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.util.Map.Entry;

public class Main {
	
	//final boolean isDebug = true;
	final boolean isDebug = false;
	String fileName = "input.txt";
	FastScanner sc;
	PrintWriter out;
	final int MOD = (int)1e9+7;
	final int INF = Integer.MAX_VALUE / 2;
	
	void test(){
		int N = 4664, h = 3498, n = 3498;
		int A = 4 * h * n;
		int B = N * n * h;
		int C = N * (n + h);
		System.out.println(A + " " + B + " " + C);
		System.out.println(A * 3498 + " " + (B + C * 3498));
	}
	
	void solve() throws Exception{
		//4hnw = N(nh + nw + hw)
		//(4hn)w = Nnh + N(n+h)w
		//(4hn - N(n+h))w = Nnh
		long N = sc.nextLong();
		for(int h = 1; h <= 3500; h++){
			for(int n = 1; n <= 3500; n++){
				long A = 4 * h * n - N * (n + h);
				long B = N * n * h;
				
				if(A == 0) continue;
				if(A >= 1 != B >= 1) continue;
				
				if(Math.abs(B) % Math.abs(A) == 0){
					long w = Math.abs(B) / Math.abs(A);
					if(w >= 1){
						System.out.println(h + " " + n + " " + w);
						return;
					}
				}
			}
		}
	}
	
	/* end solve */
	
	/* main */
	public static void main(String[] args) throws Exception {
		new Main().m();
	}
	
	void m() throws Exception {
		long S = System.currentTimeMillis();
		sc = (isDebug) ? new FastScanner(new FileInputStream(fileName)) : new FastScanner(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		if(isDebug){
			System.out.println("---Debug---");
			System.out.printf("%8d ms", (G-S));
		}
	}
	/* end main */
}
/* end Main */

class FastScanner {
    private InputStream in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(InputStream in) {
		this.in = in;
	}
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() {
    	if (hasNextByte()) return buffer[ptr++];
    	else return -1;
    }
    private static boolean isPrintableChar(int c){
    	return 33 <= c && c <= 126;
    }
    public boolean hasNext() {
    	while(hasNextByte() && !isPrintableChar(buffer[ptr]))
    		ptr++; return hasNextByte();
    }
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public String nextLine() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(b != 10) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() {
    	return Double.parseDouble(next());
    }
}