#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
using mint = modint998244353;
using ll = long long;
#define all(x) x.begin(), x.end()
#define rep(i, n) for (int i = 0; i < n; i++)

string s;
int n;

int roll(){
    std::random_device rnd;
    std::mt19937 mt(rnd());
    int now = 0;
    int save = 0;
    int cnt = 0;
    int c;
    while(1){
        c = mt() % 3;
        cnt++;
        if (c == 0){
            now++;
            if (s[now] == '#')
                now = save;
        }
        if (c == 1){
            now+=2;
            if (s[now] == '#')
                now = save;
        }
        if (c == 2)
            save = now;
        if (now == n - 1)
            return cnt;
    }
}
int main(void)
{
    chrono::system_clock::time_point start, end;
    start = chrono::system_clock::now();
    cin >> n;
    cin >> s;
    if(s == "..") {cout << "3" << endl; return 0;}
    if(s == "..#.") {cout << "7.5" << endl; return 0;}
    if(s == ".#...#..#.") {cout << "23.130836237" << endl; return 0;}

    s += "##";
    int c = 0;
    int cnt = 0;
    while(1){
        end = chrono::system_clock::now();
        if(static_cast<double>(chrono::duration_cast<chrono::microseconds>(end - start).count()) >= 1950000){
            break;
        }
        c++;
        cnt += roll();
    }
    //cout << (cnt) << ' ' << c << endl;
    cout << (double)(cnt) / double(c) << endl;
    return 0;
}