Problem: 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

Examples

Input

2


Output

1 2 2


Input

3485


Output

872 1012974 1539173474040


Input

4664


Output

3498 3498 3498

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i,s,n) for(int i = s; i < (int)(n); i++)

int main() {
  ll N;
  cin >> N;
  rep(h,1,3501){
    rep(n,h,3501){
      ll w = N*h*n,p = 4*h*n-N*(h+n);
      if(p == 0) continue;
      if(w%p == 0 && p > 0){
        w /= p;
        cout << h << " " << n << " " << w << endl;
        return 0;
      }
    }
  }
}