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>
#define r(i,n) for(long long i = 1; i<=n; i++)
typedef long long ll;
using namespace std;

int main() {
  ll N,h,a,b;
  cin >> N;
  r(n,3500){
    r(w,3500){
      if(4*n*w-N*w-N*n>0){
      h=N*n*w/(4*n*w-N*w-N*n);
      a=4*h*n*w; b=N*(h*w+n*w+n*h);
      if(a==b&&h>0){
        cout << n << " "<< h << " " << w<<endl;
        return 0;
      }
      }
    }
  }
}