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.

N = int(raw_input())
A = [int(x) for x in raw_input().split()]

m = {}

def inc(m, k, v=1):
	if not m.has_key(k):
		m[k] = v
	else:
		m[k] += v

hi = 0

for x in A:
	inc(m, x)
	i = x
	hi = max(hi, i)
	while m[i]>1:
		inc(m, i+1, m[i]>>1)
		m[i] %= 2
		i += 1
		hi = max(hi, i)

print hi+1-len(filter(lambda x:x==1, m.values()))
