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;

int main(){
	long long n, x = 0, y = 0, z = 0;
	cin >> n;
	for(int i = 1; i <= 3500; i++){
		for(int j = 1; j <= 3500; j++){
			long long a, b;
			a = n * i * j;
			b = 4LL * i * j - n * i - n * j;
			if(b <= 0) continue;
			if(a % b == 0){
				x = i, y = j, z = a / b;
				cout << x << " " << y << " " << z << endl;
				return 0;
			}
		}
	}
}