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: Accepted)

import java.util.*;

public class Main {

    public long[] solve(int N) {
        double x, y, z;
        boolean found = false;
        long[] ret = new long[3];
        for (double i = 1; i <= 3500; i++) {
            for (double j = 1; j <= 3500; j++) {
                x = 4 * i * j - N * i - N * j;
                y = N * i * j;
                z = y / x;
                if ((y % x) == 0 && z > 0) {
                    return new long[]{ (long)i, (long)j, (long)z };
                }
            }
        }
        return new long[]{0,0,0};
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        Main obj  = new Main();
        long[] ret = obj.solve(n);
        System.out.println(ret[0]+" "+ret[1]+" "+ret[2]);
    }
}