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>

using namespace std;
int main(){
	long long int N;
	cin >> N;
	for(int n=1;n<3501;n++){
		for(int h=n;h<3501;h++){
			if(4*h*n-N*n-N*h<= 0){
			continue;
			}
			long long int check =  (N*h*n)%(4*h*n-N*n-N*h);
			long long int val =  (N*h*n) / (4*h*n-N*n-N*h);
			if(check==0 && val>0){
				cout << n << " " << h <<" "<< val << endl;
				return 0;
			}
		}
	}
}