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: usize
    }

    let (x,y,z) = {
        let mut x = 0;
        let mut y = 0;
        let mut z = 0;
        for i in 0..=3500 {
            for j in i..=3500 {
                if 4*i*j > n*(i+j) {
                    if (n*i*j) % (4*i*j - n*(i+j)) == 0 {
                        x = i;
                        y = j;
                        z = (n*i*j) / (4*i*j - n*(i+j));
                        break;
                    }
                }
            }
        }
        (x,y,z)
    };

    println!("{} {} {}",x,y,z)
    
}