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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class C {

	private static StringTokenizer tokenizer;
    private static BufferedReader bf;
    private static PrintWriter out;
    
    private static int nextInt() throws IOException {
    	return Integer.parseInt(nextToken());
    }
   
	private static long nextLong() throws IOException {
    	return Long.parseLong(nextToken());
    }
    
    private static String nextToken() throws IOException {
    	while(tokenizer == null || !tokenizer.hasMoreTokens()) {
    		tokenizer = new StringTokenizer(bf.readLine());
    	}
    	return tokenizer.nextToken();
    }
    
    public static void main(String[] args) throws IOException {
		
		bf = new BufferedReader(new InputStreamReader(System.in));
    	tokenizer = null;
    	out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    	int n = nextInt();   int up = 0;
    	TreeMap<Integer, Integer> tm = new TreeMap<Integer, Integer>();
    	for(int i = 0; i < n; i++) {
    		int a = nextInt();
    		if(tm.containsKey(a)) {
    			while(tm.containsKey(a)) {
    				tm.remove(a);
    				a++;
    			}
    			tm.put(a, 1);
    		}
    		else   tm.put(a, 1);
    	}
    	int max = tm.pollLastEntry().getKey();
    	out.println(max - tm.size());
    	out.close();
    }
    
}
