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

double dp1[200200],dp2[200200],dp3[200200],dp4[200200];

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int N;
    string S;
    cin >> N >> S;
    dp1[N-1] = 0;
    dp2[N-1] = 0;
    dp3[N-1] = 0;
    dp4[N-1] = 0;
    for(int i = N-2; i >= 0; i--) {
        if(S[i] == '#') continue;
        double rep = 1.0/3,cnt = 1.0/3,suc = 0;
        for(int j = 1; j <= 2; j++) {
            if(i+j < N && S[i+j] == '.') {
                rep += 1.0/3*dp3[i+j];
                cnt += 1.0/3*dp4[i+j];
                suc += (1.0/3)*(1.0-dp3[i+j]);
            }
            else {
                rep += 1.0/3;
                cnt += 1.0/3;
            }
        }
        dp1[i] = (1.0/3)/rep*(1.0/suc-1);
        for(int j = 1; j <= 2; j++) {
            if(i+j < N && S[i+j] == '.') {
                dp1[i] += (1.0/3*dp3[i+j])/rep*(dp4[i+j]+1)*(1.0/suc-1);
                dp1[i] += ((1.0/3)*(1.0-dp3[i+j]))/suc*(dp2[i+j]+1);
            }
            else {
                dp1[i] += (1.0/3)/rep*(1.0/suc-1);
            }
        }
        suc = 1.0;
        for(int j = 1; j <= 2; j++) {
            if(i+j < N && S[i+j] == '.') {
                suc += 1.0-dp3[i+j];
            }
        }
        dp2[i] = 1.0/suc*(dp1[i]+1);
        for(int j = 1; j <= 2; j++) {
            if(i+j < N && S[i+j] == '.') {
                dp2[i] += (1.0-dp3[i+j])/suc*(dp2[i+j]+1);
                dp3[i] += 1.0/3*dp3[i+j];
            }
            else {
                dp3[i] += 1.0/3;
            }
        }
        suc = 0;
        for(int j = 1; j <= 2; j++) {
            if(i+j < N && S[i+j] == '.') {
                suc += 1.0/3*dp3[i+j];
            }
            else {
                suc += 1.0/3;
            }
        }
        for(int j = 1; j <= 2; j++) {
            if(i+j < N && S[i+j] == '.') {
                dp4[i] += (1.0/3*dp3[i+j])/suc*(dp4[i+j]+1);
            }
            else {
                dp4[i] += (1.0/3)/suc;
            }
        }
    }
    cout << fixed << setprecision(18) << dp1[0] << endl;
}