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.math.BigInteger;
import java.util.*;

public class C184
{	
	public C184()
	{
		Scanner in = new Scanner(System.in);
		
		int n = Integer.parseInt(in.nextLine());
		
		StringTokenizer st = new StringTokenizer(in.nextLine());
		int[] a = new int[n];
		for(int x = 0; x < n; x++)
			a[x] = Integer.parseInt(st.nextToken());

		boolean change;
		do
		{
			change = false;
			for(int x = 0; x < n - 1; x++)
			{
				if(a[x] == a[x + 1] && a[x] != -1)
				{
					change = true;
					a[x] = -1;
					a[x + 1]++;
				}
			}
			Arrays.sort(a);
		}while(change);
		
		int target = a[n - 1] + 1;
		for(int x = 0; x < n; x++)
			if(a[x] != -1)
				target--;
		
		System.out.println(target);
	}
	
	public static void main(String[] args)
	{
		new C184();
	}
}
