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* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* 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. *
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-----------------------------------------------------------------------------
Statistic identifier: St000626
-----------------------------------------------------------------------------
Collection: Binary words
-----------------------------------------------------------------------------
Description: The minimal period of a binary word.
This is the smallest natural number $p$ such that $w_i=w_{i+p}$ for all $i\in\{1,\dots,|w|-p\}$.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(w):
return w.minimal_period()
-----------------------------------------------------------------------------
Statistic values:
0 => 1
1 => 1
00 => 1
01 => 2
10 => 2
11 => 1
000 => 1
001 => 3
010 => 2
011 => 3
100 => 3
101 => 2
110 => 3
111 => 1
0000 => 1
0001 => 4
0010 => 3
0011 => 4
0100 => 3
0101 => 2
0110 => 3
0111 => 4
1000 => 4
1001 => 3
1010 => 2
1011 => 3
1100 => 4
1101 => 3
1110 => 4
1111 => 1
00000 => 1
00001 => 5
00010 => 4
00011 => 5
00100 => 3
00101 => 5
00110 => 4
00111 => 5
01000 => 4
01001 => 3
01010 => 2
01011 => 5
01100 => 4
01101 => 3
01110 => 4
01111 => 5
10000 => 5
10001 => 4
10010 => 3
10011 => 4
10100 => 5
10101 => 2
10110 => 3
10111 => 4
11000 => 5
11001 => 4
11010 => 5
11011 => 3
11100 => 5
11101 => 4
11110 => 5
11111 => 1
000000 => 1
000001 => 6
000010 => 5
000011 => 6
000100 => 4
000101 => 6
000110 => 5
000111 => 6
001000 => 4
001001 => 3
001010 => 5
001011 => 6
001100 => 4
001101 => 6
001110 => 5
001111 => 6
010000 => 5
010001 => 4
010010 => 3
010011 => 6
010100 => 5
010101 => 2
010110 => 5
010111 => 6
011000 => 5
011001 => 4
011010 => 5
011011 => 3
011100 => 5
011101 => 4
011110 => 5
011111 => 6
100000 => 6
100001 => 5
100010 => 4
100011 => 5
100100 => 3
100101 => 5
100110 => 4
100111 => 5
101000 => 6
101001 => 5
101010 => 2
101011 => 5
101100 => 6
101101 => 3
101110 => 4
101111 => 5
110000 => 6
110001 => 5
110010 => 6
110011 => 4
110100 => 6
110101 => 5
110110 => 3
110111 => 4
111000 => 6
111001 => 5
111010 => 6
111011 => 4
111100 => 6
111101 => 5
111110 => 6
111111 => 1
0000000 => 1
0000001 => 7
0000010 => 6
0000011 => 7
0000100 => 5
0000101 => 7
0000110 => 6
0000111 => 7
0001000 => 4
0001001 => 7
0001010 => 6
0001011 => 7
0001100 => 5
0001101 => 7
0001110 => 6
0001111 => 7
0010000 => 5
0010001 => 4
0010010 => 3
0010011 => 7
0010100 => 5
0010101 => 7
0010110 => 6
0010111 => 7
0011000 => 5
0011001 => 4
0011010 => 6
0011011 => 7
0011100 => 5
0011101 => 7
0011110 => 6
0011111 => 7
0100000 => 6
0100001 => 5
0100010 => 4
0100011 => 7
0100100 => 3
0100101 => 5
0100110 => 6
0100111 => 7
0101000 => 6
0101001 => 5
0101010 => 2
0101011 => 7
0101100 => 6
0101101 => 5
0101110 => 6
0101111 => 7
0110000 => 6
0110001 => 5
0110010 => 6
0110011 => 4
0110100 => 6
0110101 => 5
0110110 => 3
0110111 => 7
0111000 => 6
0111001 => 5
0111010 => 6
0111011 => 4
0111100 => 6
0111101 => 5
0111110 => 6
