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;
using ll=long long;

int main(){
  ll n; cin>>n;
  for(ll i=1;i<3501;i++){
    for(ll j=1;j<3501;j++){
      if(4*i*j>(i+j)*n){
        if((n*i*j)%(4*i*j-(i+j)*n)==0){
          cout<<i<<' '<<j<<' '<<(n*i*j)/(4*i*j-(i+j)*n)<<endl;
          return 0;
        }
      }
    }
  }
}