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;
	for (ll i = 1; i <= 3500; i++) {
		for (ll j = 1; j <= 3500; j++) {
			ll u = i * j * n;
			ll d = 4 * i * j - i * n - j * n;
			if (d > 0 && u % d == 0) {
				cout << i << " " << j << " " << u / d;
				return 0;
			}			
		}
	}
}