#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>

#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using namespace std;
typedef long long ll;

template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
    return vector<vector<T>>(n, vector<T>(m, v));
}

template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
    return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}

template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
    if(v.empty()) {
        cout << endl;
        return;
    }
    for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
    cout << v.back() << endl;
}

using P = pair<ll, ll>;
using T = tuple<ll, ll, double>;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    int n; cin >> n;
    vector<ll> a(n), b(n);
    for(int i = 0; i < n; i++) cin >> a[i];
    for(int i = 0; i < n; i++) cin >> b[i];
    auto f = [&](ll a, ll b){
        double x = sqrt((double)a/(double)b);
        return max(x, 1.0);
    };
    vector<T> vt;
    for(int i = n-1; i >= 0; i--){
        ll aa = a[i], bb = b[i], xx = f(a[i], b[i]);
        while(true){
            if(vt.empty()){
                vt.push_back(T(aa, bb, xx));
                break;
            }
            auto [a_next, b_next, x_next] = vt.back();
            if(xx < x_next){
                vt.push_back(T(aa, bb, xx));
                break;
            }else{
                vt.pop_back();
                aa += a_next;
                bb += b_next;
                xx = f(aa, bb);
            }
        }
        
    }
    double ans = 0.0;
    for(auto [a, b, x]: vt){
        // cout << a << ' ' << b << ' ' << x << endl;
        ans += (double)a/x + (double)b*x;
    }
    cout << ans << endl;
}