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.*;
import java.math.*;

public class Main {


	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int ans=0;
		int pos=0;
//		boolean memory[]=new boolean[20];
		int memory=0;
		for(int i=0;i<n;i++) {
			int x=sc.nextInt();
			
			int shift=Math.min(31,x-pos);
			ans+=(x-pos);
			for(int j=0;j<shift;j++) {
				if((memory>>j)%2!=0) ans--;
			}
			memory=memory>>shift;
			pos=x;
			memory++;
		}
		int tmp=0;
		for(int i=0;i<=31;i++) {
			if((memory>>i)%2==0) {
				tmp++;
			}
			else {
				ans+=tmp;
				tmp=0;
			}
		}
		
		System.out.println(ans);
	}

	

}

