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.util.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class probc {
	public static int i(String s){return Integer.parseInt(s);}
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		Map<Integer, Integer> map = new TreeMap<Integer, Integer>();
		for(int i=0;i<n;i++){
			int q = scan.nextInt();
			if(!map.containsKey(q)){
				map.put(q, 1);
			}
			else{
				int p = map.get(q)+1;
				while(p>=2){
					if(p%2==0){
						map.remove(q);
					}
					else{
						map.put(q, p%2);
					}
					map.put(q+1, (map.containsKey(q+1) ? map.get(q+1) : 0)+p/2);
					q++;
					p = map.get(q);
				}
			}
		}
		int max = 0;
		for(int i : map.keySet()){
			max = Math.max(i, max);
		}
		System.out.println(max+1-map.size());
		scan.close();
		System.exit(0);
	}
}