 010100010 => 101000101 010100011 => 101000101 010100100 => 101001001 010100101 => 101001010 010100110 => 101001011 010100111 => 101001011 010101000 => 101010001 010101001 => 101010010 010101010 => 101010101 010101011 => 101010101 010101100 => 101010101 010101101 => 101010110 010101110 => 101010111 010101111 => 101010111 010110000 => 101010001 010110001 => 101010010 010110010 => 101010101 010110011 => 101010101 010110100 => 101011001 010110101 => 101011010 010110110 => 101011011 010110111 => 101011011 010111000 => 101011001 010111001 => 101011010 010111010 => 101011101 010111011 => 101011101 010111100 => 101011101 010111101 => 101011110 010111110 => 101011111 010111111 => 101011111 011000000 => 101000001 011000001 => 101000010 011000010 => 101000101 011000011 => 101000101 011000100 => 101001001 011000101 => 101001010 011000110 => 101001011 011000111 => 101001011 011001000 => 101010001 011001001 => 101010010 011001010 => 101010101 011001011 => 101010101 011001100 => 101010101 011001101 => 101010110 011001110 => 101010111 011001111 => 101010111 011010000 => 101100001 011010001 => 101100010 011010010 => 101100101 011010011 => 101100101 011010100 => 101101001 011010101 => 101101010 011010110 => 101101011 011010111 => 101101011 011011000 => 101101001 011011001 => 101101010 011011010 => 101101101 011011011 => 101101101 011011100 => 101101101 011011101 => 101101110 011011110 => 101101111 011011111 => 101101111 011100000 => 101100001 011100001 => 101100010 011100010 => 101100101 011100011 => 101100101 011100100 => 101101001 011100101 => 101101010 011100110 => 101101011 011100111 => 101101011 011101000 => 101110001 011101001 => 101110010 011101010 => 101110101 011101011 => 101110101 011101100 => 101110101 011101101 => 101110110 011101110 => 101110111 011101111 => 101110111 011110000 => 101110001 011110001 => 101110010 011110010 => 101110101 011110011 => 101110101 011110100 => 101111001 011110101 => 101111010 011110110 => 101111011 011110111 => 101111011 011111000 => 101111001 011111001 => 101111010 011111010 => 101111101 011111011 => 101111101 011111100 => 101111101 011111101 => 101111110 011111110 => 101111111 011111111 => 101111111 100000000 => 100000001 100000001 => 100000010 100000010 => 100000101 100000011 => 100000101 100000100 => 100001001 100000101 => 100001010 100000110 => 100001011 100000111 => 100001011 100001000 => 100010001 100001001 => 100010010 100001010 => 100010101 100001011 => 100010101 100001100 => 100010101 100001101 => 100010110 100001110 => 100010111 100001111 => 100010111 100010000 => 100100001 100010001 => 100100010 100010010 => 100100101 100010011 => 100100101 100010100 => 100101001 100010101 => 100101010 100010110 => 100101011 100010111 => 100101011 100011000 => 100101001 100011001 => 100101010 100011010 => 100101101 100011011 => 100101101 100011100 => 100101101 100011101 => 100101110 100011110 => 100101111 100011111 => 100101111 100100000 => 101000001 100100001 => 101000010 100100010 => 101000101 100100011 => 101000101 100100100 => 101001001 100100101 => 101001010 100100110 => 101001011 100100111 => 101001011 100101000 => 101010001 100101001 => 101010010 100101010 => 101010101 100101011 => 101010101 100101100 => 101010101 100101101 => 101010110 100101110 => 101010111 100101111 => 101010111 100110000 => 101010001 100110001 => 101010010 100110010 => 101010101 100110011 => 101010101 100110100 => 101011001 100110101 => 101011010 100110110 => 101011011 100110111 => 101011011 100111000 => 101011001 100111001 => 101011010 100111010 => 101011101 100111011 => 101011101 100111100 => 101011101 100111101 => 101011110 100111110 => 101011111 100111111 => 101011111 101000000 => 110000001 101000001 => 110000010 101000010 => 110000101 101000011 => 110000101 101000100 => 110001001 101000101 => 110001010 101000110 => 110001011 101000111 => 110001011 101001000 => 110010001 101001001 => 110010010 101001010 => 110010101 101001011 => 110010101 101001100 => 110010101 101001101 => 110010110 101001110 => 110010111 101001111 => 110010111 101010000 => 110100001 101010001 => 110100010 101010010 => 110100101 101010011 => 110100101 101010100 => 110101001 101010101 => 110101010 101010110 => 110101011 101010111 => 110101011 101011000 => 110101001 101011001 => 110101010 101011010 => 110101101 101011011 => 110101101 101011100 => 110101101 101011101 => 110101110 101011110 => 110101111 101011111 => 110101111 101100000 => 110100001 101100001 => 110100010 