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.*;
import java.util.HashMap;

public class z1 {
	public static void main(String[] args) throws IOException {
		StreamTokenizer in = new StreamTokenizer(new BufferedReader(
				new InputStreamReader(System.in)));
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		in.nextToken();
		int n = (int) in.nval;
		HashMap<Long, Long> numbers = new HashMap<Long, Long>();
		long j;
		long max = 0;
		for (int i = 0; i < n; i++) {
			in.nextToken();
			j = (long) in.nval;
			for (; j >= 0; j++) {
				if (numbers.get(j) == null) {
					if (j > max)
						max = j;
					numbers.put(j, 1L);
					break;
				} else if (numbers.get(j) == 0) {
					if (j > max)
						max = j;
					numbers.put(j, 1L);
					break;
				} else
					numbers.put(j, 0L);
			}

		}
		Long[] a = new Long[numbers.size() + 1];
		numbers.values().toArray(a);
		for (int i = 0; i < a.length; i++)
			if (a[i] != null)
				if (a[i] == 1)
					max--;
		out.println(max + 1);
		out.flush();
	}
}