***************************************************************************** * 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: St000519 ----------------------------------------------------------------------------- Collection: Binary words ----------------------------------------------------------------------------- Description: The largest length of a factor maximising the subword complexity. Let $p_w(n)$ be the number of distinct factors of length $n$. Then the statistic is the largest $n$ such that $p_w(n)$ is maximal: $$H_w = \max\{n: p_w(n)\text{ is maximal}\}$$ A related statistic is the number of distinct factors of arbitrary length, also known as subword complexity, [[St000294]]. ----------------------------------------------------------------------------- References: [1] Berstel, J. 50ieme Seminaire Lotharingien de Combinatoire, [[www-igm.univ-mlv.fr/~berstel/Exposes/2003-03-23Lotharingien.pdf]] ----------------------------------------------------------------------------- Code: def statistic(w): m = max(len(w.factor_set(n=n)) for n in range(len(w))) return max(n for n in range(len(w)) if len(w.factor_set(n=n)) == m) ----------------------------------------------------------------------------- Statistic values: 0 => 0 1 => 0 00 => 1 01 => 1 10 => 1 11 => 1 000 => 2 001 => 2 010 => 2 011 => 2 100 => 2 101 => 2 110 => 2 111 => 2 0000 => 3 0001 => 3 0010 => 2 0011 => 2 0100 => 2 0101 => 3 0110 => 2 0111 => 3 1000 => 3 1001 => 2 1010 => 3 1011 => 2 1100 => 2 1101 => 2 1110 => 3 1111 => 3 00000 => 4 00001 => 4 00010 => 3 00011 => 3 00100 => 3 00101 => 3 00110 => 2 00111 => 3 01000 => 3 01001 => 3 01010 => 4 01011 => 3 01100 => 2 01101 => 3 01110 => 3 01111 => 4 10000 => 4 10001 => 3 10010 => 3 10011 => 2 10100 => 3 10101 => 4 10110 => 3 10111 => 3 11000 => 3 11001 => 2 11010 => 3 11011 => 3 11100 => 3 11101 => 3 11110 => 4 11111 => 4 000000 => 5 000001 => 5 000010 => 4 000011 => 4 000100 => 3 000101 => 3 000110 => 3 000111 => 3 001000 => 3 001001 => 4 001010 => 4 001011 => 3 001100 => 3 001101 => 3 001110 => 3 001111 => 4 010000 => 4 010001 => 3 010010 => 4 010011 => 3 010100 => 4 010101 => 5 010110 => 3 010111 => 3 011000 => 3 011001 => 3 011010 => 3 011011 => 4 011100 => 3 011101 => 3 011110 => 4 011111 => 5 100000 => 5 100001 => 4 100010 => 3 100011 => 3 100100 => 4 100101 => 3 100110 => 3 100111 => 3 101000 => 3 101001 => 3 101010 => 5 101011 => 4 101100 => 3 101101 => 4 101110 => 3 101111 => 4 110000 => 4 110001 => 3 110010 => 3 110011 => 3 110100 => 3 110101 => 4 110110 => 4 110111 => 3 111000 => 3 111001 => 3 111010 => 3 111011 => 3 111100 => 4 111101 => 4 111110 => 5 111111 => 5 0000000 => 6 0000001 => 6 0000010 => 5 0000011 => 5 0000100 => 4 0000101 => 4 0000110 => 4 0000111 => 4 0001000 => 4 0001001 => 4 0001010 => 4 0001011 => 3 0001100 => 3 0001101 => 3 0001110 => 3 0001111 => 4 0010000 => 4 0010001 => 4 0010010 => 5 0010011 => 4 0010100 => 4 0010101 => 5 0010110 => 3 0010111 => 3 0011000 => 3 0011001 => 4 0011010 => 3 0011011 => 4 0011100 => 3 0011101 => 3 0011110 => 4 0011111 => 5 0100000 => 5 0100001 => 4 0100010 => 4 0100011 => 3 0100100 => 5 0100101 => 4 0100110 => 3 0100111 => 3 0101000 => 4 0101001 => 4 0101010 => 6 0101011 => 5 0101100 => 3 0101101 => 4 0101110 => 3 0101111 => 4 0110000 => 4 0110001 => 3 0110010 => 3 0110011 => 4 0110100 => 3 0110101 => 4 0110110 => 5 0110111 => 4 0111000 => 3 0111001 => 3 0111010 => 3 0111011 => 4 0111100 => 4 0111101 => 4 0111110 => 5 0111111 => 6 1000000 => 6 1000001 => 5 1000010 => 4 1000011 => 4 1000100 => 4 1000101 => 3 1000110 => 3 1000111 => 3 1001000 => 4 1001001 => 5 1001010 => 4 1001011 => 3 1001100 => 4 1001101 => 3 1001110 => 3 1001111 => 4 1010000 => 4 1010001 => 3 1010010 => 4 1010011 => 3 1010100 => 5 1010101 => 6 1010110 => 4 1010111 => 4 1011000 => 3 1011001 => 3 1011010 => 4 1011011 => 5 1011100 => 3 1011101 => 4 1011110 => 4 1011111 => 5 1100000 => 5 1100001 => 4 1100010 => 3 1100011 => 3 1100100 => 4 1100101 => 3 1100110 => 4 1100111 => 3 1101000 => 3 1101001 => 3 1101010 => 5 1101011 => 4 1101100 => 4 1101101 => 5 1101110 => 4 1101111 => 4 1110000 => 4 1110001 => 3 1110010 => 3 1110011 => 3 1110100 => 3 1110101 => 4 1110110 => 4 1110111 => 4 1111000 => 4 1111001 => 4 1111010 => 4 1111011 => 4 1111100 => 5 1111101 => 5 1111110 => 6 1111111 => 6 00000000 => 7 00000001 => 7 00000010 => 6 00000011 => 6 00000100 => 5 00000101 => 5 00000110 => 5 00000111 => 5 00001000 => 4 00001001 => 4 00001010 => 4 00001011 => 4 00001100 => 4 00001101 => 4 00001110 => 4 00001111 => 4 00010000 => 4 00010001 => 5 00010010 => 5 00010011 => 4 00010100 => 4 00010101 => 5 00010110 => 3 00010111 => 3 00011000 => 4 00011001 => 4 00011010 => 3 00011011 => 4 00011100 => 3 00011101 => 3 00011110 => 4 00011111 => 5 00100000 => 5 00100001 => 4 00100010 => 5 00100011 => 4 00100100 => 6 00100101 => 5 00100110 => 4 00100111 => 4 00101000 => 4 00101001 => 4 00101010 => 6 00101011 => 5 00101100 => 3 00101101 => 4 00101110 => 3 00101111 => 4 00110000 => 4 00110001 => 4 00110010 => 4 00110011 => 5 00110100 => 3 00110101 => 4 00110110 => 5 00110111 => 4 00111000 => 3 00111001 => 4 00111010 => 3 00111011 => 4 00111100 => 4 00111101 => 4 00111110 => 5 00111111 => 6 01000000 => 6 01000001 => 5 01000010 => 4 01000011 => 4 01000100 => 5 01000101 => 4 01000110 => 3 01000111 => 3 01001000 => 5 01001001 => 6 01001010 => 4 01001011 => 4 01001100 => 4 01001101 => 3 01001110 => 3 01001111 => 4 01010000 => 4 01010001 => 4 01010010 => 4 01010011 => 4 01010100 => 6 01010101 => 7 01010110 => 5 01010111 => 5 01011000 => 3 01011001 => 3 01011010 => 4 01011011 => 5 01011100 => 3 01011101 => 4 01011110 => 4 01011111 => 5 01100000 => 5 01100001 => 4 01100010 => 3 01100011 => 4 01100100 => 4 01100101 => 3 01100110 => 5 01100111 => 4 01101000 => 3 01101001 => 3 01101010 => 5 01101011 => 4 01101100 => 5 01101101 => 6 01101110 => 4 01101111 => 4 01110000 => 4 01110001 => 3 01110010 => 3 01110011 => 4 01110100 => 3 01110101 => 4 01110110 => 4 01110111 => 5 01111000 => 4 01111001 => 4 01111010 => 4 01111011 => 4 01111100 => 5 01111101 => 5 01111110 => 6 01111111 => 7 10000000 => 7 10000001 => 6 10000010 => 5 10000011 => 5 10000100 => 4 10000101 => 4 10000110 => 4 10000111 => 4 10001000 => 5 10001001 => 4 10001010 => 4 10001011 => 3 10001100 => 4 10001101 => 3 10001110 => 3 10001111 => 4 10010000 => 4 10010001 => 4 10010010 => 6 10010011 => 5 10010100 => 4 10010101 => 5 10010110 => 3 10010111 => 3 10011000 => 4 10011001 => 5 10011010 => 3 10011011 => 4 10011100 => 4 10011101 => 3 10011110 => 4 10011111 => 5 10100000 => 5 10100001 => 4 10100010 => 4 10100011 => 3 10100100 => 5 10100101 => 4 10100110 => 3 10100111 => 3 10101000 => 5 10101001 => 5 10101010 => 7 10101011 => 6 10101100 => 4 10101101 => 4 10101110 => 4 10101111 => 4 10110000 => 4 10110001 => 3 10110010 => 3 10110011 => 4 10110100 => 4 10110101 => 4 10110110 => 6 10110111 => 5 10111000 => 3 10111001 => 3 10111010 => 4 10111011 => 5 10111100 => 4 10111101 => 4 10111110 => 5 10111111 => 6 11000000 => 6 11000001 => 5 11000010 => 4 11000011 => 4 11000100 => 4 11000101 => 3 11000110 => 4 11000111 => 3 11001000 => 4 11001001 => 5 11001010 => 4 11001011 => 3 11001100 => 5 11001101 => 4 11001110 => 4 11001111 => 4 11010000 => 4 11010001 => 3 11010010 => 4 11010011 => 3 11010100 => 5 11010101 => 6 11010110 => 4 11010111 => 4 11011000 => 4 11011001 => 4 11011010 => 5 11011011 => 6 11011100 => 4 11011101 => 5 11011110 => 4 11011111 => 5 11100000 => 5 11100001 => 4 11100010 => 3 11100011 => 3 11100100 => 4 11100101 => 3 11100110 => 4 11100111 => 4 11101000 => 3 11101001 => 3 11101010 => 5 11101011 => 4 11101100 => 4 11101101 => 5 11101110 => 5 11101111 => 4 11110000 => 4 11110001 => 4 11110010 => 4 11110011 => 4 11110100 => 4 11110101 => 4 11110110 => 4 11110111 => 4 11111000 => 5 11111001 => 5 11111010 => 5 11111011 => 5 11111100 => 6 11111101 => 6 11111110 => 7 11111111 => 7 000000000 => 8 000000001 => 8 000000010 => 7 000000011 => 7 000000100 => 6 000000101 => 6 000000110 => 6 000000111 => 6 000001000 => 5 000001001 => 5 000001010 => 5 000001011 => 5 000001100 => 5 000001101 => 5 000001110 => 5 000001111 => 5 000010000 => 5 000010001 => 5 000010010 => 5 000010011 => 4 000010100 => 4 000010101 => 5 000010110 => 4 000010111 => 4 000011000 => 4 000011001 => 4 000011010 => 4 000011011 => 4 000011100 => 4 000011101 => 4 000011110 => 4 000011111 => 5 000100000 => 5 000100001 => 5 000100010 => 6 000100011 => 5 000100100 => 6 000100101 => 5 000100110 => 4 000100111 => 4 000101000 => 4 000101001 => 4 000101010 => 6 000101011 => 5 000101100 => 3 000101101 => 4 000101110 => 3 000101111 => 4 000110000 => 4 000110001 => 5 000110010 => 4 000110011 => 5 000110100 => 3 000110101 => 4 000110110 => 5 000110111 => 4 000111000 => 4 000111001 => 4 000111010 => 3 000111011 => 4 000111100 => 4 000111101 => 4 000111110 => 5 000111111 => 6 001000000 => 6 001000001 => 5 001000010 => 5 001000011 => 4 001000100 => 6 001000101 => 5 001000110 => 4 001000111 => 4 001001000 => 6 001001001 => 7 001001010 => 5 001001011 => 5 001001100 => 4 001001101 => 4 001001110 => 4 001001111 => 4 001010000 => 4 001010001 => 4 001010010 => 5 001010011 => 4 001010100 => 6 001010101 => 7 001010110 => 5 001010111 => 5 001011000 => 3 001011001 => 4 001011010 => 4 001011011 => 5 001011100 => 3 001011101 => 4 001011110 => 4 001011111 => 5 001100000 => 5 001100001 => 4 001100010 => 4 001100011 => 5 001100100 => 4 001100101 => 4 001100110 => 6 001100111 => 5 001101000 => 3 001101001 => 4 001101010 => 5 001101011 => 4 001101100 => 5 001101101 => 6 001101110 => 4 001101111 => 4 001110000 => 4 001110001 => 4 001110010 => 4 001110011 => 5 001110100 => 3 001110101 => 4 001110110 => 4 001110111 => 5 001111000 => 4 001111001 => 4 001111010 => 4 001111011 => 4 001111100 => 5 001111101 => 5 001111110 => 6 001111111 => 7 010000000 => 7 010000001 => 6 010000010 => 5 010000011 => 5 010000100 => 5 010000101 => 4 010000110 => 4 010000111 => 4 010001000 => 6 010001001 => 5 010001010 => 4 010001011 => 4 010001100 => 4 010001101 => 3 010001110 => 3 010001111 => 4 010010000 => 5 010010001 => 5 010010010 => 7 010010011 => 6 010010100 => 5 010010101 => 5 010010110 => 4 010010111 => 4 010011000 => 4 010011001 => 5 010011010 => 4 010011011 => 4 010011100 => 4 010011101 => 3 010011110 => 4 010011111 => 5 010100000 => 5 010100001 => 4 010100010 => 4 010100011 => 4 010100100 => 5 010100101 => 5 010100110 => 4 010100111 => 4 010101000 => 6 010101001 => 6 010101010 => 8 010101011 => 7 010101100 => 5 010101101 => 5 010101110 => 5 010101111 => 5 010110000 => 4 010110001 => 3 010110010 => 4 010110011 => 4 010110100 => 4 010110101 => 5 010110110 => 6 010110111 => 5 010111000 => 3 010111001 => 3 010111010 => 4 010111011 => 5 010111100 => 4 010111101 => 4 010111110 => 5 010111111 => 6 011000000 => 6 011000001 => 5 011000010 => 4 011000011 => 4 011000100 => 4 011000101 => 3 011000110 => 5 011000111 => 4 011001000 => 4 011001001 => 5 011001010 => 4 011001011 => 4 011001100 => 6 011001101 => 5 011001110 => 4 011001111 => 4 011010000 => 4 011010001 => 3 011010010 => 4 011010011 => 4 011010100 => 5 011010101 => 6 011010110 => 5 011010111 => 4 011011000 => 5 011011001 => 5 011011010 => 6 011011011 => 7 011011100 => 4 011011101 => 5 011011110 => 4 011011111 => 5 011100000 => 5 011100001 => 4 011100010 => 3 011100011 => 4 011100100 => 4 011100101 => 3 011100110 => 4 011100111 => 5 011101000 => 3 011101001 => 3 011101010 => 5 011101011 => 4 011101100 => 4 011101101 => 5 011101110 => 6 011101111 => 5 011110000 => 4 011110001 => 4 011110010 => 4 011110011 => 4 011110100 => 4 011110101 => 4 011110110 => 4 011110111 => 5 011111000 => 5 011111001 => 5 011111010 => 5 011111011 => 5 011111100 => 6 011111101 => 6 011111110 => 7 011111111 => 8 100000000 => 8 100000001 => 7 100000010 => 6 100000011 => 6 100000100 => 5 100000101 => 5 100000110 => 5 100000111 => 5 100001000 => 5 100001001 => 4 100001010 => 4 100001011 => 4 100001100 => 4 100001101 => 4 100001110 => 4 100001111 => 4 100010000 => 5 100010001 => 6 100010010 => 5 100010011 => 4 100010100 => 4 100010101 => 5 100010110 => 3 100010111 => 3 100011000 => 5 100011001 => 4 100011010 => 3 100011011 => 4 100011100 => 4 100011101 => 3 100011110 => 4 100011111 => 5 100100000 => 5 100100001 => 4 100100010 => 5 100100011 => 4 100100100 => 7 100100101 => 6 100100110 => 5 100100111 => 5 100101000 => 4 100101001 => 5 100101010 => 6 100101011 => 5 100101100 => 4 100101101 => 4 100101110 => 3 100101111 => 4 100110000 => 4 100110001 => 4 100110010 => 5 100110011 => 6 100110100 => 4 100110101 => 4 100110110 => 5 100110111 => 4 100111000 => 4 100111001 => 5 100111010 => 3 100111011 => 4 100111100 => 4 100111101 => 4 100111110 => 5 100111111 => 6 101000000 => 6 101000001 => 5 101000010 => 4 101000011 => 4 101000100 => 5 101000101 => 4 101000110 => 3 101000111 => 3 101001000 => 5 101001001 => 6 101001010 => 5 101001011 => 4 101001100 => 4 101001101 => 4 101001110 => 3 101001111 => 4 101010000 => 5 101010001 => 5 101010010 => 5 101010011 => 5 101010100 => 7 101010101 => 8 101010110 => 6 101010111 => 6 101011000 => 4 101011001 => 4 101011010 => 5 101011011 => 5 101011100 => 4 101011101 => 4 101011110 => 4 101011111 => 5 101100000 => 5 101100001 => 4 101100010 => 3 101100011 => 4 101100100 => 4 101100101 => 4 101100110 => 5 101100111 => 4 101101000 => 4 101101001 => 4 101101010 => 5 101101011 => 5 101101100 => 6 101101101 => 7 101101110 => 5 101101111 => 5 101110000 => 4 101110001 => 3 101110010 => 3 101110011 => 4 101110100 => 4 101110101 => 4 101110110 => 5 101110111 => 6 101111000 => 4 101111001 => 4 101111010 => 4 101111011 => 5 101111100 => 5 101111101 => 5 101111110 => 6 101111111 => 7 110000000 => 7 110000001 => 6 110000010 => 5 110000011 => 5 110000100 => 4 110000101 => 4 110000110 => 4 110000111 => 4 110001000 => 5 110001001 => 4 110001010 => 4 110001011 => 3 110001100 => 5 110001101 => 4 110001110 => 4 110001111 => 4 110010000 => 4 110010001 => 4 110010010 => 6 110010011 => 5 110010100 => 4 110010101 => 5 110010110 => 4 110010111 => 3 110011000 => 5 110011001 => 6 110011010 => 4 110011011 => 4 110011100 => 5 110011101 => 4 110011110 => 4 110011111 => 5 110100000 => 5 110100001 => 4 110100010 => 4 110100011 => 3 110100100 => 5 110100101 => 4 110100110 => 4 110100111 => 3 110101000 => 5 110101001 => 5 110101010 => 7 110101011 => 6 110101100 => 4 110101101 => 5 110101110 => 4 110101111 => 4 110110000 => 4 110110001 => 4 110110010 => 4 110110011 => 4 110110100 => 5 110110101 => 5 110110110 => 7 110110111 => 6 110111000 => 4 110111001 => 4 110111010 => 5 110111011 => 6 110111100 => 4 110111101 => 5 110111110 => 5 110111111 => 6 111000000 => 6 111000001 => 5 111000010 => 4 111000011 => 4 111000100 => 4 111000101 => 3 111000110 => 4 111000111 => 4 111001000 => 4 111001001 => 5 111001010 => 4 111001011 => 3 111001100 => 5 111001101 => 4 111001110 => 5 111001111 => 4 111010000 => 4 111010001 => 3 111010010 => 4 111010011 => 3 111010100 => 5 111010101 => 6 111010110 => 4 111010111 => 4 111011000 => 4 111011001 => 4 111011010 => 5 111011011 => 6 111011100 => 5 111011101 => 6 111011110 => 5 111011111 => 5 111100000 => 5 111100001 => 4 111100010 => 4 111100011 => 4 111100100 => 4 111100101 => 4 111100110 => 4 111100111 => 4 111101000 => 4 111101001 => 4 111101010 => 5 111101011 => 4 111101100 => 4 111101101 => 5 111101110 => 5 111101111 => 5 111110000 => 5 111110001 => 5 111110010 => 5 111110011 => 5 111110100 => 5 111110101 => 5 111110110 => 5 111110111 => 5 111111000 => 6 111111001 => 6 111111010 => 6 111111011 => 6 