101100010 => 110100101 101100011 => 110100101 101100100 => 110101001 101100101 => 110101010 101100110 => 110101011 101100111 => 110101011 101101000 => 110110001 101101001 => 110110010 101101010 => 110110101 101101011 => 110110101 101101100 => 110110101 101101101 => 110110110 101101110 => 110110111 101101111 => 110110111 101110000 => 110110001 101110001 => 110110010 101110010 => 110110101 101110011 => 110110101 101110100 => 110111001 101110101 => 110111010 101110110 => 110111011 101110111 => 110111011 101111000 => 110111001 101111001 => 110111010 101111010 => 110111101 101111011 => 110111101 101111100 => 110111101 101111101 => 110111110 101111110 => 110111111 101111111 => 110111111 110000000 => 110000001 110000001 => 110000010 110000010 => 110000101 110000011 => 110000101 110000100 => 110001001 110000101 => 110001010 110000110 => 110001011 110000111 => 110001011 110001000 => 110010001 110001001 => 110010010 110001010 => 110010101 110001011 => 110010101 110001100 => 110010101 110001101 => 110010110 110001110 => 110010111 110001111 => 110010111 110010000 => 110100001 110010001 => 110100010 110010010 => 110100101 110010011 => 110100101 110010100 => 110101001 110010101 => 110101010 110010110 => 110101011 110010111 => 110101011 110011000 => 110101001 110011001 => 110101010 110011010 => 110101101 110011011 => 110101101 110011100 => 110101101 110011101 => 110101110 110011110 => 110101111 110011111 => 110101111 110100000 => 111000001 110100001 => 111000010 110100010 => 111000101 110100011 => 111000101 110100100 => 111001001 110100101 => 111001010 110100110 => 111001011 110100111 => 111001011 110101000 => 111010001 110101001 => 111010010 110101010 => 111010101 110101011 => 111010101 110101100 => 111010101 110101101 => 111010110 110101110 => 111010111 110101111 => 111010111 110110000 => 111010001 110110001 => 111010010 110110010 => 111010101 110110011 => 111010101 110110100 => 111011001 110110101 => 111011010 110110110 => 111011011 110110111 => 111011011 110111000 => 111011001 110111001 => 111011010 110111010 => 111011101 110111011 => 111011101 110111100 => 111011101 110111101 => 111011110 110111110 => 111011111 110111111 => 111011111 111000000 => 111000001 111000001 => 111000010 111000010 => 111000101 111000011 => 111000101 111000100 => 111001001 111000101 => 111001010 111000110 => 111001011 111000111 => 111001011 111001000 => 111010001 111001001 => 111010010 111001010 => 111010101 111001011 => 111010101 111001100 => 111010101 111001101 => 111010110 111001110 => 111010111 111001111 => 111010111 111010000 => 111100001 111010001 => 111100010 111010010 => 111100101 111010011 => 111100101 111010100 => 111101001 111010101 => 111101010 111010110 => 111101011 111010111 => 111101011 111011000 => 111101001 111011001 => 111101010 111011010 => 111101101 111011011 => 111101101 111011100 => 111101101 111011101 => 111101110 111011110 => 111101111 111011111 => 111101111 111100000 => 111100001 111100001 => 111100010 111100010 => 111100101 111100011 => 111100101 111100100 => 111101001 111100101 => 111101010 111100110 => 111101011 111100111 => 111101011 111101000 => 111110001 111101001 => 111110010 111101010 => 111110101 111101011 => 111110101 111101100 => 111110101 111101101 => 111110110 111101110 => 111110111 111101111 => 111110111 111110000 => 111110001 111110001 => 111110010 111110010 => 111110101 111110011 => 111110101 111110100 => 111111001 111110101 => 111111010 111110110 => 111111011 111110111 => 111111011 111111000 => 111111001 111111001 => 111111010 111111010 => 111111101 111111011 => 111111101 111111100 => 111111101 111111101 => 111111110 111111110 => 111111111 111111111 => 111111111 1010101010 => 1101010101 1010101100 => 1101010101 1010110010 => 1101010101 1010110100 => 1101011001 1010111000 => 1101011001 1011001010 => 1101010101 1011001100 => 1101010101 1011010010 => 1101100101 1011010100 => 1101101001 1011011000 => 1101101001 1011100010 => 1101100101 1011100100 => 1101101001 1011101000 => 1101110001 1011110000 => 1101110001 1100101010 => 1101010101 1100101100 => 1101010101 1100110010 => 1101010101 1100110100 => 1101011001 1100111000 => 1101011001 1101001010 => 1110010101 1101001100 => 1110010101 1101010010 => 1110100101 1101010100 => 1110101001 1101011000 => 1110101001 1101100010 => 1110100101 1101100100 => 1110101001 1101101000 => 1110110001 1101110000 => 1110110001 1110001010 => 1110010101 1110001100 => 1110010101 1110010010 => 1110100101 1110010100 => 1110101001 1110011000 => 1110101001 1110100010 => 1111000101 1110100100 => 1111001001 1110101000 => 1111010001 1110110000 => 1111010001 1111000010 => 1111000101 1111000100 => 1111001001 1111001000 => 1111010001 1111010000 => 1111100001 1111100000 => 1111100001 101010101010 => 110101010101 101010101100 => 110101010101 101010110010 => 110101010101 101010110100 => 110101011001 101010111000 => 110101011001 101011001010 => 110101010101 101011001100 => 110101010101 101011010010 => 110101100101 101011010100 => 110101101001 101011011000 => 110101101001 101011100010 => 110101100101 101011100100 => 110101101001 101011101000 => 110101110001 101011110000 => 110101110001 101100101010 => 110101010101 101100101100 => 110101010101 101100110010 => 110101010101 101100110100 => 110101011001 101100111000 => 110101011001 101101001010 => 110110010101 101101001100 => 110110010101 101101010010 => 110110100101 101101010100 => 110110101001 101101011000 => 110110101001 101101100010 => 110110100101 101101100100 => 110110101001 101101101000 => 110110110001 101101110000 => 110110110001 101110001010 => 110110010101 101110001100 => 110110010101 101110010010 => 110110100101 101110010100 => 110110101001 101110011000 => 110110101001 101110100010 => 110111000101 101110100100 => 110111001001 101110101000 => 110111010001 101110110000 => 110111010001 101111000010 => 110111000101 101111000100 => 110111001001 101111001000 => 110111010001 101111010000 => 110111100001 101111100000 => 110111100001 110010101010 => 110101010101 110010101100 => 110101010101 110010110010 => 110101010101 110010110100 => 110101011001 110010111000 => 110101011001 110011001010 => 110101010101 110011001100 => 110101010101 110011010010 => 110101100101 110011010100 => 110101101001 110011011000 => 110101101001 110011100010 => 110101100101 110011100100 => 110101101001 110011101000 => 110101110001 110011110000 => 110101110001 110100101010 => 111001010101 110100101100 => 111001010101 110100110010 => 111001010101 110100110100 => 111001011001 110100111000 => 111001011001 110101001010 => 111010010101 110101001100 => 111010010101 110101010010 => 111010100101 110101010100 => 111010101001 110101011000 => 111010101001 110101100010 => 111010100101 110101100100 => 111010101001 110101101000 => 111010110001 110101110000 => 111010110001 110110001010 => 111010010101 110110001100 => 111010010101 110110010010 => 111010100101 110110010100 => 111010101001 110110011000 => 111010101001 110110100010 => 111011000101 110110100100 => 111011001001 110110101000 => 111011010001 110110110000 => 111011010001 110111000010 => 111011000101 110111000100 => 111011001001 110111001000 => 111011010001 110111010000 => 111011100001 110111100000 => 111011100001 111000101010 => 111001010101 111000101100 => 111001010101 111000110010 => 111001010101 111000110100 => 111001011001 111000111000 => 111001011001 111001001010 => 111010010101 111001001100 => 111010010101 111001010010 => 111010100101 111001010100 => 111010101001 111001011000 => 111010101001 111001100010 => 111010100101 111001100100 => 111010101001 111001101000 => 111010110001 111001110000 => 111010110001 111010001010 => 111100010101 111010001100 => 111100010101 111010010010 => 111100100101 111010010100 => 111100101001 111010011000 => 111100101001 111010100010 => 111101000101 111010100100 => 111101001001 111010101000 => 111101010001 111010110000 => 111101010001 111011000010 => 111101000101 111011000100 => 111101001001 111011001000 => 111101010001 111011010000 => 111101100001 111011100000 => 111101100001 111100001010 => 111100010101 111100001100 => 111100010101 111100010010 => 111100100101 111100010100 => 111100101001 111100011000 => 111100101001 111100100010 => 111101000101 111100100100 => 111101001001 111100101000 => 111101010001 111100110000 => 111101010001 111101000010 => 111110000101 111101000100 => 111110001001 111101001000 => 111110010001 111101010000 => 111110100001 111101100000 => 111110100001 111110000010 => 111110000101 111110000100 => 111110001001 111110001000 => 111110010001 111110010000 => 111110100001 111110100000 => 111111000001 111111000000 => 111111000001 10101010101010 => 11010101010101 10101010101100 => 11010101010101 10101010110100 => 11010101011001 10101010111000 => 11010101011001 ----------------------------------------------------------------------------- Created: May 19, 2021 at 17:35 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 19, 2021 at 17:35 by Martin Rubey