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;
const ll INF = 1LL << 60;

int main() {
	ll N;
	cin >> N;
	for (ll n = 1; n <= 3500; n++) {
		for (ll w = 1; w <= 3500; w++) {
			ll x = 4 * n*w - N * (w + n);
			if (x > 0 && (N*n*w) % x == 0) {
				cout << (N*n*w) / x << " " << n << " " << w << endl;
				return 0;
			}
		}
	}
}