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 sys

def flip(bit, num):
	try:
		if (num[bit] == 0):
			num[bit] = 1
		else:
			num[bit] = 0
			flip(bit + 1, num)
	except:
		num[bit] = 1

def main():
	sys.stdin.readline()
	nums = map(int, sys.stdin.readline().split(" "))

	bin = {}
	for num in nums:
		flip(num, bin)

	num_ones = 0
	max_ones = 0

	for i in bin.keys():
		if bin[i] == 1:
			num_ones = num_ones + 1
			if i > max_ones:
				max_ones = i

	print max_ones + 1 - num_ones

if __name__ == '__main__':
	main()