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<stdlib.h>
#include<string.h>
#include<math.h>
typedef long long LL;
int main()
{
	LL N;
	scanf("%lld",&N);
	LL h,n;
	int flag=0;
	for(h=1;h<=3500;h++)
	{
		for(n=1;n<=3500;n++)
		{
			LL FZ=N*h*n;
			LL FM=(4*h*n-n*N-h*N);
			if(FM>0 && FZ%FM==0)
			{
				flag=1;
				printf("%lld %lld %lld\n",h,n,FZ/FM);
				break;
			}
		}
		if(flag)
			break;
	}
	return 0;
}