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

#include <boost/multiprecision/cpp_dec_float.hpp>
namespace bsmp = boost::multiprecision;
using Q = bsmp::number<bsmp::cpp_dec_float<80>>;
//using Q = long double;

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

int main() {
  int n;
  string s;
  cin >> n >> s;
  vector<Q> E(n + 1);
  vector<linear> f(n + 1);
  f[n - 1] = {0, 0};
  f[n] = {0, 1};

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