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>
using namespace std;
typedef long long ll;


int main(void) {
	ll N, h, n, bb, bs;

	cin >> N;

	for (h = 1; h <= 3500; h++) {
		for (n = h; n <= 3500; n++) {
			bs = N * h * n;
			bb = 4 * h * n - (h + n) * N;
			if (bb <= 0) continue;
			if (bs % bb == 0) {
				printf("%lld %lld %lld\n", h, n, bs / bb);
				return 0;
			}
		}
	}

	return 0;
}