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 <bits/stdc++.h>
#define ll long long


using namespace std;

const int MAXN = (int) 1e5;

pair <int, int> v[MAXN + 1];

int main() {
    //fstream cin("A.in");
    //ofstream cout("A.out");
    ll N;
    ios::sync_with_stdio(false);
    cin >> N;
    for(ll n = 1; n <= 3500; n++)
      for(ll h = 1; h <= 3500; h++) {
          if(4 * h * n > N * (n + h) && (N * h * n) % (4 * h * n - N * (n + h)) == 0) {
              cout << h << " " << n << " " << (N * h * n) / (4 * h * n - N * (n + h));
              return 0;
          }
      }
    //cin.close();
    //cout.close();
    return 0;
}