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:
def main():
    N = input()

    for h in range(1, 3501):
        for n in range(1, 3501):
            r1 = h * n * N
            r2 = 4 * h * n - h * N - n * N
            if r2 > 0 and r1 % r2 == 0:
                print "%d %d %d" % (h, n, r1 / r2)
                return

main()