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::stdin;

/**
 * C
 */
fn main() {
    let n: i64 = {
        let mut  s = String::new();
        stdin().read_line(&mut s).unwrap();
        s.trim_right().parse().unwrap()
    };

    if n % 2 == 0 { // nが偶数
        let h = n / 2;
        let w = n;
        let l = n;
        println!("{} {} {}", h, w, l)
    } else { // nが奇数
        let mut w = 0;
        let mut h = 0;
        let mut l = 0;
        'outer: for i in 1..3501 {
            'inner: for j in 1..3501 {
                if (4*i*j-n*j-n*i == 0) { continue 'inner ; }
                w = n*i*j / (4*i*j-n*j-n*i);
                h = i;
                l = j;
                if (n*i*j % (4*i*j-n*j-n*i) == 0 && w > 0) {
                    break 'outer
                }
            }
        }
        println!("{} {} {}", h, w, l)
    }


}