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;
typedef long long int LL;

int main(){
	LL n, h, w, fz;
	cin >> n;
	for(h = 3500; h; -- h)
		for(w = 3500; w; -- w){
			if((h + w) * n >= 4 * h * w)
				break;
			fz = 4 * h * w - n * w - n * h;
			if(((n * h * w) % fz) == 0){
				cout << h << ' ' << w << ' ' << n * h * w / fz << endl;
				return 0;
			}
		}
	return 0;
}