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 void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long UN = sc.nextLong();
		sc.close();
		sc = null;
		long x;
		long s = UN / 4 + 1;
		long s0,s1;
		long h=0,n=0,w=0;
		LABEL:for(h=s;h<=3500;h++) {
			for(n=h;n<=3500;n++) {
				x=h*n;
				s0=UN*x;
				s1=4*x-UN*(n+h);
				if(s1<=0)continue;
				if(s0%s1==0) {
					w=s0/s1;
					break LABEL;
				}
			}
		}
		System.out.println(h + " " + n + " " + w);
	}
}