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>
using namespace std;
using ll = long long;

int main()
{
	ll N;
	cin >> N;
	for (ll i = 1; i <= 3500; i++) {
		for (ll j = 1; j <= 3500; j++) {
			if (4 * i * j > (i + j) * N) {
				if ((N * i * j) % (4 * i * j - (i + j) * N) == 0) {
					cout << i << ' ' << j << ' ' << (N * i * j) / (4 * i * j - (i + j) * N) << endl;
					goto end;
				}
			}
		}
	}
	end:
	return 0;
}