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 defaultdict
from bisect import bisect_right
ct = defaultdict(int)
n = input()
a = map(int, raw_input().split())
for x in a:
  ct[x] += 1

a = list(set(a))
ai = a[0]
i = 0
while True:
  if ct[ai] > 1:
    ct[ai + 1] += ct[ai] / 2
    ct[ai] &= 1
  if ct[ai + 1] != 0:
    ai += 1
    if i < len(a) - 1 and a[i + 1] == ai: i += 1
  else:
    i += 1
    if i == len(a): break
    ai = a[i]

a = []
for ai in ct:
  if ct[ai] == 1: a.append(ai)

print max(a) - len(a) + 1
