#line 2 "Library/gcc_option.hpp"
#ifdef LOCAL
    #define _GLIBCXX_DEBUG
#else
    #pragma GCC optimize("O3")
    #pragma GCC target("avx,avx2")
    #pragma GCC optimize("unroll-loops")
#endif
#line 2 "codeforces-workspace/yu4.cpp"
#include <bits/stdc++.h>
// #include "extlib.hpp"
#line 5 "Library/config.hpp"
namespace config
{
    const auto start_time{std::chrono::system_clock::now()};
    int64_t elapsed()
    {
        using namespace std::chrono;
        const auto end_time{system_clock::now()};
        return duration_cast<milliseconds>(end_time - start_time).count();
    }
    __attribute__((constructor)) void setup()
    {
        using namespace std;
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout << fixed << setprecision(15);
    #ifdef _buffer_check
        atexit([]{ ofstream cnsl("CON"); char bufc; if(cin >> bufc) cnsl << "\n\033[1;35mwarning\033[0m: buffer not empty.\n\n"; });
    #endif
    }
    unsigned cases(void), caseid = 1;
    template <class C> void main() { for(const unsigned total = cases(); caseid <= total; ++caseid) C(); }
} // namespace config
#line 3 "Library/utils/iostream_overload.hpp"
namespace std
{
    template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }
    template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }
    template <class tuple_t, size_t index> struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis<tuple_t, index - 1>::apply(is, t); return is >> get<index>(t); } };
    template <class tuple_t> struct tupleis<tuple_t, SIZE_MAX> { static istream &apply(istream &is, tuple_t &t) { return is; } };
    template <class... T> istream &operator>>(istream &is, tuple<T...> &t) { return tupleis<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(is, t); }
    template <> istream &operator>>(istream &is, tuple<> &t) { return is; }
    template <class tuple_t, size_t index> struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };
    template <class tuple_t> struct tupleos<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };
    template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }
    template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; }
} // namespace std
#line 3 "Library/utils/read.hpp"
namespace workspace {
// read with std::cin.
template <class T = void>
struct read
{
    typename std::remove_const<T>::type value;
    template <class... types>
    read(types... args) : value(args...) { std::cin >> value; }
    operator T() const { return value; }
};
template <>
struct read<void>
{
    template <class T>
    operator T() const { T value; std::cin >> value; return value; }
};
} // namespace workspace
#line 3 "Library/utils/casefmt.hpp"
namespace workspace {
std::ostream &casefmt(std::ostream& os) { return os << "Case #" << config::caseid << ": "; }
} // namespace workspace
#line 3 "Library/utils/fixed_point.hpp"
namespace workspace {
// specify the return type of lambda.
template <class lambda_type>
class fixed_point
{
    lambda_type func;
public:
    fixed_point(lambda_type &&f) : func(std::move(f)) {}
    template <class... Args> auto operator()(Args &&... args) const { return func(*this, std::forward<Args>(args)...); }
};
} // namespace workspace
#line 3 "Library/utils/chval.hpp"
namespace workspace {
template <class T, class Comp = std::less<T>> bool chle(T &x, const T &y, Comp comp = Comp()) { return comp(y, x) ? x = y, true : false; }
template <class T, class Comp = std::less<T>> bool chge(T &x, const T &y, Comp comp = Comp()) { return comp(x, y) ? x = y, true : false; }
} // namespace workspace
#line 5 "Library/utils/binary_search.hpp"
namespace workspace {
// binary search on discrete range.
template <class iter_type, class pred_type, std::enable_if_t<std::is_convertible_v<std::invoke_result_t<pred_type, iter_type>, bool>, std::nullptr_t> = nullptr>
iter_type binary_search(iter_type ok, iter_type ng, pred_type pred)
{
    assert(ok != ng);
    intmax_t dist(ng - ok);
    while(std::abs(dist) > 1)
    {
        iter_type mid(ok + dist / 2);
        if(pred(mid)) ok = mid, dist -= dist / 2;
        else ng = mid, dist /= 2;
    }
    return ok;
}
// binary search on real numbers.
template <class real_type, class pred_type, std::enable_if_t<std::is_convertible_v<std::invoke_result_t<pred_type, real_type>, bool>, std::nullptr_t> = nullptr>
real_type binary_search(real_type ok, real_type ng, const real_type eps, pred_type pred)
{
    assert(ok != ng);
    while(std::abs(ok - ng) > eps)
    {
        real_type mid{(ok + ng) / 2};
        (pred(mid) ? ok : ng) = mid;
    }
    return ok;
}
} // namespace workspace
#line 2 "Library/alias.hpp"
using namespace std; using namespace __gnu_cxx;
using i32 = int_least32_t; using i64 = int_least64_t;
using p32 = pair<i32, i32>; using p64 = pair<i64, i64>;
template <class T, class Comp = less<T>> using heap = priority_queue<T, vector<T>, Comp>;
template <class T> using hashset = unordered_set<T>;
template <class Key, class Value> using hashmap = unordered_map<Key, Value>;
#line 12 "codeforces-workspace/yu4.cpp"
namespace workspace { struct solver; } int main() { config::main<workspace::solver>(); }
unsigned config::cases() {
    // return -1; // not specify
    // return read(); // given
    return 1;
}

