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: Accepted)

N = int(input())

h_upper = int(0.75*N)
for h in range(h_upper, 0, -1):
    tmp = int(2/(4/N-1/h))
    for n in range(tmp,0,-1):
        if 4*h*n-N*(h+n)>0 and (N*h*n)%(4*h*n-N*(h+n)) == 0 :
            print(h,n,(N*h*n)//(4*h*n-N*(h+n)))
            break
    else:
        continue
    break