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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static final int MAX = 3500;

	public static void main(String args[]) {

		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();

		for(int h=1;h<=MAX;h++) {
			for(int n=1;n<=MAX;n++) {
				int child = N*h*n;
				int mother = 4*h*n - N*n - N*h;

				if(mother != 0 && child%mother == 0 && child/mother > 0) {
					System.out.println(h + " " + n + " " + (child/mother));
					return;
				}

			}
		}
	}
}