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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Collections;
import java.util.LinkedList;
import java.util.ListIterator;
import java.util.StringTokenizer;

public class Ivan {
  
  
  
  public static void main(String[] args) {
    int n = nextInt(); 
    LinkedList<Long> list = new LinkedList<Long>();
    for (int i = 0; i < n; i++) {
      list.addFirst(Long.parseLong(next()));
    }
    
    boolean changed = true;
    while (changed) {
      changed = false;
      for (ListIterator<Long> iterator = list.listIterator(); iterator.hasNext();) {
        long long1 = iterator.next().longValue();
        
        if (iterator.hasNext()) {
          long long2 = iterator.next().longValue();
          iterator.previous();
          
          
          if (long1 == long2) {
            changed = true;
            iterator.previous();
            iterator.set((long1+1));
            iterator.next();
            iterator.next();
            iterator.remove();
            
            iterator.previous();
            if (iterator.hasPrevious()) {
              iterator.previous();
            }
          }
        } 
//        System.out.println(list);
      }
    }
    
    Collections.reverse(list);
//    System.out.println(list);
    
    long sum = 0;
    ListIterator<Long> iterator = list.listIterator();
    long prev = iterator.next().longValue();
    sum += prev;
    
    while(iterator.hasNext()) {
      long long1 = iterator.next().longValue();
      if (long1 <= prev) {
        throw new RuntimeException(long1 + "less than " + prev) ;
      }
      sum += long1 - prev -1L;
      prev = long1;
    }
    
    System.out.println(sum);
    
  }
  
  
  
  
  
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static {
        reader = new BufferedReader(new InputStreamReader(System.in), 32768);
        tokenizer = null;
    }

    static String nextLine(){
        try {
            return reader.readLine();
        }
        catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    static String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    static int nextInt() {
        return Integer.parseInt(next());
    }


    static long nextLong() {
        return Long.parseLong(next());
    }
}