Project Euler #110: Diophantine reciprocals II

_{This problem is a programming version of Problem 110 from projecteuler.net}

In the following equation are positive integers.

It can be verified that when = 1260 there are 113 distinct solutions and this is the least value of for which the total number of distinct solutions exceeds one hundred.

What is the least value of for which the number of distinct solutions ?

Input Format

A single line containing one number ,

Output Format

The number the answer to a problem.

Sample Input

Sample Output