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.util.*;

public class C184C
{

private static StringTokenizer st;
    
    public static void nextLine(BufferedReader br) throws IOException
    {
        st = new StringTokenizer(br.readLine());
    }
    
    public static int nextInt()
    {
        return Integer.parseInt(st.nextToken());
    }
    
    public static String next()
    {
        return st.nextToken();
    }
    
    public static long nextLong()
    {
        return Long.parseLong(st.nextToken());
    }

    public static double nextDouble()
    {
        return Double.parseDouble(st.nextToken());
    }

    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        nextLine(br);
        int n = nextInt();
        nextLine(br);
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
        {
            arr[i] = nextLong();
        }
        ArrayList<Long> list = new ArrayList<Long>();
        int pos = 0;
        int npos = 0;
        long val = 0;
        int count = 0;
        while (pos < n)
        {
            while (count > 0 && val < arr[pos])
            {
                if (count % 2 == 1)
                {
                    list.add(val);
                }
                val++;
                count /= 2;
            }
            npos = pos;
            while (npos + 1 < n && arr[npos+1] == arr[pos])
            {
                npos++;
            }
            int d = npos - pos + 1 + count;
            if (d % 2 == 1)
            {
                list.add(arr[pos]);
            }
            count = d / 2;
            val = arr[pos] + 1;
            pos = npos + 1;
        }
        while (count > 0)
        {
            if (count % 2 == 1)
            {
                list.add(val);
            }
            val++;
            count /= 2;
        }
        System.out.println(list.get(list.size() - 1) - list.size() + 1);
    }

}