0111111 => 7
1000000 => 7
1000001 => 6
1000010 => 5
1000011 => 6
1000100 => 4
1000101 => 6
1000110 => 5
1000111 => 6
1001000 => 7
1001001 => 3
1001010 => 5
1001011 => 6
1001100 => 4
1001101 => 6
1001110 => 5
1001111 => 6
1010000 => 7
1010001 => 6
1010010 => 5
1010011 => 6
1010100 => 7
1010101 => 2
1010110 => 5
1010111 => 6
1011000 => 7
1011001 => 6
1011010 => 5
1011011 => 3
1011100 => 7
1011101 => 4
1011110 => 5
1011111 => 6
1100000 => 7
1100001 => 6
1100010 => 7
1100011 => 5
1100100 => 7
1100101 => 6
1100110 => 4
1100111 => 5
1101000 => 7
1101001 => 6
1101010 => 7
1101011 => 5
1101100 => 7
1101101 => 3
1101110 => 4
1101111 => 5
1110000 => 7
1110001 => 6
1110010 => 7
1110011 => 5
1110100 => 7
1110101 => 6
1110110 => 7
1110111 => 4
1111000 => 7
1111001 => 6
1111010 => 7
1111011 => 5
1111100 => 7
1111101 => 6
1111110 => 7
1111111 => 1
00000000 => 1
00000001 => 8
00000010 => 7
00000011 => 8
00000100 => 6
00000101 => 8
00000110 => 7
00000111 => 8
00001000 => 5
00001001 => 8
00001010 => 7
00001011 => 8
00001100 => 6
00001101 => 8
00001110 => 7
00001111 => 8
00010000 => 5
00010001 => 4
00010010 => 7
00010011 => 8
00010100 => 6
00010101 => 8
00010110 => 7
00010111 => 8
00011000 => 5
00011001 => 8
00011010 => 7
00011011 => 8
00011100 => 6
00011101 => 8
00011110 => 7
00011111 => 8
00100000 => 6
00100001 => 5
00100010 => 4
00100011 => 8
00100100 => 3
00100101 => 8
00100110 => 7
00100111 => 8
00101000 => 6
00101001 => 5
00101010 => 7
00101011 => 8
00101100 => 6
00101101 => 8
00101110 => 7
00101111 => 8
00110000 => 6
00110001 => 5
00110010 => 7
00110011 => 4
00110100 => 6
00110101 => 8
00110110 => 7
00110111 => 8
00111000 => 6
00111001 => 5
00111010 => 7
00111011 => 8
00111100 => 6
00111101 => 8
00111110 => 7
00111111 => 8
01000000 => 7
01000001 => 6
01000010 => 5
01000011 => 8
01000100 => 4
01000101 => 6
01000110 => 7
01000111 => 8
01001000 => 7
01001001 => 3
01001010 => 5
01001011 => 8
01001100 => 7
01001101 => 6
01001110 => 7
01001111 => 8
01010000 => 7
01010001 => 6
01010010 => 5
01010011 => 8
01010100 => 7
01010101 => 2
01010110 => 7
01010111 => 8
01011000 => 7
01011001 => 6
01011010 => 5
01011011 => 8
01011100 => 7
01011101 => 6
01011110 => 7
01011111 => 8
01100000 => 7
01100001 => 6
01100010 => 7
01100011 => 5
01100100 => 7
01100101 => 6
01100110 => 4
01100111 => 8
01101000 => 7
01101001 => 6
01101010 => 7
01101011 => 5
01101100 => 7
01101101 => 3
01101110 => 7
01101111 => 8
01110000 => 7
01110001 => 6
01110010 => 7
01110011 => 5
01110100 => 7
01110101 => 6
01110110 => 7
01110111 => 4
01111000 => 7
01111001 => 6
01111010 => 7
01111011 => 5
01111100 => 7
01111101 => 6
01111110 => 7
01111111 => 8
10000000 => 8
10000001 => 7
10000010 => 6
10000011 => 7
10000100 => 5
10000101 => 7
10000110 => 6
10000111 => 7
10001000 => 4
10001001 => 7
10001010 => 6
10001011 => 7
10001100 => 5
10001101 => 7
10001110 => 6
10001111 => 7
10010000 => 8
10010001 => 7
10010010 => 3
10010011 => 7
10010100 => 5
10010101 => 7
10010110 => 6
10010111 => 7
10011000 => 8
10011001 => 4
10011010 => 6
10011011 => 7
10011100 => 5
