#include <bits/stdc++.h>
using namespace std;

// f(x) = a + bx
using linear = pair<double, double>;
linear operator+(linear f, linear g) {
  return {f.first + g.first, f.second + g.second};
}
linear operator+(linear f, double a) { return {f.first + a, f.second}; }
linear operator/(linear f, double a) { return {f.first / a, f.second / a}; }
// f(x) = 0
double solve(linear f) { return -f.first / f.second; }
// f(a)
double eval(linear f, double a) { return f.first + f.second * a; }

int main() {
  int n;
  string s;
  cin >> n >> s;
  s.push_back('#');
  vector E(n + 1, vector<double>(n));
  for (int j = n - 2; j >= 0; j--) {
    if (s[j] == '#') continue;
    vector<linear> f(n + 1);
    for (int i = n; i > j; i--) {
      if (i == n - 1) {
        f[i] = {0, 0};
      } else if (s[i] == '.') {
        f[i] = (f[i + 1] + f[i + 2] + E[i][i]) / 3 + 1;
      } else {
        f[i] = {0, 1};
      }
    }
    E[j][j] = solve((f[j + 1] + f[j + 2] + linear{0, -2}) / 3 + 1);
    for (int i = j + 1; i <= n; i++) E[i][j] = eval(f[i], E[j][j]);
  }
  cout << setprecision(20) << setiosflags(ios::fixed);
  cout << E[0][0] << "\n";
}