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;

typedef long long ll;

int main() {
  ll N; cin >> N;
  ll h, n, w;

  for(n=1; n<=3500; n++){
    for(w=1; w<=3500; w++){
      if(((4*n*w) - (N*w) - (N*n)) <= 0) continue;
      ll a,b;
      a = N*n*w; b = (4*n*w) - (N*w) - (N*n);
      if(b > 0 && a%b==0){
        cout << a/b <<" "<< n <<" "<< w << endl;
        return 0;
      }
    }
  }
}