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.*;

public class Ci
{
	public static void main (String args[])
	{
		Scanner sc = new Scanner(System.in);
		int k = sc.nextInt();

		long total = 0;
		long count = 0;
		long curr = 0;

		for(int i = 0; i < k; i++)
		{
			long n = sc.nextInt();
			long temp = n - curr;
			curr = n;
			for(int j = 0; j < Math.min(temp,64); j++)
			{
				if(count%2==1) temp--;
				count/=2;
			}
			total+=temp;
			count++;
		}
		while(count > 0)
		{
			if(count%2==0) total++;
			count/=2;
		}
		System.out.println(total);
	}
}