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;

int main() {
	long long N, h, n, w;
	cin >> N;
	for (int i = 1; i <= 3500; i++) {
		for (int j = 1; j <= 3500; j++) {
			long long X = 4 * i * j - N * (i + j);
			if (X > 0 && (N * i * j) % X == 0) {
				h = i;
				n = j;
				w = (N * i * j) / X;
				goto END;
			}
		}
	}
END:
	cout << h << " " << n << " " << w;
}