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.
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
const int INF = 1000001000;
const long long INFLL = INF * 1LL * INF;
const int mod = 1000 * 1000 * 1000 + 7;
const int mod9 = 1000 * 1000 * 1000 + 9;
const int modr = 99990001;
const long double PI = 3.1415926535897932385;
template <class T>
void zero(T val, T& first) {
  first = val;
}
template <class T, class... Targs>
void zero(T val, T& first, Targs&... Fargs) {
  first = val;
  zero(val, Fargs...);
}
template <class T, class T2>
std::istream& operator>>(std::istream& is, pair<T, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T>
std::istream& readN(T& first, int n, int st = 0) {
  for (int i = st, iend = (st + n - 1); i <= iend; i++) cin >> first[i];
  return cin;
}
template <class T>
std::istream& readS(set<T>& first, int n) {
  T second = *first.rbegin();
  for (int i = 0, iend = (n - 1); i <= iend; i++) {
    cin >> second;
    first.insert(second);
  }
  return cin;
}
template <class T>
std::istream& read(T& first) {
  return cin >> first;
}
template <class T, class... Targs>
std::istream& read(T& first, Targs&... Fargs) {
  return read(first), read(Fargs...);
}
template <class T, class T2>
std::ostream& operator<<(std::ostream& os, pair<T, T2> p) {
  return os << p.first << " " << p.second;
}
template <class T>
std::ostream& operator<<(std::ostream& os, vector<T> v) {
  bool f = true;
  for (auto second : v) {
    if (!f) os << ' ';
    os << second;
    f = false;
  }
  return os;
}
template <class T>
std::ostream& operator<<(std::ostream& os, set<T> v) {
  bool f = true;
  for (auto second : v) {
    if (!f) os << ' ';
    os << second;
    f = false;
  }
  return os;
}
template <class T>
std::ostream& operator<<(std::ostream& os, multiset<T> v) {
  bool f = true;
  for (auto second : v) {
    if (!f) os << ' ';
    os << second;
    f = false;
  }
  return os;
}
template <class T, class T2>
std::ostream& operator<<(std::ostream& os, map<T, T2> v) {
  bool f = true;
  for (pair<T, T2> second : v) {
    if (!f) os << ' ';
    os << second.first << "=>" << second.second;
    f = false;
  }
  return os;
}
template <class T>
std::ostream& outV(T first, char del = ' ') {
  bool f = true;
  for (auto second : first) {
    if (!f) cout << del;
    cout << second;
    f = false;
  }
  return cout;
}
template <class T>
std::ostream& outN(T first, int n = -1, int st = 0) {
  for (int i = st, iend = (n == -1 ? (int)first.size() - 1 : st + n - 1);
       i <= iend; i++) {
    cout << first[i];
    if (i < iend) cout << ' ';
  }
  return cout;
}
template <class T>
std::ostream& outAN(T first, int n = -1, int st = 0) {
  for (int i = st, iend = (n - 1); i <= iend; i++) {
    cout << first[i];
    if (i < iend) cout << ' ';
  }
  return cout;
}
template <class T>
std::ostream& outA2(T first, int n, int m) {
  for (int i = 0, iend = (n - 1); i <= iend; i++) {
    for (int j = 0, jend = (m - 1); j <= jend; j++)
      cout << first[i][j] << (j == m - 1 ? '\n' : ' ');
  }
  return cout;
}
template <class T>
std::ostream& out(T first) {
  return cout << first;
}
template <class T, class... Targs>
std::ostream& out(T first, Targs... Fargs) {
  return out(first) << " ", out(Fargs...);
}
template <typename T>
void srt(T& a, int st, int fn, bool isArr) {
  sort(a + st, a + fn + 1);
}
template <class T>
void srt(T& a, int st = 0, int fn = 0) {
  sort(a.begin() + st, fn ? a.begin() + fn + 1 : a.end());
}
template <typename T>
T rev_num(T a) {
  T r = 0;
  for (; a; a /= 10) r = r * 10 + a % 10;
  return r;
}
template <typename T>
void rev(T& a, int st, int fn, bool isArr) {
  reverse(a + st, a + fn + 1);
}
template <class T>
void rev(T& a, int st = 0, int fn = 0) {
  reverse(a.begin() + st, fn ? a.begin() + fn + 1 : a.end());
}
long long sqr(long long a) { return a * a; };
long long sqr(int a) { return a * 1LL * a; };
long double sqr(long double a) { return a * a; };
long long sqDist(pair<long long, long long> first,
                 pair<long long, long long> second) {
  return sqr(first.first - second.first) + sqr(first.second - second.second);
}
long double dist(pair<long long, long long> first,
                 pair<long long, long long> second) {
  return sqrtl(sqDist(first, second));
}
long long phi(int n) {
  int res = n;
  for (long long i = 2; i * i <= n; i++)
    if (n % i == 0) {
      while (n % i == 0) n /= i;
      res -= res / i;
    }
  if (n > 1) res -= res / n;
  return res;
}
long long bpm(long long a, long long n = -2, long long m = mod) {
  n = n < 0 ? n + m : n;
  long long r = 1;
  while (n) {
    if (n & 1) r = (r * a) % m;
    a = (a * a) % m;
    n >>= 1;
  }
  return r;
}
unsigned long long gcd(unsigned long long a, unsigned long long b) {
  while (b) {
    a %= b;
    swap(a, b);
  }
  return a;
}
vector<int> ero_p, ero_l;
void ero(int n) {
  ero_l.resize(n + 1);
  ero_l[0] = -1;
  for (int i = 2, iend = (n); i <= iend; i++)
    if (!ero_l[i]) {
      ero_p.push_back(i);
      ero_l[i] = i;
      for (long long j = i * 1LL * i; j <= n; j += i) {
        ero_l[j] = i;
      }
    }
}
long long gcd_cb(long long a, long long b, long long& first,
                 long long& second) {
  if (!b) {
    first = 1;
    second = 0;
    return a;
  }
  long long x1, y1, g;
  g = gcd_cb(b, a % b, x1, y1);
  first = y1;
  second = x1 - a / b * y1;
  return g;
}
vector<long long> fact;
void fact_prec(int n = 20) {
  fact.resize(n + 1);
  fact[0] = 1;
  for (int i = 1, iend = (n); i <= iend; i++) {
    fact[i] = fact[i - 1] * i;
  }
}
vector<long double> factd;
void fact_precd(int n = 146) {
  factd.resize(n + 1);
  factd[0] = 1;
  for (int i = 1, iend = (n); i <= iend; i++) {
    factd[i] = factd[i - 1] * i;
  }
}
string str(long long a) {
  string r = "";
  for (; a; a /= 10) r += a % 10 + '0';
  rev(r);
  return r;
}
template <class T>
int bitc(T first) {
  int r = 0;
  for (T d = first; d > 0; d >>= 1) {
    r += d & 1;
  }
  return r;
}
int sum_num(long long n) {
  int d = 0;
  for (; n; n /= 10) d += n % 10;
  return d;
}
const int N = 100005;
int main() {
  int n, a, b;
  read(n, a, b);
  string s;
  read(s);
  s += '*';
  int sum = 0;
  int len = 0;
  for (auto c : s) {
    if (c == '.') {
      len++;
    } else {
      if (a > b) {
        swap(a, b);
      }
      int mn = min(len / 2, a);
      int mx = min(len - len / 2, b);
      sum += mn + mx;
      a -= mn;
      b -= mx;
      len = 0;
    }
  }
  out(sum) << "\n";
  return 0;
}
