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 <stdio.h>
#include <math.h>

int main(void){
	double n,i,j,k,ans,ap;
	scanf("%lf",&n);
	ans = 4/n;
	for (i=1;i<5000;i++)
	{
		for (j=1;j<5000;j++)
		{
			ap = ans - 1/i - 1/j;
			if (ap >0)
			{
				ap = 1.0/ap;
				ap = roundl(ap * 10000000) / 10000000;
				if ((int)(ap) == ap) 
				{
					printf("%d %d %d",(int)(i),(int)(j),(int)(ap));
					return 0;
				}
			}
		}
	}
	return 0;
}