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;
#define ll long long
int main(){
  ll n,a,b,sum;
  cin>>n;
  for(a=1;a<=3500;a++)
    for(b=a;b<=3500;b++){
      ll l=1,r=3501,m;
      while(r-l>1){
	m=(l+r)/2;
	sum=a*b*m*4;
	ll t=(a*b+b*m+m*a);
	if(sum==n*t){
	  cout<<a<<" "<<b<<" "<<m<<endl;
	  return 0; 
	} 
	else if(n*t<sum)r=m;
	else l=m;  
      }
    }
  return 0;
}