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: Wrong Answer)

use std::io::*;
use std::str::*;

fn read<T: FromStr>() -> Option<T> {
    let stdin = stdin();
    let s = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok()
}

fn main() {
    let N: i64 = read().unwrap();
    if N == 0 {
        println!("0 0 0");
    }
    for n in 1..3501 {
        for w in 1..3501 {
            let t = 4 * n * w - N * (w + n);
            if 4 * n * w - N * (w + n) > 0 {
                let u = ((N * n * w) as f64 / t as f64) as i64;
                println!("{} {} {}", u, n, w);
                return;
            }
        }
    }
}