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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Teste {
	
	public static void main(String args[]) {
		
		//Input values
		Scanner input = new Scanner(System.in);
        int n = input.nextInt();
		Set<Long> long_set = new HashSet<>();
        for (int i = 0; i < n; i++) {
            long a = input.nextLong();
            while(long_set.contains(a)) {
            	long_set.remove(a);
                a++;
            }
            long_set.add(a);
        }
        input.close();
        
        //Logic
        long elems = long_set.size();
        long max = -1;
        for(long o : long_set) {
        	max = Math.max(o, max);
        }

        System.out.println(max+1-elems);
	}
}
 		   		 	 	 		 	 	  				 		 		