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.
from collections import deque
import itertools

def min_quantity(numbers):
    pairs = deque()
    for number, group in itertools.groupby(numbers):
        pairs.append((number, len(list(group))))
    current_index = 0
    to_be_filled = 0
    while pairs:
        value, counts = pairs.popleft()
        if current_index < value:
            to_be_filled += value - current_index
        if counts > 1:
            if counts % 2 == 0:
                to_be_filled += 1
            counts /= 2
            if pairs and pairs[0][0] == value + 1:
                pairs[0] = (pairs[0][0], pairs[0][1] + counts)
            else:
                pairs.appendleft((value + 1, counts))
        current_index = value + 1
    return to_be_filled

def main():
    number_count = int(raw_input())
    numbers = map(int, raw_input().split())
    print min_quantity(numbers)

if __name__ == '__main__':
    main()
