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>
#include <vector>
using namespace std;

typedef long long int lli;

int main(){
	lli n;
	cin >> n;
	
	for(lli i=1; i<=3500; i++){
		for(lli j=1; j<=3500; j++){
			if(4*i*j != (i+j)*n && i*j*n % (4*i*j-(i+j)*n) == 0){
				lli k = i*j*n / (4*i*j-(i+j)*n);
				if(k<=0) continue;
				cout << i << " " << j << " " << k << endl;
				return 0;
			}
		}
	}
	return -1;
}