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;
typedef long long ll;

int main() {
	ll N;
	cin >> N;
	ll h, n, w = 0;
	for (h = 1; h <= 3500; h++) {
		for (n = 1; n <= 3500; n++) {
			ll a, b;
			a = 4 * h * n - N * h - N * n;
			b = N * h * n;
			if (a > 0 && b % a == 0) {
				w = b / a;
				break;
			}
		}
		if (w) {
			break;
		}
	}
	cout << h << ' ' << n << ' ' << w << endl;
	return 0;
}