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 (5.6.30) (judge verdict: Wrong Answer)

<?php
$n = trim(fgets(STDIN));
if($n % 4 == 0){
    $n =  $n / 4 * 3;
    echo $n ." ". $n ." ". $n;
}elseif($n % 4 == 2){
    $m = $n / 2;
    echo $m ." ". $n ." ". $n;
}elseif($n % 4 == 3){
    $m = (($n - 3) / 4) + 1;
    $l = 2 * $n * $m;
    echo $m ." ". $l ." ". $l;
}else{
    $m = (($n - 1) / 4) + 1;
    if($n % 3 == 0 || $m % 3 == 0){
        $l = $m / 3 * $n * 2;
        echo $m ." ". $l ." ". $l;
    }else{
        $l = floor($m / 3 * $n) + 1;
        $k = $n * $m / ($l * 3 - $n * $m) * $l;
        echo $m ." ". $l ." ". $k;
    }
}