#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}; }
double solve(linear f) { return -f.first / f.second; } // f(x) = 0

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