Students in Railway Carriage

Description:

Input:

The first line contain three integers $$$n$$$, $$$a$$$ and $$$b$$$ ($$$1 \le n \le 2\cdot10^{5}$$$, $$$0 \le a, b \le 2\cdot10^{5}$$$, $$$a + b > 0$$$) — 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.

Output:

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.

Sample Input:

5 1 1
*...*

Sample Output:

2

Sample Input:

6 2 3
*...*.

Sample Output:

4

Sample Input:

11 3 10
.*....**.*.

Sample Output:

7

Sample Input:

3 2 3
***

Sample Output:

0

Note:

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.