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 Rust (1.15.1) (judge verdict: Accepted)

fn main() {
  let x: f64 = read();
  
  for h in 1 .. 3501 {
    for n in 1 .. 3501 {
      let w = x / (4.0 - x/(h as f64) - x/(n as f64));
      let w2 = w.round();
      if w > 0.0 && w <= 3500.0 && (w-w2).abs() < 0.0000001 {
        println!("{} {} {} ", h, n, w2);
        return;
      }
    }
  }
}

fn read<T: std::str::FromStr>() -> T {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().parse::<T>().ok().unwrap()
}