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()
{
	long long N,h,n,w,t,x,y;
	scanf("%lld",&N);
	for(h=1;h<=3500;h++)
	{
		for(w=1;w<=3500;w++)
			if(4*h*w-N*w-N*h>0 && N*h*w%(4*h*w-N*w-N*h)==0) break;
		if(4*h*w-N*w-N*h>0 && N*h*w%(4*h*w-N*w-N*h)==0) break;
	} 
	n=N*h*w/(4*h*w-N*w-N*h);
	printf("%lld %lld %lld\n",h,w,n);
}