#include <bits/extc++.h>

int main(){
    using namespace std;
    unsigned long N;
    cin >> N;
    vector<pair<unsigned long, unsigned long>> problems(N);
    for(auto&& [a, _] : problems)cin >> a;
    for(auto&& [_, b] : problems)cin >> b;
    reverse(begin(problems), end(problems));
    vector<pair<unsigned long, unsigned long>> stack;
    while(!empty(problems)){
        auto [a, b]{problems.back()};
        problems.pop_back();
        while(!empty(stack) && stack.back().first * b >= stack.back().second * a){
            a += stack.back().first;
            b += stack.back().second;
            stack.pop_back();
        }
        stack.emplace_back(a, b);
    }
    long double ans{};
    for(const auto& [a, b] : stack)ans += a < b ? a + b : sqrt(static_cast<long double>(4 * a * b));
    cout << fixed << setprecision(30) << ans << endl;
    return 0;
}