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<cstdio>
#include<iostream>
#include<cmath>
#define eps 1e-6
using namespace std;
double i,j,n,x;
int main()
{
	scanf("%lf",&n);
	for(i=1;i<=3500;i++)
		for(j=1;j<=3500;j++)
		{
			x=1/(4/n-1/i-1/j);
			if(fabs(x-int(x+eps))<eps)
			{
				cout<<int(i+eps)<<" "<<int(j+eps)<<" "<<int(x+eps)<<endl;
				return 0;
			}
		}
}