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;

int main() {
	ios_base::sync_with_stdio(false); cin.tie(0);
	int N; cin >> N;

	for (int a = 1; a <= 3500; ++a) for (int b = 1; b <= 3500; ++b) {
		long long ts = 1LL * N * a * b;
		long long ms = 4LL * a * b - N * a - N * b;
		if (ms <= 0) continue;
		if (ts % ms) continue;
		ts /= ms;
		cout << a << ' ' << b << ' ' << ts << endl;
		return 0;
	}
}