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 <cmath>

using std::floor;
using std::abs;

const double EPS=1e-8;

int main(){
	double N,w;
	scanf("%lf",&N);
	N=4/N;
	for(int i=1;i<=3500;++i){
		for(int j=1;j<=3500;++j){
			w=N-(double)1/i-(double)1/j;
			if(w<EPS) continue;
			if(abs(1/w-floor(1/w))<EPS){
				printf("%d %d %lld",i,j,(long long)(1/w+0.5));
				return 0;
			}
		}
	}
}