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.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;


public class Template {

    long MODULO = 1L * 1000 * 1000 * 1000 * 1000 * 1000 ;
    long b = 31;
    String fileName = "";
    class Point{
        int x, y;
        Point(int x, int y){
            this.x = x;
            this.y = y;
        }
    }

    void solve() throws IOException {
        int n = readInt();
        int a = readInt();
        int b = readInt();

        char[] s = readString().toCharArray();
        char last = 'e';
        int ans = 0;
        for(int i=0; i<n; ++i){
            if(s[i] == '*'){
                last = 'e';
                continue;
            }
            if(last == 'e'){
                if(a>b&&a>0){
                    ans++;
                    last = 'a';
                    a--;
                }else if(b>0){
                    last = 'b';
                    ans++;
                    b--;
                }
            }else if(last == 'a'){
                if(b>0){
                    b--;
                    last = 'b';
                    ans++;
                }else{
                    last = 'e';
                }
            } else if(last == 'b'){
                if(a>0){
                    a--;
                    ans++;
                    last = 'a';
                }else{
                    last = 'e';
                }
            }
        }

        out.println(ans);
    }

    class Dsu{
        int[] parent;
        int countSets;
        Dsu(int n){
            countSets = n;
            parent = new int[n];
            for(int i=0; i<n; ++i){
                parent[i] = i;
            }
        }
        int findSet(int a){
            if(parent[a] == a) return a;
            parent[a] = findSet(parent[a]);
            return parent[a];
        }
        void unionSets(int a, int b){
            a = findSet(a);
            b = findSet(b);
            if(a!=b){
                countSets--;
                parent[a] = b;
            }
        }
    }
    int checkBit(int mask, int bit) {
        return (mask >> bit) & 1;
    }
    boolean isLower(char c){
        return c >= 'a' && c <= 'z';
    }

    ////////////////////////////////////////////////////////////
    class Pair implements Comparable<Pair>{
        int ind,val;
        Pair(int a, int b){
            this.ind = a;
            this.val = b;
        }

        @Override
        public int compareTo(Pair o) {
            return this.val - o.val;
        }
    }
    class SegmentTree{
        int[] t;
        int n;
        SegmentTree(int n){
            t = new int[4*n];
            build(new int[n+1], 1, 1, n);
        }
        void build (int a[], int v, int tl, int tr) {
            if (tl == tr)
                t[v] = a[tl];
            else {
                int tm = (tl + tr) / 2;
                build (a, v*2, tl, tm);
                build (a, v*2+1, tm+1, tr);
            }
        }

        void update (int v, int tl, int tr, int l, int r, int add) {
            if (l > r)
                return;
            if (l == tl && tr == r)
                t[v] += add;
            else {
                int tm = (tl + tr) / 2;
                update (v*2, tl, tm, l, Math.min(r,tm), add);
                update (v*2+1, tm+1, tr, Math.max(l,tm+1), r, add);
            }
        }

        int get (int v, int tl, int tr, int pos) {
            if (tl == tr)
                return t[v];
            int tm = (tl + tr) / 2;
            if (pos <= tm)
                return t[v] + get (v*2, tl, tm, pos);
            else
                return t[v] + get (v*2+1, tm+1, tr, pos);
        }
    }
    class Fenwik {
        long[] t;
        int length;

        Fenwik(int[] a) {
            length = a.length + 100;
            t = new long[length];

            for (int i = 0; i < a.length; ++i) {
                inc(i, a[i]);
            }
        }

        void inc(int ind, int delta) {
            for (; ind < length; ind = ind | (ind + 1)) {
                t[ind] += delta;
            }
        }

        long getSum(int r) {
            long sum = 0;
            for (; r >= 0; r = (r & (r + 1)) - 1) {
                sum += t[r];
            }
            return sum;
        }
    }
    int gcd(int a, int b){
        return b == 0 ? a : gcd(b, a%b);
    }

    long binPow(long a, long b, long m) {
        if (b == 0) {
            return 1;
        }
        if (b % 2 == 1) {
            return ((a % m) * (binPow(a, b - 1, m) % m)) % m;
        } else {
            long c = binPow(a, b / 2, m);
            return (c * c) % m;
        }

    }
    int minInt(int... values) {
        int min = Integer.MAX_VALUE;
        for (int value : values) min = Math.min(min, value);
        return min;
    }

    int maxInt(int... values) {
        int max = Integer.MIN_VALUE;
        for (int value : values) max = Math.max(max, value);
        return max;
    }
    public static void main(String[] args) throws NumberFormatException, IOException {
        // TODO Auto-generated method stub
        new Template().run();
    }

    void run() throws NumberFormatException, IOException {
        solve();
        out.close();
    };

    BufferedReader in;
    PrintWriter out;

    StringTokenizer tok;
    String delim = " ";
    Random rnd = new Random();

    Template() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            if (fileName.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new PrintWriter(fileName + ".out");
            }

        }
        tok = new StringTokenizer("");
    }

    String readLine() throws IOException {
        return in.readLine();
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) {
                return null;
            }

            tok = new StringTokenizer(nextLine);
        }
        return tok.nextToken();
    }

    int readInt() throws NumberFormatException, IOException {
        return Integer.parseInt(readString());
    }
    byte readByte() throws NumberFormatException, IOException {
        return Byte.parseByte(readString());
    }
    int[] readIntArray (int n) throws NumberFormatException, IOException {
        int[] a = new int[n];
        for(int i=0; i<n; ++i){
            a[i] = readInt();
        }
        return a;
    }
    long readLong() throws NumberFormatException, IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(readString());
    }
}