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>
#include <assert.h>

using namespace std;

int main()
{
	int ni;
	cin >> ni;
	for (int h = 1; h <= 3500; h++)
		for (int n = 1; n <= 3500; n++)
		{
			long long t = (long long)ni * h * n, d = (long long)4 * h * n - ni * h - ni * n;
			if (0 < d && t % d == 0)
			{
				cout << h << " " << n << " " << t / d << endl;
				return 0;
			}
		}
}