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.PriorityQueue;
import java.util.Scanner;

public class Prob309C {
	public static void main(String[] Args) {
		Scanner scan = new Scanner(System.in);
		PriorityQueue<Integer> pq = new PriorityQueue<Integer>();
		int x = scan.nextInt();
		for (int i = 0; i < x; i++)
			pq.add(scan.nextInt());

		int answer = 0;
		int max = 0;
		int count = 0;
		while (pq.size() >= 2)
		{
			int pop1 = pq.poll();
			int pop2 = pq.poll();
			if (pop1 == pop2)
				pq.add(pop1+1);
			else
			{
				count++;
				max = pop1;
				pq.add(pop2);
			}
		}
		count++;
		max = pq.poll();

		System.out.println(max - count + 1);
	}
}
