#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
ll ILL=2167167167167167167;
const int INF=2100000000;
const int mod=998244353;
#define rep(i,a,b) for (ll i=a;i<b;i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";}
template<class T> void vec_out(vector<T> &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}
template<class T> T min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T sum(vector<T> &a){assert(!a.empty());T ans=a[0]-a[0];for(auto &x:a) ans+=x;return ans;}



void solve();
// oddloop
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	
	int t=1;
	//cin>>t;
	rep(i,0,t) solve();
}

void solve(){
	int N;
	cin>>N;
	string S;
	cin>>S;
	S+="#";
	vector<ld> ans(N),goal_p(N),goal_v(N),ret_p(N),ret_v(N),save_p(N),save_v(N);
	goal_p[N-1]=1;
	goal_p[N-1]=1;
	ld P=(ld)(1)/(ld)(3);
	for(int i=N-2;i>=0;i--){
		if(S[i]=='#') continue;
		rep(j,1,3){
			if(S[i+j]=='#'){
				ret_p[i]+=P;
				ret_v[i]+=P;
			}else{
				save_p[i]+=save_p[i+j]*P;
				save_v[i]+=(save_p[i+j]+save_v[i+j])*P;
				goal_p[i]+=goal_p[i+j]*P;
				goal_v[i]+=(goal_p[i+j]+goal_v[i+j])*P;
				ret_p[i]+=ret_p[i+j]*P;
				ret_v[i]+=(ret_p[i+j]+ret_v[i+j])*P;
			}
		}
		ld tmp=ret_v[i]+save_v[i]+goal_v[i]+P;
		ld A=1-P-ret_p[i];
		ans[i]=tmp/A;
		save_p[i]+=P;
		save_v[i]+=P*ans[i]+P;
	}
	/*
	vec_out(ans);
	vec_out(save_p);
	vec_out(save_v);
	vec_out(goal_p);
	vec_out(goal_v);
	vec_out(ret_p);
	vec_out(ret_v);*/
	cout<<fixed<<setprecision(20)<<ans[0]<<"\n";
}