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.DataInputStream;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.TreeSet;


public class ProblemC { 

    
    
    public static void main(String[] args) throws Exception {
        
        Parserdoubt7777 s = new Parserdoubt7777(System.in);
        
        int n = s.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = s.nextInt();
        }
        
        
        TreeSet<Integer> bits = new TreeSet<Integer>();
        for (int i = 0; i < n; i++) {
            int bit = a[i];
            
            if(!bits.contains(bit)){
                bits.add(bit);
                continue;
            }
            
            bits.remove(bit);
            
            int carry = 1;
            
            if(!bits.contains(bit+1)){
                bits.add(bit+1);
                continue;
            }
            
            int nextbit = bit + 1;
            while(true){
                if(!bits.contains(nextbit)) {
                    bits.add(nextbit);
                    break;
                }
                bits.remove(nextbit);
                nextbit++;
            }
        }
        
        int b[] = new int[bits.size()];
        int ix = 0;
        for(int val : bits)
            b[ix++] = val;
        
        
        int ans = 0;
        
//      System.out.println(Arrays.toString(b));
        for (int i = b.length - 1; i > 0; i--) {
            int len = b[i] - b[i-1] - 1;
            ans += len;
        }
        ans += b[0];
        System.out.println(ans);
        
        
    }

}


class Parserdoubt7777
{
   final private int BUFFER_SIZE = 1 << 17;
 
   private DataInputStream din;
   private byte[] buffer;
   private int bufferPointer, bytesRead;
 
   public Parserdoubt7777(InputStream in)
   {
      din = new DataInputStream(in);
      buffer = new byte[BUFFER_SIZE];
      bufferPointer = bytesRead = 0;
   }
   public String nextString() throws Exception
   {
       StringBuffer sb=new StringBuffer("");
       byte c = read();
       while (c <= ' ') c = read();
       do
       {
           sb.append((char)c);
           c=read();
       }while(c>' ');
       return sb.toString();
   }
   public char nextChar() throws Exception
   {
       byte c=read();
       while(c<=' ') c= read();
       return (char)c;
   }
   public int nextInt() throws Exception
   {
      int ret = 0;
      byte c = read();
      while (c <= ' ') c = read();
      boolean neg = c == '-';
      if (neg) c = read();
      do
      {
          ret = ret * 10 + c - '0';
         c = read();
      } while (c > ' ');
      if (neg) return -ret;
      return ret;
   }
   public long nextLong() throws Exception
   {
      long ret = 0;
      byte c = read();
      while (c <= ' ') c = read();
      boolean neg = c == '-';
      if (neg) c = read();
      do
      {
          ret = ret * 10 + c - '0';
         c = read();
      } while (c > ' ');
      if (neg) return -ret;
      return ret;
   }
   private void fillBuffer() throws Exception
   {
      bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
      if (bytesRead == -1) buffer[0] = -1;
   }
 
   private byte read() throws Exception
   {
      if (bufferPointer == bytesRead) fillBuffer();
      return buffer[bufferPointer++];
   }
} 