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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.TreeSet;

public class C {

	private void work() {
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(
				System.in)));
		while (sc.hasNextInt()) {
			int n = sc.nextInt();
			TreeSet<Integer> s = new TreeSet<Integer>();
			while (n-- > 0) {
				int next = sc.nextInt();
				update(s, next);
			}
			System.out.println(s.last() + 1 - s.size());
		}
	}

	private void update(TreeSet<Integer> s, int k) {
		if (s.contains(k)) {
			s.remove(k);
			update(s, k + 1);
		} else {
			s.add(k);
		}
	}

	public static void main(String[] args) {
		new C().work();
	}
}
