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.*;

public class Main
{
    public static void main(String[] args)
    {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
//        stack<Integer> stack = new LinkedList<Integer>();
        Stack<Integer> stack = new Stack<Integer>();
        TreeSet<Integer> set = new TreeSet<Integer>();

        while (n -- > 0)
        {
            stack.add(in.nextInt());
        }

        while (! stack.isEmpty())
        {
            int head = stack.pop();
            if (set.contains(head))
            {
                set.remove(head);
                stack.push(head + 1);
            }
            else
            {
                set.add(head);
            }
        }
        System.out.println(set.last() - set.size() + 1);
    }
}