#line 1 "Library/data_structure/union_find/union_find.hpp"



#line 6 "Library/data_structure/union_find/union_find.hpp"

class union_find
{
    std::vector<int> link;

public:
    explicit union_find(const unsigned n = 0) : link(n, -1) {}

    unsigned find(unsigned x)
    {
        assert(x < size());
        return link[x] < 0 ? x : (link[x] = find(link[x]));
    }

    unsigned size() const { return link.size(); }

    unsigned size(const unsigned x)
    {
        assert(x < size());
        return -link[find(x)];
    }

    bool same(const unsigned x, const unsigned y)
    {
        assert(x < size() && y < size());
        return find(x) == find(y);
    }

    bool unite(unsigned x, unsigned y)
    {
        assert(x < size() && y < size());
        x = find(x), y = find(y);
        if(x == y) return false;
        if(link[x] > link[y]) std::swap(x, y);
        link[x] += link[y];
        link[y] = x;
        return true;
    }
}; // class union_find


#line 4 "Library/modulus/modint.hpp"
template <int_fast64_t mod = 0> // compile-time defined modulo.
struct modint
{
    static_assert(mod > 0);
    template <bool i32, class = void> struct modif { using value_type = int_least32_t; };
    template <class void_t> struct modif<false, void_t> { using value_type = int_least64_t; };
    using value_type = typename modif<mod < (1 << 30)>::value_type;
    constexpr static modint one() noexcept { return 1; }
    constexpr operator value_type() const noexcept { return value; }
    constexpr modint() noexcept = default;
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint(int_type n) noexcept : value((n %= mod) < 0 ? mod + n : n) {}
    constexpr modint operator++(int) noexcept { modint t{*this}; return operator+=(1), t; }
    constexpr modint operator--(int) noexcept { modint t{*this}; return operator-=(1), t; }
    constexpr modint &operator++() noexcept { return operator+=(1); }
    constexpr modint &operator--() noexcept { return operator-=(1); }
    constexpr modint operator-() const noexcept { return value ? mod - value : 0; }
    constexpr modint &operator+=(const modint &rhs) noexcept { return (value += rhs.value) < mod ? 0 : value -= mod, *this; }
    constexpr modint &operator-=(const modint &rhs) noexcept { return (value += mod - rhs.value) < mod ? 0 : value -= mod, *this; }
    constexpr modint &operator*=(const modint &rhs) noexcept { return value = (int_fast64_t)value * rhs.value % mod, *this; }
    constexpr modint &operator/=(const modint &rhs) noexcept { return operator*=(rhs.inverse()); }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint operator+(const int_type &rhs) const noexcept { return modint{*this} += rhs; }
    constexpr modint operator+(const modint &rhs) const noexcept { return modint{*this} += rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint operator-(const int_type &rhs) const noexcept { return modint{*this} -= rhs; }
    constexpr modint operator-(const modint &rhs) const noexcept { return modint{*this} -= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint operator*(const int_type &rhs) const noexcept { return modint{*this} *= rhs; }
    constexpr modint operator*(const modint &rhs) const noexcept { return modint{*this} *= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr modint operator/(const int_type &rhs) const noexcept { return modint{*this} /= rhs; }
    constexpr modint operator/(const modint &rhs) const noexcept { return modint{*this} /= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr friend modint operator+(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) + rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr friend modint operator-(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) - rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr friend modint operator*(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) * rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    constexpr friend modint operator/(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) / rhs; }
    constexpr modint inverse() const noexcept
    {
        assert(value);
        value_type a{mod}, b{value}, u{}, v{1}, t{};
        while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
        return {u};
    }
    constexpr static modint pow(modint rhs, int_fast64_t e) noexcept
    {
