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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

/**
 * http://codeforces.com/problemset/problem/340/C
 * 
 * @author sultan.of.swing
 *
 */

public class TaskC {

	public FasterScanner mFScanner;
	public PrintWriter mOut;

	public TaskC() {
		mFScanner = new FasterScanner();
		mOut = new PrintWriter(System.out);
	}

	public void solve() {
		int n;
		int array[];
		long diff;
		int i;
		long num;
		long denum;
		long gcd;

		n = mFScanner.nextInt();
		array = mFScanner.nextIntArray(n);
		num = 0;

		Arrays.sort(array);
		long sum = array[0];
		num = array[0];

		for (i = 1; i < n; i++) {
			diff = 1L * (i) * array[i] - sum;
			sum += array[i];
			num += 2 * diff;
			num += array[i];
		}

		denum = n;

		gcd = gcd(num, denum);
		num /= gcd;
		denum /= gcd;

		mOut.print(num);
		mOut.print(" ");
		mOut.println(denum);

	}

	public long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	public void flush() {
		mOut.flush();
	}

	public void close() {
		mOut.close();
	}

	public static void main(String[] args) {
		TaskC mSol = new TaskC();
		mSol.solve();
		mSol.flush();
		mSol.close();
	}

	class FasterScanner {
		private InputStream mIs;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FasterScanner() {
			this(System.in);
		}

		public FasterScanner(InputStream is) {
			mIs = is;
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = mIs.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public double nextDouble() {
			Double next;
			next = Double.parseDouble(nextString());
			return next;
		}

		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public char[] nextCharArray(int N) {
			int i;
			char[] array;
			String str;

			array = new char[N];

			i = 0;

			str = nextLine();

			for (i = 0; i < N && i < str.length(); i++) {
				array[i] = str.charAt(i);
			}

			return array;
		}

		public char[][] nextChar2DArray(int M, int N) {
			int i;
			char[][] array;

			array = new char[M][N];

			i = 0;

			for (i = 0; i < M; i++) {
				array[i] = nextCharArray(N);
			}

			return array;
		}

		public int[] nextIntArray(int N) {
			int i;
			int[] array;

			array = new int[N];

			i = 0;

			for (i = 0; i < N; i++) {
				array[i] = nextInt();
			}

			return array;
		}

		public int[][] nextInt2DArray(int M, int N) {
			int i;
			int[][] array;

			array = new int[M][N];

			i = 0;

			for (i = 0; i < M; i++) {
				array[i] = nextIntArray(N);
			}

			return array;
		}

		public long[] nextLongArray(int N) {
			int i;
			long[] array;

			array = new long[N];

			i = 0;

			for (i = 0; i < N; i++) {
				array[i] = nextLong();
			}

			return array;
		}

		public long[][] nextLong2DArray(int M, int N) {
			int i;
			long[][] array;

			array = new long[M][N];

			i = 0;

			for (i = 0; i < M; i++) {
				array[i] = nextLongArray(N);
			}

			return array;
		}

		public double[] nextDoubleArray(int N) {
			int i;
			double[] array;

			array = new double[N];

			for (i = 0; i < N; i++) {
				array[i] = nextDouble();
			}

			return array;
		}

		public double[][] nextDouble2DArray(int M, int N) {
			int i;
			double[][] array;

			array = new double[M][N];

			for (i = 0; i < M; i++) {
				array[i] = nextDoubleArray(N);
			}

			return array;
		}

	}
}