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.*;

// Tenakaichi 
// https://yukicoder.me/problems/no/325	

public class Main {
	
	public static void main (String[] args) throws InterruptedException {
		Scanner in = new Scanner(System.in);
		
		double E = 1e-9;
		
		double N = in.nextDouble();
		boolean answerFound = false;
		double d = 4 / N;
		
		for (double i = 3500; i > 0 && 1 / i < d && !answerFound; i--) {
			double dd = d - 1 / i;
			
			for (double j = 3500; j > 0 && 1 / j < dd && !answerFound; j--) {
				double ddd = dd - 1 / j;
				
				double x = 1 / ddd;
				int k = 0;
				
				if (Math.abs(Math.ceil(x) - x) <= E) {
					k = (int) Math.ceil(x);
					answerFound = true;
				} else if (Math.abs(Math.floor(x) - x) <= E) {
					k = (int) Math.floor(x);
					answerFound = true;
				}
				
				if (answerFound) {
					System.out.printf("%d %d %d\n", (int) i, (int) j, k);
				}
			}
		}
	}
	
	
}