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>
#include<algorithm>
#include<string>
using namespace std;
typedef long long ll;
int main() {
	int N; cin >> N;
	for (ll h = 1; h <= 3500; h++) {
		for (ll n = h; n <= 3500; n++) {
			if (N*(h + n) >= 4 * h*n)continue;
			ll w = -N*h*n / (N*(h + n) - 4 * h*n);
			if (4 * h*n*w == N*(h*n + n*w + w*h)) {
				cout << h << ' ' << n << ' ' << w << endl;
				return 0;
			}
		}
	}
}