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<bits/stdc++.h>
using namespace std;
typedef long long LL;
int N;
int main(){
	scanf("%d",&N);
	int n,h;
	for(n=1;n<=3500;n++){
		for(h=1;h<=3500;h++){
			LL u=4LL*(LL)n*(LL)h-(LL)N*(LL)n-(LL)N*(LL)h;
			long long d=(LL)n*(LL)h*(LL)N;
			if(u==0 || u<0) continue;
			if(d%u==0LL){
				cout<<h<<' '<<n<<' '<<d/u;
				return 0;
			}
		}
	}
	return 0;
}