Description:
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).
Input Format:
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 Format:
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.
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.