10011101 => 7
10011110 => 6
10011111 => 7
10100000 => 8
10100001 => 7
10100010 => 6
10100011 => 7
10100100 => 8
10100101 => 5
10100110 => 6
10100111 => 7
10101000 => 8
10101001 => 7
10101010 => 2
10101011 => 7
10101100 => 8
10101101 => 5
10101110 => 6
10101111 => 7
10110000 => 8
10110001 => 7
10110010 => 6
10110011 => 7
10110100 => 8
10110101 => 5
10110110 => 3
10110111 => 7
10111000 => 8
10111001 => 7
10111010 => 6
10111011 => 4
10111100 => 8
10111101 => 5
10111110 => 6
10111111 => 7
11000000 => 8
11000001 => 7
11000010 => 8
11000011 => 6
11000100 => 8
11000101 => 7
11000110 => 5
11000111 => 6
11001000 => 8
11001001 => 7
11001010 => 8
11001011 => 6
11001100 => 4
11001101 => 7
11001110 => 5
11001111 => 6
11010000 => 8
11010001 => 7
11010010 => 8
11010011 => 6
11010100 => 8
11010101 => 7
11010110 => 5
11010111 => 6
11011000 => 8
11011001 => 7
11011010 => 8
11011011 => 3
11011100 => 8
11011101 => 4
11011110 => 5
11011111 => 6
11100000 => 8
11100001 => 7
11100010 => 8
11100011 => 6
11100100 => 8
11100101 => 7
11100110 => 8
11100111 => 5
11101000 => 8
11101001 => 7
11101010 => 8
11101011 => 6
11101100 => 8
11101101 => 7
11101110 => 4
11101111 => 5
11110000 => 8
11110001 => 7
11110010 => 8
11110011 => 6
11110100 => 8
11110101 => 7
11110110 => 8
11110111 => 5
11111000 => 8
11111001 => 7
11111010 => 8
11111011 => 6
11111100 => 8
11111101 => 7
11111110 => 8
11111111 => 1
000000000 => 1
000000001 => 9
000000010 => 8
000000011 => 9
000000100 => 7
000000101 => 9
000000110 => 8
000000111 => 9
000001000 => 6
000001001 => 9
000001010 => 8
000001011 => 9
000001100 => 7
000001101 => 9
000001110 => 8
000001111 => 9
000010000 => 5
000010001 => 9
000010010 => 8
000010011 => 9
000010100 => 7
000010101 => 9
000010110 => 8
000010111 => 9
000011000 => 6
000011001 => 9
000011010 => 8
000011011 => 9
000011100 => 7
000011101 => 9
000011110 => 8
000011111 => 9
000100000 => 6
000100001 => 5
000100010 => 4
000100011 => 9
000100100 => 7
000100101 => 9
000100110 => 8
000100111 => 9
000101000 => 6
000101001 => 9
000101010 => 8
000101011 => 9
000101100 => 7
000101101 => 9
000101110 => 8
000101111 => 9
000110000 => 6
000110001 => 5
000110010 => 8
000110011 => 9
000110100 => 7
000110101 => 9
000110110 => 8
000110111 => 9
000111000 => 6
000111001 => 9
000111010 => 8
000111011 => 9
000111100 => 7
000111101 => 9
000111110 => 8
000111111 => 9
001000000 => 7
001000001 => 6
001000010 => 5
001000011 => 9
001000100 => 4
001000101 => 9
001000110 => 8
001000111 => 9
001001000 => 7
001001001 => 3
001001010 => 8
001001011 => 9
001001100 => 7
001001101 => 9
001001110 => 8
001001111 => 9
001010000 => 7
001010001 => 6
001010010 => 5
001010011 => 9
001010100 => 7
001010101 => 9
001010110 => 8
001010111 => 9
001011000 => 7
001011001 => 6
001011010 => 8
001011011 => 9
001011100 => 7
001011101 => 9
001011110 => 8
001011111 => 9
001100000 => 7
001100001 => 6
001100010 => 8
001100011 => 5
001100100 => 7
001100101 => 9
001100110 => 4
001100111 => 9
001101000 => 7
001101001 => 6
001101010 => 8
001101011 => 9
001101100 => 7
001101101 => 9
001101110 => 8
