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

    void solve() throws IOException {
        BufferedReader in = new BufferedReader(new
                InputStreamReader(System.in));
        String[] sp;
        Scanner sc = new Scanner(System.in);

        int n = Integer.parseInt(in.readLine());
        sp = in.readLine().split(" ");
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = Long.parseLong(sp[i]);
        }

        int count = 0;
        long prevNum = 0;
        int prevCount = 0;
        for (int i = 0; i < n; i++) {
            while (prevNum < a[i] && prevCount > 0) {
                count += prevCount % 2;
                prevNum++;
                prevCount /= 2;
            }
            prevCount++;
            prevNum = a[i];
        }

        while (prevCount > 0) {
            count += prevCount % 2;
            prevNum++;
            prevCount /= 2;
        }

        System.out.println(prevNum - count);
    }
}

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