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:
n = int(input())

for h in range(1, 3501):
    for w in range(1, 3501):
        bns = n * h * w
        bnb = 4 * h * w - n * (h + w)
        if bnb >= 1 and bns % bnb == 0:
            print(h, w, bns // bnb)
            exit()