Ivan has got an array of n non-negative integers a 1, a 2, ..., a n . Ivan knows that the array is sorted in the non-decreasing order. Ivan wrote out integers 2 a 1 , 2 a 2 , ..., 2 a n on a piece of paper. Now he wonders, what minimum number of integers of form 2 b (b ≥ 0) need to be added to the piece of paper so that the sum of all integers written on the paper equalled 2 v - 1 for some integer v (v ≥ 0). Help Ivan, find the required quantity of numbers.

输入描述:

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.

输出描述:

Print a single integer — the answer to the problem.

备注:

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.