CF962B.Students in Railway Carriage

There are $n$ consecutive seat places in a railway carriage. Each place is either empty or occupied by a passenger.

The university team for the Olympiad consists of $a$ student-programmers and $b$ student-athletes. Determine the largest number of students from all $a+b$ students, which you can put in the railway carriage so that:

• no student-programmer is sitting next to the student-programmer;
• and no student-athlete is sitting next to the student-athlete.

In the other words, there should not be two consecutive (adjacent) places where two student-athletes or two student-programmers are sitting.

Consider that initially occupied seat places are occupied by jury members (who obviously are not students at all).

铁路车厢中有 $n$ 个连续的座位。每个座位要么为空，要么已被一名乘客占据。

奥林匹克竞赛的大学代表队由 $a$ 名学生程序员和 $b$ 名学生运动员组成。请确定：在满足以下条件的前提下，最多能在车厢中安排多少名来自这全部 $a+b$ 名学生的成员：

• 任意两名学生程序员不能相邻而坐；
• 任意两名学生运动员不能相邻而坐。

换言之，在所有座位中，不能存在两个相邻（即紧挨着）的座位，其上均坐着学生运动员，也不能存在两个相邻的座位，其上均坐着学生程序员。

注意：初始已被占据的座位上坐的是裁判员（显然他们完全不是学生）。

The first line contain three integers $n$, $a$ and $b$ ($1 \le n \le 2\cdot10^{5}$, $0 \le a, b \le 2\cdot10^{5}$, $a + b \gt 0$) — total number of seat places in the railway carriage, the number of student-programmers and the number of student-athletes.

The second line contains a string with length $n$, consisting of characters "." and "*". The dot means that the corresponding place is empty. The asterisk means that the corresponding place is occupied by the jury member.

第一行包含三个整数 $n$、$a$ 和 $b$（$1 \le n \le 2\cdot10^{5}$，$0 \le a, b \le 2\cdot10^{5}$，$a + b \gt 0$）—— 分别表示火车车厢中的总座位数、学生程序员人数和学生运动员人数。

第二行包含一个长度为 $n$ 的字符串，由字符 “.” 和 “*” 组成。其中，“.” 表示对应位置为空座，“*” 表示对应位置被评委占用。

Print the largest number of students, which you can put in the railway carriage so that no student-programmer is sitting next to a student-programmer and no student-athlete is sitting next to a student-athlete.

输出最多可以安排在火车车厢中的学生人数，使得任意两名编程学生不相邻，且任意两名运动学生也不相邻。

In the first example you can put all student, for example, in the following way: *.AB*

In the second example you can put four students, for example, in the following way: *BAB*B

In the third example you can put seven students, for example, in the following way: B*ABAB**A*B

The letter A means a student-programmer, and the letter B — student-athlete.

在第一个例子中，你可以将所有学生按如下方式安排：*.AB*

在第二个例子中，你可以安排四名学生，例如按如下方式：*BAB*B

在第三个例子中，你可以安排七名学生，例如按如下方式：B*ABAB**A*B

字母 A 表示编程方向的学生，字母 B 表示体育方向的学生。