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.
# def _add(d, key, delta):
#     if key in d:
#         d[key] += delta
#     else:
#         d[key] = delta

n = int(raw_input())
# a = map(int, raw_input().split())

# cnt = {}
# for i in a:
#     if i not in cnt:
#         cnt[i] = 1
#     else:
#         cnt[i] += 1
#         j = i
#         while cnt[j] == 2:
#             cnt[j] = 0
#             _add(cnt, j+1, 1)
#             j += 1

def insert(key, x):
    if key not in x:
        x.add(key)
    else:
        x.remove(key)
        insert(key+1, x)     
a = set()
b = map(lambda x: insert(x, a), map(int, raw_input().split()))
print max(a) - len(a) + 1
