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 static final int MAX = 3501;
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        long n = Long.parseLong(sc.next());
        
        for(long x=1; x<MAX; x++){
            for(long y=x; y<MAX; y++){
                long u = n*x*y;
                long d = 4L*x*y-n*x-n*y;
                if(d!=0 && u%d==0 && u/d>0){
                    long z = u/d;
                    System.out.println(x+" "+y+" "+z);
                    return;
                }
            }
        }
    }
}