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 PYTHON):

Solution:
import math

originN = int(raw_input())

isValid = False
for h in xrange(1, 3501):
    for n in xrange(1, 3501):
        if (4*n*h-n*originN-h*originN) > 0 and (originN*n*h) % (4*n*h-n*originN-h*originN) == 0:
            isValid = True
            print str(h)+" "+str(n)+" "+str((originN*n*h)/(4*n*h-n*originN-h*originN))
            break
    if isValid: break