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 h=1;h<=3500;h++){
    for(ll n=1;n<=3500;n++){
      ll a = 4*h*n-n*N-N*h;
      if(a<=0)continue;
      ll b =N*h*n;
      if(b%a==0){
        printf("%lld %lld %lld\n", h,n,b/a);
        return 0;
      }
    }
  }
}