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: Wrong Answer)

<?php

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

// define('MOD', 1000000007);

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

$target = 4 / $N;
$start = ceil($N / 4);

for ($i = 1; $i <= 3500; $i++) {
    for ($j = 1; $j <= 3500; $j++) {
        $calc = 1 / $i + 1 / $j;
        if ($calc < $target) {
            $rest = $target - $calc;
            $num3 = 1 / $rest;
            if ($num3 == (int)$num3) {
                echo "{$i} {$j} {$num3}\n";
                exit;
            }
        }
    }
}