Problem:
Score : 300 points

Problem Statement

You have a pot and N ingredients. Each ingredient has a real number parameter called value, and the value of the i-th ingredient (1 \leq i \leq N) is v_i.

When you put two ingredients in the pot, they will vanish and result in the formation of a new ingredient. The value of the new ingredient will be (x + y) / 2 where x and y are the values of the ingredients consumed, and you can put this ingredient again in the pot.

After you compose ingredients in this way N-1 times, you will end up with one ingredient. Find the maximum possible value of this ingredient.

Constraints

2 \leq N \leq 50

1 \leq v_i \leq 1000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
v_1 v_2 \ldots v_N

Output

Print a decimal number (or an integer) representing the maximum possible value of the last ingredient remaining.

Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.

Sample Input 1

2
3 4

Sample Output 1

3.5

If you start with two ingredients, the only choice is to put both of them in the pot. The value of the ingredient resulting from the ingredients of values 3 and 4 is (3 + 4) / 2 = 3.5.

Printing 3.50001, 3.49999, and so on will also be accepted.

Sample Input 2

3
500 300 200

Sample Output 2

375

You start with three ingredients this time, and you can choose what to use in the first composition. There are three possible choices:

Use the ingredients of values 500 and 300 to produce an ingredient of value (500 + 300) / 2 = 400. The next composition will use this ingredient and the ingredient of value 200, resulting in an ingredient of value (400 + 200) / 2 = 300.

Use the ingredients of values 500 and 200 to produce an ingredient of value (500 + 200) / 2 = 350. The next composition will use this ingredient and the ingredient of value 300, resulting in an ingredient of value (350 + 300) / 2 = 325.

Use the ingredients of values 300 and 200 to produce an ingredient of value (300 + 200) / 2 = 250. The next composition will use this ingredient and the ingredient of value 500, resulting in an ingredient of value (250 + 500) / 2 = 375.

Thus, the maximum possible value of the last ingredient remaining is 375.

Printing 375.0 and so on will also be accepted.

Sample Input 3

5
138 138 138 138 138

Sample Output 3

138

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;

public class Main {

    public static void main(String[] args) {
	InputStream inputStream = System.in;
	OutputStream outputStream = System.out;
	MyInput in = new MyInput(inputStream);
	PrintWriter out = new PrintWriter(outputStream);
	TaskX solver = new TaskX();
	solver.solve(1, in, out);
	out.close();
    }

    static int INF = 1 << 30;
    static long LINF = 1L << 55;
    static int MOD = 1000000007;
    static int[] mh4 = { 0, -1, 1, 0 };
    static int[] mw4 = { -1, 0, 0, 1 };
    static int[] mh8 = { -1, -1, -1, 0, 0, 1, 1, 1 };
    static int[] mw8 = { -1, 0, 1, -1, 1, -1, 0, 1 };

    static class TaskX {

	public void solve(int testNumber, MyInput in, PrintWriter out) {

	    int n = in.nextInt();
	    double[] a = in.nextDoubleArray(n);

	    Arrays.parallelSort(a);

	    for (int i = 1; i < n; i++) {
		a[i] = (a[i-1] + a[i]) / 2;
	    }
	    out.println(a[n-1]);
	}
    }

    static class MyInput {
	private final BufferedReader in;
	private static int pos;
	private static int readLen;
	private static final char[] buffer = new char[1024 * 8];
	private static char[] str = new char[500 * 8 * 2];
	private static boolean[] isDigit = new boolean[256];
	private static boolean[] isSpace = new boolean[256];
	private static boolean[] isLineSep = new boolean[256];

	static {
	    for (int i = 0; i < 10; i++) {
		isDigit['0' + i] = true;
	    }
	    isDigit['-'] = true;
	    isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
	    isLineSep['\r'] = isLineSep['\n'] = true;
	}

	public MyInput(InputStream is) {
	    in = new BufferedReader(new InputStreamReader(is));
	}

	public int read() {
	    if (pos >= readLen) {
		pos = 0;
		try {
		    readLen = in.read(buffer);
		} catch (IOException e) {
		    throw new RuntimeException();
		}
		if (readLen <= 0) {
		    throw new MyInput.EndOfFileRuntimeException();
		}
	    }
	    return buffer[pos++];
	}

	public int nextInt() {
	    int len = 0;
	    str[len++] = nextChar();
	    len = reads(len, isSpace);
	    int i = 0;
	    int ret = 0;
	    if (str[0] == '-') {
		i = 1;
	    }
	    for (; i < len; i++)
		ret = ret * 10 + str[i] - '0';
	    if (str[0] == '-') {
		ret = -ret;
	    }
	    return ret;
	}

	public long nextLong() {
	    int len = 0;
	    str[len++] = nextChar();
	    len = reads(len, isSpace);
	    int i = 0;
	    long ret = 0;
	    if (str[0] == '-') {
		i = 1;
	    }
	    for (; i < len; i++)
		ret = ret * 10 + str[i] - '0';
	    if (str[0] == '-') {
		ret = -ret;
	    }
	    return ret;
	}

	public char nextChar() {
	    while (true) {
		final int c = read();
		if (!isSpace[c]) {
		    return (char) c;
		}
	    }
	}

	public String nextString() {
	    return new String(nextChars());
	}

	public char[] nextChars() {
	    int len = 0;
	    str[len++] = nextChar();
	    len = reads(len, isSpace);
	    return Arrays.copyOf(str, len);
	}

	public char[][] next2DChars(int h, int w) {
	    char[][] s = new char[h][w];
	    for (int i = 0; i < h; i++) {
		s[i] = nextChars();
	    }
	    return s;
	}

	int reads(int len, boolean[] accept) {
	    try {
		while (true) {
		    final int c = read();
		    if (accept[c]) {
			break;
		    }
		    if (str.length == len) {
			char[] rep = new char[str.length * 3 / 2];
			System.arraycopy(str, 0, rep, 0, str.length);
			str = rep;
		    }
		    str[len++] = (char) c;
		}
	    } catch (MyInput.EndOfFileRuntimeException e) {
	    }
	    return len;
	}

	public int[] nextIntArray(final int n) {
	    final int[] res = new int[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextInt();
	    }
	    return res;
	}

	public int[] nextIntArray1Index(final int n) {
	    final int[] res = new int[n + 1];
	    for (int i = 1; i < n + 1; i++) {
		res[i] = nextInt();
	    }
	    return res;
	}

	public int[] nextIntArrayDec(final int n) {
	    final int[] res = new int[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextInt() - 1;
	    }
	    return res;
	}

	public long[] nextLongArray(final int n) {
	    final long[] res = new long[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextLong();
	    }
	    return res;
	}

	public long[] nextLongArray1Index(final int n) {
	    final long[] res = new long[n + 1];
	    for (int i = 1; i < n + 1; i++) {
		res[i] = nextLong();
	    }
	    return res;
	}

	public long[] nextLongArrayDec(final int n) {
	    final long[] res = new long[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextLong() - 1;
	    }
	    return res;
	}

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

	public double[] nextDoubleArray(int n) {
	    double[] res = new double[n];
	    for (int i = 0; i < n; i++) {
		res[i] = nextDouble();
	    }
	    return res;
	}

	static class EndOfFileRuntimeException extends RuntimeException {
	}

    }

}