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;
	ll h, n, w;
	for(h=1;h<=3500LL;h++) {
		for(n=h;n<=3500LL;n++) {
			if(4*h*n <= N*(n+h)) continue;
			w = (N*h*n) / (4*h*n - N*(n+h));
			if(4*w*h*n == N*(n*w+h*w+h*n) and h <= n and n <= w) {
				cout << h << " " << n << " " << w << endl;
				return 0;
			}
		}
	}
}