Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main(void) {
	long N;
	scanf("%ld", &N);
	for (long h = 1; h <= 3500; h++) {
		for (long n = 1; n <= 3500; n++) {
			if (4 * h * n - N * n - N * h <= 0) continue;
			if (N * h * n % (4 * h * n - N * n - N * h)) continue;
			long w = N * h * n / (4 * h * n - N * n - N * h);
			printf("%ld %ld %ld", h, n, w);
			return 0;
		}
	}
	return 0;
}