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
$n = intval(trim(fgets(STDIN)));
for($a = 1; $a <= 3500; $a++){
  for($b = 1; $b <= 3500; $b++){
    $c1 = $n * $a * $b;
    $c2 = 4*$a*$b - $n*($a+$b);
    if($c2 > 0 && $c1 % $c2 == 0){
      printf("%d %d %d\n", $a,$b,$c1/$c2);
      exit;
    }
  }
}