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.awt.*;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.List;
import java.util.concurrent.ConcurrentHashMap;

public class Main {
    static void zap() throws IOException {
        int n = nextInt();
        TreeMap<Integer, Integer> my = new TreeMap<Integer, Integer>();
        for(int i=0;i<n;i++)
        {
            int number = nextInt();
            if(my.containsKey(number))
                my.put(number, my.get(number) + 1);
            else
                my.put(number, 1);
        }
        for(Integer thisKey=my.firstKey();thisKey!=null;thisKey=my.higherKey(thisKey))
        {
            int occur = my.get(thisKey);
            if(occur == 1)
                continue;
            int incrNext = occur / 2;
            if(my.containsKey(thisKey+1))
                my.put(thisKey+1, my.get(thisKey+1) + incrNext);
            else
                my.put(thisKey+1, incrNext);
            if(occur % 2 == 0)
                my.remove(thisKey);
            else
                my.put(thisKey, 1);
        }
        out.println(my.lastKey() + 1 - my.size());
    }

    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter out;

    public static void main(String[] args) throws IOException {
        InputStream input = System.in;
        br = new BufferedReader(new InputStreamReader(input));
        out = new PrintWriter(System.out);
        zap();
        out.close();
    }

    static long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    static String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) {
                return null;
            }
            st = new StringTokenizer(line);
        }
        return st.nextToken();
    }
}