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Fractions Again?!

Fractions Again?!

\includegraphics{http://uva.onlinejudge.org/external/109/p10976a.gif} It is easy to see that for every fraction in the form (\textbf{k} > 0), we can always find two positive integers \textbf{x} and \textbf{y}, \textbf{x} ≥ \textbf{y}, such that: \includegraphics{http://uva.onlinejudge.org/external/109/p10976b.gif} Now our question is: can you write a program that counts how many such pairs of \textbf{x} and \textbf{y} there are for any given \textbf{k}? \InputFile Input contains no more than \textbf{100} lines, each giving a value of \textbf{k} (\textbf{0} < \textbf{k} ≤ \textbf{10000}). \OutputFile For each \textbf{k}, output the number of corresponding (\textbf{x}, \textbf{y}) pairs, followed by a sorted list of the values of \textbf{x} and \textbf{y}, as shown in the sample output.
Time limit 3 seconds
Memory limit 64 MiB
Input example #1
2
12
Output example #1
2
1/2 = 1/6 + 1/3
1/2 = 1/4 + 1/4
8
1/12 = 1/156 + 1/13
1/12 = 1/84 + 1/14
1/12 = 1/60 + 1/15
1/12 = 1/48 + 1/16
1/12 = 1/36 + 1/18
1/12 = 1/30 + 1/20
1/12 = 1/28 + 1/21
1/12 = 1/24 + 1/24