Problems
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.
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