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.
//package contest;

import java.io.*;
import java.util.*;

public class ProblemC {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

    PrintWriter writer = new PrintWriter(new OutputStreamWriter(System.out));

    int[] readInts() throws IOException {
        String[] strings = reader.readLine().split(" ");
        int[] ints = new int[strings.length];
        for(int i = 0; i < ints.length; i++) {
            ints[i] = Integer.parseInt(strings[i]);
        }
        return ints;
    }

    int[] tt = null;
    int ti = 0;
    int readInt() throws IOException {
        if(tt == null || ti == tt.length) {
            tt = readInts();
            ti = 0;
        }
        return tt[ti++];
    }

    long[] readLongs() throws IOException {
        String[] strings = reader.readLine().split(" ");
        long[] ints = new long[strings.length];
        for(int i = 0; i < ints.length; i++) {
            ints[i] = Long.parseLong(strings[i]);
        }
        return ints;
    }


    void solve() throws IOException {
        int n = readInt();
        int[] a = readInts();
        int ans = 0;
        PriorityQueue<Integer> q = new PriorityQueue<Integer>(n);
        for(int x: a) q.add(x);
        int last = -1;
        while(q.size() > 1) {
            int x = q.poll();
            int y = q.poll();
            if(x == y) q.add(x + 1);
            else {
                q.add(y);
                ans += x - last - 1;
                last = x;
            }
        }
        ans += q.peek() - last - 1;
        writer.println(ans);
        writer.flush();
    }


    public static void main(String[] args) throws IOException {
        new ProblemC().solve();
    }
}
