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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;


int main(void) {
	long long N;
	cin >> N;
	
	for (int h = 1; h <= 3500; h++) {
		for (int n = 1; n <= 3500; n++) {
			long long a = h*n*N;
			long long b = 4*h*n-h*N-n*N;
			if (b<=0) continue;
			if ((a%b)==0) {
				cout << h << " " << n << " " << a/b << endl;
				return 0;
			}
		}
	}
	return 0;
}