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 LL;

LL n, a, b, c, x, y;

int main(){
	scanf("%lld", &n);
	for (a=1; a<=3500; a++)
		for (b=a; b<=3500; b++){
			x = n * a * b;
			y = 4 * a * b - b * n - a * n;
			if (y > 0 && x % y == 0){
				printf("%lld %lld %lld\n", a, b, x/y);
				return 0;
			}
		}
	return 0;
}