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 ll long long
using namespace std;
const ll MOD = 1e9+7;

int main(){
  ll N;
  cin>>N;
  for(ll h=1;h<=3500;h++){
	for(ll n=1;n<=3500;n++){
	  if(4*h*n-N*h-N*n<=0)continue;
	  if((N*n*h)%(4*h*n-N*h-N*n))continue;
	  cout<<h<<" "<<n<<" "<<(N*n*h)/(4*h*n-N*h-N*n)<<endl;
	  return 0;
	}
  }
}