#P305C. Ivan and Powers of Two
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ID: 5728
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: 5
Uploaded By:
Hydro
Tags> Ivan and Powers of Two
Description
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.
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.
Print a single integer — the answer to the problem.
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.
Samples
4
0 1 1 1
0
1
3
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.