#include <bits/stdc++.h>
using namespace std;
int main(){
  cout << fixed << setprecision(20);
  int N;
  cin >> N;
  string S;
  cin >> S;
  S += '#';
  vector<double> dp_gameover_p(N, 0);
  vector<double> dp_gameover_pe(N, 0);
  vector<double> dp_goal_p(N, 0);
  vector<double> dp_goal_pe(N, 0);
  dp_goal_p[N - 1] = 1;
  for (int i = N - 2; i >= 0; i--){
    if (S[i] == '.'){
      for (int j = i + 1; j <= i + 2; j++){
        if (S[j] == '#'){
          dp_gameover_p[i] += (double) 1 / 3;
          dp_gameover_pe[i] += (double) 1 / 3;
        } else {
          dp_gameover_p[i] += dp_gameover_p[j] / 3;
          dp_gameover_pe[i] += (dp_gameover_p[j] + dp_gameover_pe[j]) / 3;
          dp_goal_p[i] += dp_goal_p[j] / 3;
          dp_goal_pe[i] += (dp_goal_p[j] + dp_goal_pe[j]) / 3;
        }
      }
    }
  }
  vector<double> dp(N, 0);
  vector<double> dp2_p(N, 0), dp2_pe(N, 0);
  for (int i = N - 2; i >= 0; i--){
    if (S[i] == '.'){
      double gameover_p = dp_gameover_p[i] + (double) 1 / 3;
      double gameover_pe = dp_gameover_pe[i] + (double) 1 / 3;
      dp[i] += (1 / (1 - gameover_p) - 1) * (gameover_pe / gameover_p);
      dp[i] += dp_goal_pe[i] / (1 - gameover_p);
      for (int j = i + 1; j <= i + 2; j++){
        if (S[j] == '.' && j < N - 1){
          dp2_p[i] += (double) 1 / 9;
          dp2_pe[i] += (2 + dp[j]) / 9;
          dp2_p[i] += dp2_p[j] / 3;
          dp2_pe[i] += (dp2_p[j] + dp2_pe[j]) / 3;
        }
      }
      dp[i] += dp2_pe[i] / (1 - gameover_p);
    }
  }
  cout << dp[0] << endl;
}