Problem:
Score : 300 points

Problem Statement

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

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in PyPy3 (7.3.0) (judge verdict: Accepted)

from itertools import product
def main():
    n = int(input())
    for x, y in product(range(1, 3501), repeat = 2):
        if 4 * x * y - n * (x + y) != 0:
            z = n * x * y / (4 * x * y - n * (x + y))
        else:
            continue
        if z.is_integer() and z > 0:
            print(x, y, int(z))
            break

if __name__ == '__main__':
    main()