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: Time Limit Exceeded)

import sys
import socket

if socket.gethostname() == 'N551J':
    sys.stdin = open('c1.in')


def read_int_list():
    return list(map(int, input().split()))


def read_int():
    return int(input())


def read_str_list():
    return input().split()


def read_str():
    return input()


def solve():
    n = read_int()
    for a in range(1, 3501):
        for b in range(1, 3501):
            d = 4 * a * b - n * b - n * a
            if d != 0:
                if (n * a * b) % d == 0:
                    c = n * a * b // d
                    if c > 0:
                        return a, b, c
    return 0


def main():
    res = solve()
    print(*res)


if __name__ == '__main__':
    main()