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;

int main(){
	long long int n;
	cin>>n;
	
	for(long long int i=1;i<3501;i++){
		for(long long int j=1;j<3501;j++){
			long long int p=n*i*j;
			long long int q=4*i*j-n*i-n*j;
			if(q>0&&p%q==0){
				cout<<i<<" "<<j<<" "<<p/q<<endl;
				return 0;
			}
		}
	}
	
	return 0;
}