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  1. All Contests
  2. ProjectEuler+
  3. Project Euler #180: Rational zeros of a function of three variables.

Project Euler #180: Rational zeros of a function of three variables.

This problem is a programming version of Problem 180 from projecteuler.net

For any integer , consider the three functions

and their combination

We call a golden triple of order if , and are all rational numbers of the form with and there is (at least) one integer , so that .

Let . Let be the sum of all distinct for all golden triples of order . All the and must be in reduced form.

Find .

Input Format

Input contains the only integer which is the order of golden triples.

Constraints

Output Format

Output the only number which is the answer to the problem.

Sample Input 0

2

Sample Output 0

1

Explanation 0

There are no such , and that for , so and you should output .