Project Euler #91: Right triangles with integer coordinates

_{This problem is a programming version of Problem 91 from projecteuler.net}

The points and are plotted at integer co-ordinates and are joined to the origin, , to form .

There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between and inclusive; that is, .

Given that , how many right triangles can be formed?

Input Format

First and only line contains .

Constraints

Output Format

Output the required count.

Sample Input

Sample Output