001101111 => 9
001110000 => 7
001110001 => 6
001110010 => 8
001110011 => 5
001110100 => 7
001110101 => 9
001110110 => 8
001110111 => 9
001111000 => 7
001111001 => 6
001111010 => 8
001111011 => 9
001111100 => 7
001111101 => 9
001111110 => 8
001111111 => 9
010000000 => 8
010000001 => 7
010000010 => 6
010000011 => 9
010000100 => 5
010000101 => 7
010000110 => 8
010000111 => 9
010001000 => 4
010001001 => 7
010001010 => 6
010001011 => 9
010001100 => 8
010001101 => 7
010001110 => 8
010001111 => 9
010010000 => 8
010010001 => 7
010010010 => 3
010010011 => 9
010010100 => 5
010010101 => 7
010010110 => 8
010010111 => 9
010011000 => 8
010011001 => 7
010011010 => 6
010011011 => 9
010011100 => 8
010011101 => 7
010011110 => 8
010011111 => 9
010100000 => 8
010100001 => 7
010100010 => 6
010100011 => 9
010100100 => 8
010100101 => 5
010100110 => 8
010100111 => 9
010101000 => 8
010101001 => 7
010101010 => 2
010101011 => 9
010101100 => 8
010101101 => 7
010101110 => 8
010101111 => 9
010110000 => 8
010110001 => 7
010110010 => 6
010110011 => 9
010110100 => 8
010110101 => 5
010110110 => 8
010110111 => 9
010111000 => 8
010111001 => 7
010111010 => 6
010111011 => 9
010111100 => 8
010111101 => 7
010111110 => 8
010111111 => 9
011000000 => 8
011000001 => 7
011000010 => 8
011000011 => 6
011000100 => 8
011000101 => 7
011000110 => 5
011000111 => 9
011001000 => 8
011001001 => 7
011001010 => 8
011001011 => 6
011001100 => 4
011001101 => 7
011001110 => 8
011001111 => 9
011010000 => 8
011010001 => 7
011010010 => 8
011010011 => 6
011010100 => 8
011010101 => 7
011010110 => 5
011010111 => 9
011011000 => 8
011011001 => 7
011011010 => 8
011011011 => 3
011011100 => 8
011011101 => 7
011011110 => 8
011011111 => 9
011100000 => 8
011100001 => 7
011100010 => 8
011100011 => 6
011100100 => 8
011100101 => 7
011100110 => 8
011100111 => 5
011101000 => 8
011101001 => 7
011101010 => 8
011101011 => 6
011101100 => 8
011101101 => 7
011101110 => 4
011101111 => 9
011110000 => 8
011110001 => 7
011110010 => 8
011110011 => 6
011110100 => 8
011110101 => 7
011110110 => 8
011110111 => 5
011111000 => 8
011111001 => 7
011111010 => 8
011111011 => 6
011111100 => 8
011111101 => 7
011111110 => 8
011111111 => 9
100000000 => 9
100000001 => 8
100000010 => 7
100000011 => 8
100000100 => 6
100000101 => 8
100000110 => 7
100000111 => 8
100001000 => 5
100001001 => 8
100001010 => 7
100001011 => 8
100001100 => 6
100001101 => 8
100001110 => 7
100001111 => 8
100010000 => 9
100010001 => 4
100010010 => 7
100010011 => 8
100010100 => 6
100010101 => 8
100010110 => 7
100010111 => 8
100011000 => 5
100011001 => 8
100011010 => 7
100011011 => 8
100011100 => 6
100011101 => 8
100011110 => 7
100011111 => 8
100100000 => 9
100100001 => 8
100100010 => 7
100100011 => 8
100100100 => 3
100100101 => 8
100100110 => 7
100100111 => 8
100101000 => 9
100101001 => 5
100101010 => 7
100101011 => 8
100101100 => 6
100101101 => 8
100101110 => 7
100101111 => 8
100110000 => 9
100110001 => 8
100110010 => 7
100110011 => 4
100110100 => 6
100110101 => 8
100110110 => 7
100110111 => 8
100111000 => 9
100111001 => 5
