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 = map(int, raw_input().split())

f = []
c = 0

def handle(x, c, f):
    if len(f) == 0:
        f = [x]
    elif x > f[-1]:
        c += len(f)
        f = [x]
    elif x in f:
        f.remove(x)
        (c, f) = handle(x+1, c, f)
    else:
        f.append(x)
        f.sort()
    return (c, f)

for x in a:
    (c, f) = handle(x, c, f)

v = f[-1] + 1
print v - len(f) - c