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 PYTHON3):

Solution:

def main():
	N = int(input())
	for n in range(1, 3502):
		for h in range(1,3502):
			t = n*h*N
			p = 4*n*h-(n*N+h*N)
			if p>0 and t%p==0:
				w = t//p
				print(n , h, w)
				exit()


if __name__=="__main__":
	main()