100111010 => 7
100111011 => 8
100111100 => 6
100111101 => 8
100111110 => 7
100111111 => 8
101000000 => 9
101000001 => 8
101000010 => 7
101000011 => 8
101000100 => 9
101000101 => 6
101000110 => 7
101000111 => 8
101001000 => 9
101001001 => 8
101001010 => 5
101001011 => 8
101001100 => 9
101001101 => 6
101001110 => 7
101001111 => 8
101010000 => 9
101010001 => 8
101010010 => 7
101010011 => 8
101010100 => 9
101010101 => 2
101010110 => 7
101010111 => 8
101011000 => 9
101011001 => 8
101011010 => 5
101011011 => 8
101011100 => 9
101011101 => 6
101011110 => 7
101011111 => 8
101100000 => 9
101100001 => 8
101100010 => 7
101100011 => 8
101100100 => 9
101100101 => 6
101100110 => 7
101100111 => 8
101101000 => 9
101101001 => 8
101101010 => 7
101101011 => 5
101101100 => 9
101101101 => 3
101101110 => 7
101101111 => 8
101110000 => 9
101110001 => 8
101110010 => 7
101110011 => 8
101110100 => 9
101110101 => 6
101110110 => 7
101110111 => 4
101111000 => 9
101111001 => 8
101111010 => 7
101111011 => 5
101111100 => 9
101111101 => 6
101111110 => 7
101111111 => 8
110000000 => 9
110000001 => 8
110000010 => 9
110000011 => 7
110000100 => 9
110000101 => 8
110000110 => 6
110000111 => 7
110001000 => 9
110001001 => 8
110001010 => 9
110001011 => 7
110001100 => 5
110001101 => 8
110001110 => 6
110001111 => 7
110010000 => 9
110010001 => 8
110010010 => 9
110010011 => 7
110010100 => 9
110010101 => 8
110010110 => 6
110010111 => 7
110011000 => 9
110011001 => 4
110011010 => 9
110011011 => 7
110011100 => 5
110011101 => 8
110011110 => 6
110011111 => 7
110100000 => 9
110100001 => 8
110100010 => 9
110100011 => 7
110100100 => 9
110100101 => 8
110100110 => 6
110100111 => 7
110101000 => 9
110101001 => 8
110101010 => 9
110101011 => 7
110101100 => 9
110101101 => 5
110101110 => 6
110101111 => 7
110110000 => 9
110110001 => 8
110110010 => 9
110110011 => 7
110110100 => 9
110110101 => 8
110110110 => 3
110110111 => 7
110111000 => 9
110111001 => 8
110111010 => 9
110111011 => 4
110111100 => 9
110111101 => 5
110111110 => 6
110111111 => 7
111000000 => 9
111000001 => 8
111000010 => 9
111000011 => 7
111000100 => 9
111000101 => 8
111000110 => 9
111000111 => 6
111001000 => 9
111001001 => 8
111001010 => 9
111001011 => 7
111001100 => 9
111001101 => 8
111001110 => 5
111001111 => 6
111010000 => 9
111010001 => 8
111010010 => 9
111010011 => 7
111010100 => 9
111010101 => 8
111010110 => 9
111010111 => 6
111011000 => 9
111011001 => 8
111011010 => 9
111011011 => 7
111011100 => 9
111011101 => 4
111011110 => 5
111011111 => 6
111100000 => 9
111100001 => 8
111100010 => 9
111100011 => 7
111100100 => 9
111100101 => 8
111100110 => 9
111100111 => 6
111101000 => 9
111101001 => 8
111101010 => 9
111101011 => 7
111101100 => 9
111101101 => 8
111101110 => 9
111101111 => 5
111110000 => 9
111110001 => 8
111110010 => 9
111110011 => 7
111110100 => 9
111110101 => 8
111110110 => 9
111110111 => 6
111111000 => 9
111111001 => 8
111111010 => 9
111111011 => 7
111111100 => 9
111111101 => 8
111111110 => 9
111111111 => 1
0000000001 => 10
0010000001 => 7
0010101101 => 10
0010101011 => 10
0010100111 => 10
