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.util.*;
import java.io.*;
public class CF305C {
   public static void main(String[] args) throws FileNotFoundException {
      Scanner sc = new Scanner(System.in);
      //Scanner sc = new Scanner(new File("tests.in"));
      int N = sc.nextInt();
      
      HashSet<Long> s = new HashSet<Long>();
      for(int i = 0; i < N; i++) {
         long a = sc.nextLong();
         while(s.contains(a)) {
            s.remove(a);
            a++;
         }
         s.add(a);
      }
      long max = -1;
      for(long x : s)
         max = Math.max(max, x);
      System.out.println(max + 1 - s.size());
   }
}

