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


ll dp[2][310][310][310];
int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int n;
    cin>>n;
    vector<double> a(n),b(n);
    for(int i = 0;i<n;i++) cin>>a[i];
    for(int i = 0;i<n;i++) cin>>b[i];
    vector<pair<double,double>> st;
    for(int i = 0;i<n;i++){
        if(st.empty()){
            st.push_back(make_pair(a[i],b[i]));
            continue;
        }
        st.push_back(make_pair(a[i],b[i]));
        while(st.size()>=2){
            auto now = st.back();
            st.pop_back();
            auto nxt = st.back();
            st.pop_back();
            if(now.first/now.second <= nxt.first/nxt.second){
                now.first += nxt.first;
                now.second += nxt.second;
                st.push_back(now);
            }else{
                st.push_back(nxt);
                st.push_back(now);
                break;
            }
        }
    }
    double ans = 0;
    for(int i = 0;i<st.size();i++){
        auto now = st[i];
        double use = now.first / now.second;
        if(use<1) use = 0;
        else{
            use = sqrt(use) - 1;
        }
        ans += now.first /(1+use)  + now.second * (1+use);
    }
    cout<<setprecision(30)<<fixed<<ans<<endl;

}