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>

using namespace std;

typedef long long ll;

int main(){
	ll N; cin >> N;
	for(ll h = 1; h <= 3500; h++) for(ll n = 1; n <= 3500; n++){
		if(4 * h * n - N * n - N * h <= 0) continue;
		if(N * h * n % (4 * h * n - N * n - N * h) == 0){
			cout << h << " " << n << " " << N * h * n / (4 * h * n - N * n - N * h) << endl;
			return 0;
		}
	}
}