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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
    input! {
        n: isize
    }

    for a in 1..=3500 {
        for b in 1..=3500 {
            let denom = 4 * a * b - n * a - n * b;
            if denom == 0 {
                continue;
            }
            let numer = n * a * b;
            if numer % denom != 0 {
                continue;
            }
            
            let c = numer / denom;
            if c <= 0 {
                continue;
            }
            println!("{} {} {}", a, b, c);
            return;
        }
    }
}