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::{
    fastout, input,
    marker::{Bytes, Chars, Isize1, Usize1},
};

fn main() {
    input! {
        N:isize,
    }
    for n in 1..=3500 {
        for w in 1..=3500 {
            let p = n * w * N;
            let q = 4 * n * w - n * N - w * N;
            if q > 0 && p % q == 0 {
                //dbg!(p, q);
                println!("{} {} {}", n, w, p / q);
                return;
            }
        }
    }
}