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: Wrong Answer)

//#define _GLIBCXX_DEBUG

#include<bits/stdc++.h>
#define PI 3.14159265359
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
const int INF= 1e9+5;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vector<int> >vvi;
const ll MOD=1000000007LL;
int main(){
  ll N;
  cin>>N;
  for(int h=1;h<=3500;h++){
    for(int n=1;n<=3500;n++){
      if(N*h*n%4*h*n-N*(n+h)==0){
        cout<<h<<" "<<n<<" "<<N*h*n/(4*h*n-N*(n+h))<<endl;
        return 0;
      }
    }
  }
}