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(3501):
    for w in range(3501):
        if 4*h*w-N*h-N*w <= 0:
            continue
        n = N*h*w/(4*h*w-N*h-N*w)
        if int(n) == n:
            print(h,int(n),w)
            exit()