Problems
Cantor Fractions
Cantor Fractions
In the late \textbf{XIX}-th century the German mathematician George Cantor argued that the set of positive fractions \textbf{Q^\{+\}} is equipotent to the set of positive integers \textbf{N}, meaning that they are both infinite, but of the same class. To justify this, he exhibited a mapping from \textbf{N} to \textbf{Q^\{+\}} that is onto. This mapping is just traversal of the \textbf{N}x\textbf{N} plane that covers all the pairs:
\includegraphics{http://uva.onlinejudge.org/external/8/p880a.gif}
The first fractions in the Cantor mapping are:
\includegraphics{http://uva.onlinejudge.org/external/8/p880b.gif}
Write a program that finds the \textbf{i}-th Cantor fraction following the mapping outlined above.
\InputFile
The inputs consists of several lines with a positive integer number \textbf{i} each one.
\OutputFile
The output consists of a line per input case, that contains the \textbf{i}-th fraction, with numerator and denominator separed by a slash (\textbf{/}). The fraction should not be in the most simple form.
Input example #1
6
Output example #1
1/3