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>
using namespace std;
using ll = long long;

int main() {
	ll n;
	cin >> n;
	for (ll h = 1;h <= 3500;h++) {
		for (ll w = 1;w <= 3500;w++) {
			ll t = n * w*h;
			if (4 * h*w - n * w - n * h <= 0) continue;
			if (t % (4 * h*w - n * w - n * h) == 0) {
				printf("%d %d %d\n", h, w, t / (4 * h*w - n * w - n * h));
				return 0;
			}
		}
	}
}