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.*; //Scanner;
import java.io.PrintWriter; //PrintWriter

public class R184_Div2_C
{
	public static void main(String[] args) {
		Scanner      in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		solve(in, out);
		out.close();
		in.close();	
	}
	
    //Performance is improved when searching a "SortedList".
    //Adding to a SortedList places item in sorted order.
    //Methods "Contains" and "Indexof" use a binary search algorithm.
    static TreeSet<Integer> pow = new TreeSet<Integer>();
	
	public static void solve(Scanner in, PrintWriter out)
	{
		int n = in.nextInt();	

		int a;
		for (int i = 0; i < n; i++) 
		{
			a = in.nextInt();
        	Insert(a);
		}

	    int max = pow.last(); // Keys[pow.size() - 1];
	    int sum = max + 1 - pow.size();    
		
		out.println(sum);		
	}
	
    static void Insert(int num)
    {
        if(pow.contains(num))
        {
            pow.remove(num);
            Insert(num + 1);
        }
        else
            pow.add(num);
    }
}
