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 static java.lang.System.in;
import static java.lang.System.out;

import java.util.Scanner;


public class C305 {

	public static Scanner sc=new Scanner(in);
	public void run(){
		// TODO Auto-generated method stub
		int n=sc.nextInt();
		int num=0;
		int ans=0;
		int k=0;
		for (int i=0; i<n; i++){
			int a=sc.nextInt();
			while (num<a && k>0){
				if (k%2==0) ans++;
				k/=2;
				num++;
			}
			if (k==0 && num<a) {
				ans+=a-num;
				num=a;
			}
			k++;
		}
		while(k>0){
			if (k%2==0) ans++;
			k/=2;
			num++;
		}
		ln(ans);
	}
	
	public static void main(String[] args) {
		new C305().run();
	}
	public static void ln(Object obj){
		out.println(obj);
	}

}
