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;

long long N;

int main(){
//	cin.tie(0);
//	ios::sync_with_stdio(false);
	cin >> N;
	for(int h=1; h<=3500; ++h)
		for(int n=1; n<=3500; ++n)
			if(4*h*n != N*(n+h) && N*h*n % (4*h*n-N*n-N*h) == 0 && (4*h*n-N*n-N*h) > 0){
				cout << h << " " << n << " " << N*h*n / (4*h*n-N*n-N*h) << "\n";
				return 0;
			}
}