CF305C.Ivan and Powers of Two

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.

伊万有一个由 $n$ 个非负整数组成的数组 $a_1, a_2, \dots, a_n$。伊万知道该数组按非递减顺序排列。

伊万在一张纸上写下了整数 $2^{a_1}, 2^{a_2}, \dots, 2^{a_n}$。现在他想知道：至少需要往这张纸上再添加多少个形如 $2^b$（其中 $b \geq 0$）的整数，才能使纸上所有整数之和等于某个整数 $v$（$v \geq 0$）对应的 $2^v - 1$？

请帮助伊万求出所需添加的数字个数。

The first line contains integer n (1 ≤ n ≤ 105). The second input line contains n space-separated integers _a_1, _a_2, ..., a__n (0 ≤ a__i ≤ 2·109). It is guaranteed that _a_1 ≤ _a_2 ≤ ... ≤ a__n.

第一行包含一个整数 $n$（$1 \leq n \leq 10^5$）。第二行包含 $n$ 个用空格分隔的整数 $a_1, a_2, \dots, a_n$（$0 \leq a_i \leq 2 \cdot 10^9$）。保证 $a_1 \leq a_2 \leq \dots \leq a_n$。

Print a single integer — the answer to the problem.

输出一个整数——该问题的答案。

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.

在第一个样例中，你无需添加任何数，当前数字之和已经等于 $2^3 - 1 = 7$。

在第二个样例中，你需要添加数字 $2^0,\,2^1,\,2^2$。