0010011101 => 10
0010011011 => 10
0010010111 => 10
0010001111 => 10
0001110101 => 10
0001110011 => 10
0001101101 => 10
0001101011 => 10
0001100111 => 10
0001011101 => 10
0001011011 => 10
0001010111 => 10
0001001111 => 10
0000111101 => 10
0000111011 => 10
0000110111 => 10
0000101111 => 10
0000011111 => 10
0000000000 => 1
0000000110 => 9
0000011000 => 7
0000011110 => 9
0000010010 => 9
0001100000 => 7
0001100110 => 9
0001111000 => 7
0001111110 => 9
0001110010 => 9
0001001000 => 7
0001001110 => 9
0001000010 => 5
0001011010 => 9
0010101010 => 9
0010101000 => 8
0010101100 => 8
0010100100 => 8
0010010100 => 8
0001010100 => 8
0010101110 => 9
0010100000 => 8
0010000100 => 5
0000010100 => 8
0000000010 => 9
0000001110 => 9
0000111110 => 9
0000000100 => 8
0000001010 => 9
0000010110 => 9
0000101110 => 9
0001011110 => 9
0001101110 => 9
0001110110 => 9
0001111010 => 9
0001111100 => 8
0000000101 => 10
0000001101 => 10
0000011101 => 10
0001111101 => 10
0000001001 => 10
0000010101 => 10
0000101101 => 10
0010110001 => 7
0001100001 => 6
0001000001 => 6
0000111111 => 10
0001110100 => 8
0001101100 => 8
0010011100 => 8
0001011100 => 8
0000111100 => 8
0001101010 => 9
0010011010 => 9
0000111010 => 9
0010100110 => 9
0010010110 => 9
0001010110 => 9
0000110110 => 9
0010001110 => 9
0001101001 => 10
0000110001 => 10
0000010001 => 10
0000001100 => 8
0000011001 => 10
0000110011 => 10
0000110100 => 8
0000000011 => 10
0000011011 => 10
0001101111 => 10
0000110101 => 10
0010000010 => 6
0001000011 => 10
0010011110 => 9
0001010000 => 7
0001000100 => 4
0001010101 => 10
0001001011 => 10
0001100011 => 5
0001110111 => 10
0010000000 => 8
0000000111 => 10
0000001111 => 10
0001111111 => 10
0000001011 => 10
0000010111 => 10
0001011111 => 10
0001111001 => 10
0000011010 => 9
0000101010 => 9
0000100101 => 10
0010010001 => 7
0010000101 => 10
0010010101 => 10
0010010011 => 10
0000101011 => 10
0001000111 => 10
0000100111 => 10
0010010010 => 3
0001001010 => 9
0001001001 => 10
0001000101 => 10
0000100011 => 10
0000100100 => 8
0000100010 => 9
0010110000 => 8
0000011100 => 8
0000001000 => 7
0000101100 => 8
0010101111 => 10
0000101000 => 7
0010001000 => 4
0001001100 => 8
0001000110 => 9
0001100100 => 8
0001100010 => 9
0000100110 => 9
0000110010 => 9
0010010000 => 8
0001010010 => 9
0001000000 => 7
0001011001 => 10
0001100101 => 10
0001110001 => 6
0010011001 => 7
0010100101 => 5
0010101001 => 7
0010011111 => 10
0000111001 => 10
0010001101 => 10
0001001101 => 10
0001010001 => 6
0001010011 => 10
0001111011 => 10
0010011000 => 8
0001011000 => 7
0000100000 => 6
0010001011 => 10
0010000111 => 10
0000010011 => 10
0010001100 => 8
0010000110 => 9
0000110000 => 6
0000100001 => 5
0010100011 => 10
0010100001 => 7
0000111000 => 7
0001101000 => 7
0000010000 => 6
0000101001 => 10
0010100010 => 6
0010001001 => 7
0010000011 => 10
0010001010 => 9
0001110000 => 7
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Created: Oct 16, 2016 at 22:07 by Martin Rubey
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Last Updated: Oct 16, 2016 at 22:07 by Martin Rubey