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.util.*;
    import java.math.*;
    import java.util.concurrent.*;
     
    class Main
    {
        static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    	static FastScanner sc=new FastScanner(br);
        static PrintWriter out=new PrintWriter(System.out);
    	static Random rnd=new Random();
    	static int maxn=(int)(3501);
    	
    	static long gcd(long a,long b)
    	{
    		if(b==0)
    		{
    			return a;
    		}
    		else
    		{
    			return gcd(b,a%b);
    		}
    	}
    	
        public static void main(String args[]) throws Exception
        {
    		long n=sc.nextLong();long val1=-1,val2=-1,val3=-1;
    		
    		outer:
    		for(long i=1;i<maxn;i++)
    		{
    			for(long j=i;j<maxn;j++)
    			{	
					long prod=(n*i);
					
    				long num=(4*(prod/n))-(prod/i),den=prod;
    				
    				prod=den*j;
    				
    				long num2=(num*(prod/den))-(prod/j),den2=prod;
    				
    				if(num2>0 && den2%num2==0 && den2>0)
    				{
    					val1=i;val2=j;val3=den2/num2;
    					
    					break outer;
    				}
     
					else if(den2<0)
					{
						break;
					}
    			}
    		}
    		
    		out.println(val1+" "+val2+" "+val3);out.close();
        }
    }
    class FastScanner
    {
        BufferedReader in;
        StringTokenizer st;
     
        public FastScanner(BufferedReader in) {
            this.in = in;
        }
    	
        public String nextToken() throws Exception {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(in.readLine());
            }
            return st.nextToken();
        }
    	
    	public String next() throws Exception {
    		return nextToken().toString();
    	}
    	
        public int nextInt() throws Exception {
            return Integer.parseInt(nextToken());
        }
     
        public long nextLong() throws Exception {
            return Long.parseLong(nextToken());
        }
     
        public double nextDouble() throws Exception {
            return Double.parseDouble(nextToken());
        }
    }