Iahub is a big fan of tourists. He wants to become a tourist himself, so he planned a trip. There are n destinations on a straight road that Iahub wants to visit. Iahub starts the excursion from kilometer 0. The n destinations are described by a non-negative integers sequence a1, a2, ..., an. The number ak represents that the kth destination is at distance ak kilometers from the starting point. No two destinations are located in the same place. 

Iahub wants to visit each destination only once. Note that, crossing through a destination is not considered visiting, unless Iahub explicitly wants to visit it at that point. Also, after Iahub visits his last destination, he doesn't come back to kilometer 0, as he stops his trip at the last destination. 

The distance between destination located at kilometer x and next destination, located at kilometer y, is |x - y| kilometers. We call a "route" an order of visiting the destinations. Iahub can visit destinations in any order he wants, as long as he visits all n destinations and he doesn't visit a destination more than once. 

Iahub starts writing out on a paper all possible routes and for each of them, he notes the total distance he would walk. He's interested in the average number of kilometers he would walk by choosing a route. As he got bored of writing out all the routes, he asks you to help him.

Input

The first line contains integer n (2 ≤ n ≤ 105). Next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ 107).

Output

Output two integers — the numerator and denominator of a fraction which is equal to the wanted average number. The fraction must be irreducible.

Examples

Input

3
2 3 5


Output

22 3

Note

Consider 6 possible routes:

  * [2, 3, 5]: total distance traveled: |2 – 0| + |3 – 2| + |5 – 3| = 5; 
  * [2, 5, 3]: |2 – 0| + |5 – 2| + |3 – 5| = 7; 
  * [3, 2, 5]: |3 – 0| + |2 – 3| + |5 – 2| = 7; 
  * [3, 5, 2]: |3 – 0| + |5 – 3| + |2 – 5| = 8; 
  * [5, 2, 3]: |5 – 0| + |2 – 5| + |3 – 2| = 9; 
  * [5, 3, 2]: |5 – 0| + |3 – 5| + |2 – 3| = 8. 



The average travel distance is <image> = <image> = <image>.
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Safronov Alexey (safronov.aa@gmail.com)
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
    public void solve(int testNumber, FastScanner in, PrintWriter out) {
        int count = in.nextInt();
        int[] poses = new int[count];
        for (int i = 0; i < count; i++)
            poses[i] = in.nextInt();
        Arrays.sort(poses);
        long top = 0, bottom = count;
        for (int i = 0; i < count; i++) {
            top -= poses[i];
            long left = (i + 1), right = count - i - 1;
            top += 2 * poses[i] * left;
            top -= 2 * poses[i] * right;
        }
        long gcd = getGCD(top, bottom);
        top /= gcd;
        bottom /= gcd;
        out.println(top + " " + bottom);
    }

    private long getGCD(long a, long b) {
        if (b == 0) return a;
        return getGCD(b, a % b);
    }
}

class FastScanner extends BufferedReader {
    private StringTokenizer stringTokenizer;

    public FastScanner(InputStream stream) {
        super(new InputStreamReader(stream));
    }

    public String next() {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            String line;
            try {

                line = readLine();
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (line == null)
                return null;
            stringTokenizer = new StringTokenizer(line);
        }
        return stringTokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    }
