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.io.*;
import java.math.*;
import java.util.*;
public class Main { 
 
	public static void main(String[] args) { 
		Scanner input = new Scanner(System.in);
		long N = input.nextLong();
		boolean found=false;
		for (long h = 1;h<=3500;h++) {
			for (long w = 1; w <= 3500; w++) {
				long Num = N*h*w;
				long Den = 4*h*w-N*w-N*h; //n=Nhw/(4hw-Nw-Nh) -> Analysis in programming handbook
				if (Den>0&&Num%Den==0) {
					long ans = Num/Den;
					System.out.println(h+" "+ans+" "+w);
					found=true;
					break;
				}
			}
			if (found) break;
		}
	}	
}