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 Ruby (2.7.1) (judge verdict: Runtime Error)

use std::io::Read;

fn main(){
  let mut buf = String::new();
  std::io::stdin().read_to_string(&mut buf).unwrap();
  let N : u32 = buf.parse().unwrap();
  for a in 1 .. 3500 {
    for b in a .. 3500 {
      let div = 4 * a * b - N * b  - N  * a;
      if div <= 0 {
        continue;
      }

      let m = (N * a * b) % (4 * a * b  - N * b  - N * a);
      let c = (N * a * b) / (4 * a * b  - N * b  - N * a);
      if m > 0 || c <= 0 {
        continue;
      }
      
      println!("{} {} {}", a,b,c);
      return;
      
    }
  }
}