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;

int main(){
	long long n,p,q,a,b;
	cin >> n;
	for(long long i = 1;i <= 3500;i++){
		for(long long j = 1;j <= i;j++){
			a = i,b = j;
			p = 4 * a * b - n * a - n * b;
			q = n * a * b;
			if(p > 0 && q % p == 0){
				cout << i << ' ' << j << ' ' << q / p;
				return 0;
			}
		}
	}
}