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;
typedef long long ll;

int main(void) {
	ll N, a, b, c, A, B;
	cin >> N;
	for (a = 1; a <= 3500; a++) {
		for (b = a; b <= 3500; b++) {
			B = 4 * a * b - N * (a + b);
			if (B <= 0)
				continue;
			A = N * a * b;
			if (A % B == 0) {
				c = A / B;
				printf("%lld %lld %lld\n", a, b, c);
				return 0;
			}
		}
	}
	return 0;
}