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 ≤ n ≤ 2⋅10^{5}, 0 ≤ a, b ≤ 2⋅10^{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: *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.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.invoke.MethodHandles;
import java.nio.file.Files;
import java.nio.file.Paths;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Objects;
import java.util.Optional;
import java.util.Random;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.stream.Collectors;

public class Main {

    public static void main(String[] args) {
        parseAndGenerate();
        try (PrintWriter out = new PrintWriter(System.out)) {
            FastScanner scanner = new FastScanner();
            int n = scanner.nextInt();
            int a = scanner.nextInt();
            int b = scanner.nextInt();
            String str = scanner.next();
            str = '*' + str + '*';
            int count = 0;
            StringBuffer buffer = new StringBuffer(str);
            for (int i = 1; i < buffer.length(); i++) {
                char prev = buffer.charAt(i - 1);
                if (buffer.charAt(i) == '.') {
                    if (prev == '*') {
                        if (a > b) {
                            buffer.setCharAt(i, '0');
                            a--;
                        } else if (b != 0) {
                            buffer.setCharAt(i, '1');
                            b--;
                        }
                    } else if (prev == '1' && a > 0) {
                        buffer.setCharAt(i, '0');
                        a--;
                    } else if (prev == '0' && b > 0) {
                        buffer.setCharAt(i, '1');
                        b--;
                    } else if (prev == '.') {
                        if (a > 0) {
                            buffer.setCharAt(i, '0');
                            a--;
                        } else if (b > 0) {
                            buffer.setCharAt(i, '1');
                            b--;
                        }
                    }
                }
            }
            for (int i = 0; i < buffer.length(); i++) {
                char ch = buffer.charAt(i);
                if (ch == '0' || ch == '1') {
                    count++;
                }
            }
            out.println(count);
        }
    }

    static final Random random = new Random();

    static void ruffleSort(long[] a) {
        // shuffle, then sort
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n);
            long temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    static class FastScanner {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long[] readArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        Integer[] readArrayInt(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }

    static class Pair {

        int first;

        int second;

        public Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }
            Pair pair = (Pair) o;
            return first == pair.first && second == pair.second;
        }

        @Override
        public int hashCode() {
            return Objects.hash(first, second);
        }
    }

    static class Equation {

        // ax+by=c;
        int a, b, c;

        public Equation(int x1, int y1, int x2, int y2) {
            int a = y2 - y1;
            int b = x1 - x2;
            int c = a * x1 + b * y1;
        }

        public Equation(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

        public boolean isPointOnLine(int x, int y) {
            return a * x + b * y == c;
        }
    }

    private static void buildGraph(HashMap<Integer, Set<Integer>> map, int first, int second) {
        Set<Integer> set = map.getOrDefault(first, new HashSet<>());
        set.add(second);
        map.put(first, set);
        set = map.getOrDefault(second, new HashSet<>());
        set.add(first);
    }

    public static void parseAndGenerate() {
    }

    private static void print2dArr(PrintWriter out, int[][] arr) {
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr[i].length; j++) {
                out.print(arr[i][j] + " ");
            }
            out.println();
        }
    }

    private static boolean[] sieve(int n) {
        boolean[] isPrime = new boolean[n + 1];
        Arrays.fill(isPrime, true);
        isPrime[0] = isPrime[1] = false;
        for (int i = 2; i <= n; i++) {
            if (isPrime[i] && ((long) i * i) <= n) {
                for (int j = i * i; j <= n; j += i) {
                    isPrime[j] = false;
                }
            }
        }
        return isPrime;
    }
}
