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
#include<iostream>
#include<algorithm>
#include<cmath>
#include<string>
#include<vector>
using namespace std;
int main() {
  long long n,k,l;
  cin >> n;
  for(long long i=1; i<=3500; i++) {
    for(long long j=1; j<=3500; j++) {
      k=4*i*j-n*j-n*i;
      l=n*i*j;
      if(k>0&&l%k==0) {
        cout << i << " " << j << " " << l/k << endl;
        return 0;
      }
    }
  }
}
