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;

long long N;

int main(void)
{
	cin >> N;
	
	long long a, b, n, w, h;
	for(n = 1; n <= 3500; n++){
		for(w = 1; w <= 3500; w++){
			a = n * w * N;
			b = 4 * n * w - n * N - w * N;
			if(b == 0) continue;
			if(a % b == 0){
				h = a / b;
				if(h > 0) goto end;
			}
		}
	}
	
	end:
	cout << h << " " << n << " " << w << endl;
	return 0;
}