Ivan and Powers of Two

 Ivan and Powers of Two

Time Limit:500MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

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Description

Ivan has got an array of n non-negative integers a₁, a₂, ..., a_n. Ivan knows that the array is sorted in the non-decreasing order.

Ivan wrote out integers 2^a₁, 2^a₂, ..., 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.

Input

The first line contains integer n (1 ≤ n ≤ 10⁵). The second input line contains n space-separated integers a₁, a₂, ..., a_n(0 ≤ a_i ≤ 2·10⁹). It is guaranteed that a₁ ≤ a₂ ≤ ... ≤ a_n.

Output

Print a single integer — the answer to the problem.

Sample Input

Input

40 1 1 1

Output

0

Input

13

Output

3

Hint

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.

用set模拟一下，每次读取x，判断x是否存在，如果存在那么删去x，插入x+1

需要注意的是，上面所说的过程需要一直循环进行，如果x+1也存在，那么删去x+1，再看x+2，如果x+2也存在，那么删去x+2.。。。直到x+i不存在，插入x+i