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;

int main(){
  int n;
  cin >> n;
  for(int i=1; i<=3500; ++i) for(int j=i; j<=3500; ++j){
    ll r = 4*i*j - n*(i+j);
    ll l = (ll)n*i*j;
    if(r>0 && l%r == 0){
      cout << i << " " << j << " " << l/r << endl;
      return 0;
    }
  }
}