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.math.*;
import java.util.*;

public class Main {
    
    
    void run() {
        Queue<Integer> Q = new PriorityQueue<Integer>();
        List<Integer> L = new ArrayList<Integer>();
        int n = cin.nextInt();
        for (int i = 0; i < n; ++i) {
            int a = cin.nextInt();
            Q.add(a);
        }
        while (!Q.isEmpty()) {
            int a = Q.poll();
            if (!Q.isEmpty()) {
                if (a == Q.peek()) {
                    Q.poll();
                    Q.add(a + 1);
                } else {
                    L.add(a);
                }
            } else {
                L.add(a);
            }
        }
        int pre = -1, result = 0;
        
        for (int i = 0; i < L.size(); ++i) {
            result += L.get(i) - pre - 1;
            pre = L.get(i);
        }
        System.out.println(result);
    }

    public static void main(String[] args){
        Main solved = new Main();
        solved.run();
        solved.out.close();
    }
    
    Scanner cin = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
}