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(){
  int n;
  cin>>n;
  for(int64_t i=1;i<=3500;i++){
    for(int64_t j=1;j<=3500;j++){
      if(4*i*j-n*j-i*n>0&&n*i*j%(4*i*j-n*j-i*n)==0){
        cout<<i<<' '<<j<<' '<<n*i*j/(4*i*j-n*j-i*n)<<endl;
        return 0;
      }
    }
  }
}