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<cstring>
#include<algorithm>
#include<cmath>
using namespace std;

int n;

int main(){
	scanf("%d",&n);
	int i,j;
	for(i=1;i<=3500;i++){
		for(j=1;j<=3500;j++){
			double c=(1.0*i*j*n)/(4.0*i*j-1.0*i*n-1.0*j*n);
			double tmp=(int) c;
			if(fabs(tmp-c)<1e-6 && tmp>0){
				printf("%d %d %.0lf\n",i,j,tmp);
				return 0;
			}
		}
	}
	return 0;
}