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;

int main(){
  long long N;
  cin >> N;

  for(long long h=1;h<=3500;h++){
    for(long long n=h;n<=3500;n++){
      long long a=N*h*n;
      long long b=4*h*n-N*h-N*n;
      if(b<=0)  continue;
      if(a%b!=0)  continue;
      cout << h << " " << n << " " << a/b << endl;
      return 0;
    }
  }

  return 0;
}