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 C {
	public static void main(String [] args){
		Scanner s = new Scanner(System.in);
		final int n = s.nextInt();
		final long [] a = new long[n];
		for (int i = 0; i < n; ++i){
			a[i] = s.nextLong();
		}
		Stack<Long> stack = new Stack<Long>();
		stack.push(a[a.length - 1]);
		long max = a[a.length - 1];
		for (int i = a.length - 2; i >= 0; --i){
			long next = a[i];
			while (!stack.isEmpty() && next == stack.peek()){
				next++;
				stack.pop();
			}
			stack.push(next);
			max = Math.max(max, next);
		}
		System.out.println(max + 1 - stack.size());
		s.close();
	}
}
