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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;

class Main{
  public static void main(String[] args){
    Scanner sc=new Scanner(System.in);
    long x=sc.nextLong();
    for(long h=1;h<=3500;h++){
      for(long n=h;n<=3500;n++){
        if((4*h*n-n*x-h*x)>0&&(h*n*x)%(4*h*n-n*x-h*x)==0){
          System.out.println(h+" "+n+" "+((h*n*x)/(4*h*n-n*x-h*x)));
          return;
        }
      }
    }
  }
}