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.
/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
//package Practice;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Set;

/**
 *
 * @author Rohan
 */
public class Main {

    /**
     * @param args the command line arguments
     */
    static Long[] A=new Long[100010];
    static Set<Long> S=new HashSet<Long>();
    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        Integer n=Integer.parseInt(br.readLine());
        array(br.readLine().split(" "));
        long max=-1;
        for(int i=0;i<n;i++){
            if(S.contains(A[i])){
                long temp=A[i];
                while(S.contains(temp)){
                    S.remove(temp);
                    ++temp;
                }
                S.add(temp);
                if(temp>max) max=temp;
            }
            else{
                S.add(A[i]);
                if(A[i]>max) max=A[i];
            }
        }
        System.out.println(max+1-S.size());
    }
    static public void array(String[] S){
        for(int i=0;i<S.length;i++){
            A[i]=Long.parseLong(S[i]);
        }
    }
}
