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.IOException;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class ProblemC {

	public static void main(String[] args) throws IOException {
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		long[] a = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.nextLong();
		}
		
		Set<Long> set = new HashSet<Long>();
		for (int i = 0 ; i < n ; i++) {
			long p = a[i];
			while (set.contains(p)) {
				set.remove(p);
				p++;
			}
			set.add(p);
		}
		
		
		long max = 0;
		for (long x : set) {
			max = Math.max(max, x);
		}
		out.println(max + 1 - set.size());
		out.flush();
	}
	

	public static void debug(Object... o) {
		System.err.println(Arrays.deepToString(o));
	}
}
