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 sys import stdin


def task():
    stdin.readline()
    a = map(int, stdin.readline().split())
    a.reverse()
    result = 0
    i = 0
    reminder = 0
    while a or reminder:
        while a and a[-1] == i:
            reminder += 1
            a.pop()
        result += reminder % 2 == 0
        reminder /= 2
        if reminder > 0:
            i += 1
        elif a:
            result += a[-1] - i - 1
            i = a[-1]
    print result


task()