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;
#define int long long
signed main(){
	int n;cin>>n;
	for(int h=1;h<=3500;h++){
	for(int w=1;w<3500;w++){
		int x=4*h*w-n*(w+h);
		if(x>0&& (n*h*w)%x==0){
			int y=(n*h*w)/x;
			cout<<h<<" "<<w<<" "<<y<<endl;
			return 0;
		}
	}
	}
}