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 m;
  cin >> m;
 
 for(long long h=1;h<=3500;h++){
  for(long long n=1;n<=3500;n++){
     long long w=m*h*n;
     long long d=4*h*n-m*n-m*h;
    if(d>0&&w%d==0) {
     cout << h << " " << n << " " << w/d << endl;
      return 0;
    }
  } 
 }
}