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 Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input())
for h in range(1, 3500+1):
    for n in range(1, 3501):

        # 4/N - 1/h - 1/n = 1/w
        # 4hw - Nn - Nh / nhN = 1/w
        # w = nhN / 4hw - Nn - Nh

        if (4*h*n - N*n - N*h) != 0 and n*h*N % (4*h*n - N*n - N*h) == 0:
            w = int(4*h*n - N*n - N*h)
            if w > 0:
                print(h, n, w)
                exit(0)