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 com.sun.media.sound.MidiOutDeviceProvider;

import java.io.*;
import java.util.*;

public class C
{
	public static void main(String [] args) throws IOException
	{
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter writer = new PrintWriter(new OutputStreamWriter(System.out));

		int n = Integer.parseInt(reader.readLine());

		long need = 0;

		long now = -1;
		int counter = 0;
		StringTokenizer tokenizer = new StringTokenizer(reader.readLine());

		for(int i = 0 ; i < n ; i++)
		{
			long number = Integer.parseInt(tokenizer.nextToken());

			if(number != now)
			{
				while(counter > 1 && now < number)
				{
					if((counter & 1) == 0)
						need++;
					counter/=2;
					now++;
				}

				if(now != number)
					need += number - now - 1;
				if(now != number)
					counter = 0;

				counter ++;
				now = number;
			}
			else
				counter++;
		}

		while(counter > 1)
		{
			if((counter & 1) == 0)
				need++;
			counter/=2;
			now++;
		}

		System.out.println(need);
	}

}