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>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define int long long
//#define _GLIBCXX_DEBUG

signed main() {
  int N; cin >> N;
  
  if(N%2 == 0) {
    cout << N << " " << N << " " << N/2 << endl;
    return 0;
  }
  if(N == 3) {
    cout << 2 << " " << 2 << " " << 3 << endl;
    return 0;
  }
  
  for(int h=(int)(N/4)+1; h<3501; h++) 
  for(int n=h; n<3501; n++) 
  for(int w=n; w<3501; w++) {
    if(N*(h*n+n*w+w*h) == 4*h*n*w) {
      cout << h << " " << n << " " << w << endl;
      return 0;
    }
  }

}