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 PHP (7.4.4) (judge verdict: Accepted)

<?php
list($n) = ints();
for ($a = 1; $a <= 3500; ++$a) {
    for ($b = $a; $b <= 3500; ++$b) {
        $x = $n * $a * $b;
        $y = 4 * $a * $b - $n * ($a + $b);
        if ($y > 0 && $x % $y === 0) {
            $c = intdiv($x, $y);
            break 2;
        }
    }
}
echo implode(' ', [$a, $b, $c]);
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}