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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

// define('DEBUG', true);
define('DEBUG', false);

// define('MOD', 1000000007);

fscanf(STDIN, "%d", $N);

for ($h = 1; $h <= 3500; $h++) {
    for ($n = 1; $n <= 3500; $n++) {
        $base = 4 * $h * $n - $N * $n - $N * $h;
        if ($base == 0) continue;
        $w = ($N * $h * $n) / $base;

        if ($w == intval($w) && $w > 0) {
            echo "{$h} {$n} {$w}\n";
            exit;
        }
    }
}