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)

use std::io::{self, Read, BufRead};
use std::process::exit;

fn main() {
    let n: i64 = {
        let mut s = String::new();
        io::stdin().read_line(&mut s).unwrap();
        s.trim().parse().unwrap()
    };
    let mut x = 1i64;
    let x_max = ((0.75 * n as f64) + 0.01) as i64;
    while x <= x_max {
        let mut y = 1i64;
        let y_max = (((2 * n * x) as f64 / (4 * x - n) as f64) + 0.01) as i64;
        while y <= y_max {
            let a = x * y * n;
            let b = 4 * x * y - y * n - x * n;
            if b > 0 && a % b == 0 {
                println!("{} {} {}", x, y, a / b);
                exit(0);
            }
            y += 1;
        }
        x += 1;
    }
}