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 (3.8.2) (judge verdict: Accepted)

import sys

from numba import njit

input = sys.stdin.readline


@njit("Tuple((i8,i8,i8))(i8)")
def solve(N):
    for h in range(1, 3501):
        for n in range(1, 3501):
            a = N * h * n
            b = 4 * h * n - (h + n) * N
            if b > 0 and a % b == 0:
                w = a // b
                return h, n, w
    return -1, -1, -1


def main():
    N = int(input())
    h, n, w = solve(N)
    print(h, n, w)


if __name__ == "__main__":
    main()