Cantor Fractions#1022
At the end of the nineteenth century, the German mathematician Georg Cantor claimed that the set of positive fractions \textbf{Q}^+ is equivalent to the set of natural numbers , meaning that both are infinite and have the same cardinality. To demonstrate this, he exhibited a mapping from to \textbf{Q}^+, which is illustrated for the \textbf{N} \times \textbf{N} plane below and covers all pairs of numbers:
The first fractions in the Cantor mapping are:
Write a program that finds the -th Cantor fraction according to the mapping described above.
The input consists of several lines, each containing a single positive integer .
The output should contain the same number of lines as the input. Each line must contain the -th Cantor fraction in the form "numerator/denominator", where the numerator and denominator are separated by a slash (). The fraction must not be reduced.
Example 1