Ivan has got an array of n non-negative integers a1, a2, ..., an. Ivan knows that the array is sorted in the non-decreasing order. 

Ivan wrote out integers 2a1, 2a2, ..., 2an on a piece of paper. Now he wonders, what minimum number of integers of form 2b (b ≥ 0) need to be added to the piece of paper so that the sum of all integers written on the paper equalled 2v - 1 for some integer v (v ≥ 0). 

Help Ivan, find the required quantity of numbers.

Input

The first line contains integer n (1 ≤ n ≤ 105). The second input line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 2·109). It is guaranteed that a1 ≤ a2 ≤ ... ≤ an.

Output

Print a single integer — the answer to the problem.

Examples

Input

4
0 1 1 1


Output

0


Input

1
3


Output

3

Note

In the first sample you do not need to add anything, the sum of numbers already equals 23 - 1 = 7.

In the second sample you need to add numbers 20, 21, 22.
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.Set;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.HashSet;
import java.io.InputStream;

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

class TaskC {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int count = in.nextInt();
        int answer = 0;
        int next = 0;
        Set<Integer> a = new HashSet<Integer>();
        for (int i = 0; i < count; ++i) {
            next = in.nextInt();
            while (a.contains(next)) {
                a.remove(next);
                next++;
            }
            a.add(next);
        }
        for (int i : a)
            if (i > next)
                next = i;
        out.println(next + 1 - a.size());
    }

}

class InputReader {

    private static BufferedReader bufferedReader;
    private static StringTokenizer stringTokenizer;

    public InputReader(InputStream inputStream) {
        bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        stringTokenizer = null;
    }

    public String next() {
        while(stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            try {
                stringTokenizer = new StringTokenizer(bufferedReader.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return stringTokenizer.nextToken();
    }

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

    }