111111100 => 7 111111101 => 7 111111110 => 8 111111111 => 8 0000000001 => 9 0010000001 => 6 0010101101 => 5 0010101011 => 7 0010100111 => 4 0010011101 => 4 0010011011 => 4 0010010111 => 5 0010001111 => 4 0001110101 => 4 0001110011 => 5 0001101101 => 6 0001101011 => 4 0001100111 => 5 0001011101 => 4 0001011011 => 5 0001010111 => 5 0001001111 => 4 0000111101 => 4 0000111011 => 4 0000110111 => 4 0000101111 => 4 0000011111 => 5 0000000000 => 9 0000000110 => 7 0000011000 => 5 0000011110 => 5 0000010010 => 5 0001100000 => 5 0001100110 => 6 0001111000 => 4 0001111110 => 6 0001110010 => 4 0001001000 => 6 0001001110 => 4 0001000010 => 6 0001011010 => 4 0010101010 => 8 0010101000 => 6 0010101100 => 5 0010100100 => 5 0010010100 => 5 0001010100 => 6 0010101110 => 5 0010100000 => 5 0010000100 => 6 0000010100 => 5 0000000010 => 8 0000001110 => 6 0000111110 => 5 0000000100 => 7 0000001010 => 6 0000010110 => 5 0000101110 => 4 0001011110 => 4 0001101110 => 4 0001110110 => 4 0001111010 => 4 0001111100 => 5 0000000101 => 7 0000001101 => 6 0000011101 => 5 0001111101 => 5 0000001001 => 6 0000010101 => 5 0000101101 => 4 0010110001 => 4 0001100001 => 5 0001000001 => 5 0000111111 => 6 0001110100 => 3 0001101100 => 5 0010011100 => 4 0001011100 => 3 0000111100 => 4 0001101010 => 5 0010011010 => 4 0000111010 => 4 0010100110 => 4 0010010110 => 5 0001010110 => 5 0000110110 => 5 0010001110 => 4 0001101001 => 4 0000110001 => 5 0000010001 => 5 0000001100 => 6 0000011001 => 5 0000110011 => 5 0000110100 => 4 0000000011 => 8 0000011011 => 5 0001101111 => 4 0000110101 => 4 0010000010 => 5 0001000011 => 5 0010011110 => 4 0001010000 => 4 0001000100 => 7 0001010101 => 7 0001001011 => 5 0001100011 => 6 0001110111 => 5 0010000000 => 7 0000000111 => 7 0000001111 => 6 0001111111 => 7 0000001011 => 6 0000010111 => 5 0001011111 => 5 0001111001 => 4 0000011010 => 5 0000101010 => 6 0000100101 => 5 0010010001 => 6 0010000101 => 5 0010010101 => 5 0010010011 => 7 0000101011 => 5 0001000111 => 5 0000100111 => 4 0010010010 => 8 0001001010 => 5 0001001001 => 7 0001000101 => 6 0000100011 => 5 0000100100 => 6 0000100010 => 6 0010110000 => 4 0000011100 => 5 0000001000 => 6 0000101100 => 4 0010101111 => 5 0000101000 => 4 0010001000 => 7 0001001100 => 4 0001000110 => 5 0001100100 => 4 0001100010 => 5 0000100110 => 4 0000110010 => 4 0010010000 => 6 0001010010 => 5 0001000000 => 6 0001011001 => 4 0001100101 => 4 0001110001 => 5 0010011001 => 5 0010100101 => 6 0010101001 => 6 0010011111 => 5 0000111001 => 4 0010001101 => 4 0001001101 => 4 0001010001 => 5 0001010011 => 4 0001111011 => 4 0010011000 => 4 0001011000 => 4 0000100000 => 5 0010001011 => 5 0010000111 => 4 0000010011 => 5 0010001100 => 4 0010000110 => 4 0000110000 => 5 0000100001 => 6 0010100011 => 4 0010100001 => 4 0000111000 => 4 0001101000 => 4 0000010000 => 5 0000101001 => 4 0010100010 => 5 0010001001 => 6 0010000011 => 5 0010001010 => 5 0001110000 => 4 ----------------------------------------------------------------------------- Created: Jun 01, 2016 at 09:54 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jun 07, 2016 at 19:55 by Martin Rubey