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>
#define LL long long
using namespace std;
LL a,b,c,n;
int main(){
	cin >> n;
	for(a = 1; a <= 3500; a ++){
		for(b = 1; b <= 3500; b ++){
			if(4ll * a * b - n * b - n * a > 0 && ((n * a * b) % (4ll * a * b - n * b - n * a) == 0)){
				cout << a << ' ' << b << ' ' << (n * a * b) / (4 * a * b - n * b - n * a) << endl;
				return 0;
			}
		}
	} return 0;
}