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-----

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.

-----Examples-----

Input 5 1 1 ...

Output 2

Input 6 2 3 ....

Output 4

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

Output 7

Input 3 2 3

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: BABB

In the third example you can put seven students, for example, in the following way: BABAB**AB

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