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.util.Set;
import java.util.Scanner;
import java.io.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.TreeSet;
import java.util.Collection;
import java.util.Collections;
import java.io.InputStream;

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

class TaskC {
    public void solve(int testNumber, Scanner in, PrintWriter out) {
        int n = in.nextInt();
        long[] numbers = new long[n];
        for (int i = 0; i < n; i++) {
            numbers[i] = in.nextLong();
        }

        Set<Long> nums = new TreeSet<Long>();
        int k = 0;
        while (k < numbers.length) {
            Long tmp = numbers[k];
            if (!nums.contains(tmp)) {
                nums.add(tmp);
            } else {
                long cur = tmp;
                while (nums.contains(cur)) {
                    nums.remove(cur);
                    cur++;
                }
                nums.add(cur);
            }

            k++;
        }

        long max = Collections.max(nums);

        out.print(max + 1 - nums.size());

    }
}

