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 <cstdio>
using namespace std;

typedef long long ll;
ll n;
int main()
{
	ll i, j, t;
	cin >> n;
	for (i = 1; i <= 3500; i++) {
		for (j = 1; j <= 3500; j++) {
			t = 4 * i * j - i * n - j * n;
			if (t > 0 && n * i * j % t == 0 && n * i * j / t > 0) {
				printf("%lld %lld %lld", i, j, n * i * j / t);
				return 0;
			}
		}
	}
    return 0;
}