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.*;
import java.util.*;
/**
 *
 * @author Sourav Kumar Paul (spaul100)
 * NIT Silchar
 * Dircti
 */

public class SolveB {

    public static Reader in;
    public static PrintWriter out;
    public static long mod = 1000000007;
    public static long inf = 100000000000000000l;
    public static long fac[],inv[];
    public static int union[];

    public static void solve(){

        int n = in.nextInt();
        int a = in.nextInt();
        int b = in.nextInt();
        String arr[] = in.next().split("\\*");
        long ans =0;
        for(int i=0; i<arr.length; i++) {
            int high = (int)(Math.ceil(arr[i].length()/2.0));
            int low = (int)(Math.floor(arr[i].length()/2.0));

            int max = Math.max(a, b);
            int min = Math.min(a,b);
            a = max;
            b = min;
            int x = Math.min(a, high);
            ans += x;
            a -= x;
            x = Math.min(b, low);
            ans += x;
            b -= x;

        }
        out.println(ans);

        out.flush();
        out.close();
    }


    /**
     *  ############################### Template ################################
     */


    public static class Pair implements Comparable{
        int x,y;

        Pair(int x, int y)
        {
            this.x = x;
            this.y = y;
        }
        @Override
        public int compareTo(Object o)
        {
            Pair pp = (Pair)o;
            if(pp.x == x)
                return 0;
            else if (x>pp.x)
                return 1;
            else
                return -1;
        }
    }


    public static void init()
    {
        for(int i=0; i<union.length; i++)
            union[i] = i;
    }
    public static int find(int n)
    {
        return (union[n]==n)?n:(union[n]=find(union[n]));
    }
    public static void unionSet(int i ,int j)
    {
        union[find(i)]=find(j);
    }
    public static boolean connected(int i,int j)
    {
        return union[i]==union[j];
    }

    public static long gcd(long a, long b) {
        long x = Math.min(a,b);
        long y = Math.max(a,b);
        while(x!=0)
        {
            long temp = x;
            x = y%x;
            y = temp;
        }
        return y;
    }

    public static long modPow(long base, long exp, long mod) {
        base = base % mod;
        long result =1;
        while(exp > 0)
        {
            if(exp % 2== 1)
            {
                result = (result * base) % mod;
                exp --;
            }
            else
            {
                base = (base * base) % mod;
                exp = exp >> 1;
            }

        }
        return result;
    }

    public static void cal()
    {
        fac = new long[1000005];
        inv = new long[1000005];
        fac[0]=1;
        inv[0]=1;
        for(int i=1; i<=1000000; i++)
        {
            fac[i]=(fac[i-1]*i)%mod;
            inv[i]=(inv[i-1]*modPow(i,mod-2,mod))%mod;
        }
    }
    public static long ncr(int n, int r)
    {
        return (((fac[n]*inv[r])%mod)*inv[n-r])%mod;
    }


    SolveB() throws IOException {
        in = new Reader(new InputStreamReader(System.in));
        out = new PrintWriter(new OutputStreamWriter(System.out));
        solve();
        out.flush();
        out.close();
    }

    public static void main(String args[]) {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    new SolveB();
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
        }, "1", 1 << 26).start();
    }

    public static class Reader {
        public BufferedReader reader;
        public StringTokenizer st;

        public Reader(InputStreamReader stream) {
            reader = new BufferedReader(stream);
            st = null;
        }
        public Reader(FileReader stream)
        {
            reader = new BufferedReader(stream);
            st = null;
        }
        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public String nextLine() throws IOException{
            return reader.readLine();
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }

    }
}