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.awt.Label;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;

import java.util.Scanner;
import java.util.regex.Matcher;
import java.util.regex.Pattern;


public class C {
	
	public static void main(String[] args) throws IOException{
		Scanner sc = new Scanner(System.in);
		
		final int n = sc.nextInt();
		
		int[] array = new int[n];
		//BitSet set = new BitSet();
		for(int i = 0; i < n; i++){
			array[i] = sc.nextInt();
			//set.set(array[i]);
		}
		
		int count = 0;
		int prev_number = 0;
		int prev_count = 0;
		for(int i = 0; i < n; i++){
			while(prev_number != array[i]){
				if(prev_count != 0){
					count += 1 - prev_count % 2;
					prev_count /= 2;
					prev_number++;
				}else{
					count += array[i] - prev_number;
					prev_number = array[i];
				}
				
			}
			
			prev_count++;
		}
		
		while(prev_count > 0){
			count += 1 - prev_count % 2;
			prev_count /= 2;
		}
		
		System.out.println(count);
	}
	
	public static class Scanner {
		
		private BufferedReader br;
		private StringTokenizer tok;
		
		public Scanner(InputStream is) throws IOException{
			br = new BufferedReader(new InputStreamReader(is));
			getLine();
		}
		
		private void getLine() throws IOException{
			while(tok == null || !tok.hasMoreTokens()){
				tok = new StringTokenizer(br.readLine());
			}
		}
		
		private boolean hasNext(){
			return tok.hasMoreTokens();
		}
		
		public int nextInt() throws IOException{
			if(hasNext()){
				return Integer.parseInt(tok.nextToken());
			}else{
				getLine();
				return Integer.parseInt(tok.nextToken());
			}
		}
		
		public long nextLong() throws IOException{
			if(hasNext()){
				return Long.parseLong(tok.nextToken());
			}else{
				getLine();
				return Long.parseLong(tok.nextToken());
			}
		}
		
		public double nextDouble() throws IOException{
			if(hasNext()){
				return Double.parseDouble(tok.nextToken());
			}else{
				getLine();
				return Double.parseDouble(tok.nextToken());
			}
		}
	}
}