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 _int long long
int main() {
	_int N;
	
	scanf("%lld",&N);
	for(_int h=1;h<=3500;h++)
	{
		for(_int n=1;n<=3500;n++)
		{
		   _int x=4*h*n-n*N-N*h;
		   _int y=N*h*n;
		   
		   if(x>0 && (y%x==0))
		   {
		   	cout<<h<<" "<<n<<" "<<y/x<<endl;
		   	return 0;
		   }
		}
			
	}
	
	return 0;
}