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<iostream>
typedef long long ll;
ll n;
int main(void){
	std::cin>>n;
	for(ll h=1;h<=4000;h++){
		for(ll w=1;w<=4000;w++){
			ll tmp=4*h*w-n*h-n*w;
			ll r=n*h*w;
			if(tmp>0&&r%tmp==0){
				std::cout<<h<<' '<<w<<' '<<r/tmp<<std::endl;
				return 0;
			}
		}
	}
	return 0;
}