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()
{
	int N;
	cin >> N;

	long long h, n, w, temp;
	for(h = 1; h <= 3500; ++h) {
		for(n = 1; n <= 3500; ++n) {
			temp = 4 * h * n - N * n - N * h;
			if(temp == 0) {
				continue;
			}
			w = (N * h * n) / temp;
			if(w >= 0 && N * (h * n + n * w + w * h) == 4 * h * n * w) {
				goto end;
			}
		}
	}
end:
	cout << h << " " << n << " " << w;
}