        if(e < 0) e = e % (mod - 1) + mod - 1;
        modint res{1};
        while(e) { if(e & 1) res *= rhs; rhs *= rhs, e >>= 1; }
        return res;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint &rhs) noexcept { return os << rhs.value; }
    friend std::istream &operator>>(std::istream &is, modint &rhs) noexcept { value_type value; rhs = (is >> value, value); return is; }
protected:
    value_type value = 0;
}; // class modint
template <> // runtime defined modulo as default(mod = 0).
struct modint<0>
{
    using value_type = int_fast64_t;
    static value_type &mod() noexcept { static value_type mod{}; return mod; }
    static modint one() noexcept { return 1; }
    operator value_type() const noexcept { return value; }
    modint() noexcept = default;
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint(int_type n) noexcept : value{ (assert(mod()), n %= mod()) < 0 ? n + mod() : n} {}
    modint operator++(int) noexcept { modint t{*this}; return operator+=(1), t; }
    modint operator--(int) noexcept { modint t{*this}; return operator-=(1), t; }
    modint &operator++() noexcept { return operator+=(1); }
    modint &operator--() noexcept { return operator-=(1); }
    modint operator-() const noexcept { return value ? mod() - value : 0; }
    modint &operator+=(const modint &rhs) noexcept { return (value += rhs.value) < mod() ? 0 : value -= mod(), *this; }
    modint &operator-=(const modint &rhs) noexcept { return (value += mod() - rhs.value) < mod() ? 0 : value -= mod(), *this; }
    modint &operator*=(const modint &rhs) noexcept { return (value *= rhs.value) %= mod(), *this; }
    modint &operator/=(const modint &rhs) noexcept { return operator*=(rhs.inverse()); }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint operator+(const int_type &rhs) const noexcept { return modint{*this} += rhs; }
    modint operator+(const modint &rhs) const noexcept { return modint{*this} += rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint operator-(const int_type &rhs) const noexcept { return modint{*this} -= rhs; }
    modint operator-(const modint &rhs) const noexcept { return modint{*this} -= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint operator*(const int_type &rhs) const noexcept { return modint{*this} *= rhs; }
    modint operator*(const modint &rhs) const noexcept { return modint{*this} *= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    modint operator/(const int_type &rhs) const noexcept { return modint{*this} /= rhs; }
    modint operator/(const modint &rhs) const noexcept { return modint{*this} /= rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    friend modint operator+(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) + rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    friend modint operator-(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) - rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    friend modint operator*(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) * rhs; }
    template <class int_type, std::enable_if_t<std::is_integral<int_type>::value, std::nullptr_t> = nullptr>
    friend modint operator/(const int_type &lhs, const modint &rhs) noexcept { return modint(lhs) / rhs; }
    modint inverse() const noexcept
    {
        assert(mod() && value);
        long long a{mod()}, b{value}, u{}, v{1}, t{};
        while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
        return {u};
    }
    static modint pow(modint rhs, int_fast64_t e) noexcept
    {
        if(e < 0) e = e % (mod() - 1) + mod() - 1;
        modint res{1};
        while(e) { if(e & 1) res *= rhs; rhs *= rhs, e >>= 1; }
        return res;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint &rhs) noexcept { return os << rhs.value; }
    friend std::istream &operator>>(std::istream &is, modint &rhs) noexcept { long long value; rhs = modint((is >> value, value)); return is; }
protected:
    value_type value = 0;
}; // class modint<0>
using modint_runtime = modint<0>;
#line 21 "codeforces-workspace/yu4.cpp"

struct workspace::solver { // start here!

using mint=modint<(int)1e9+7>;

solver()
{
    int n; cin>>n;
    vector<long double> p(n),q(n); cin>>p>>q;
    auto f=[&](long double u)->double
    {
        long double ret=0;
        for(int i=0;i<n;i++)
        {
            ret+=p[i]*(1-q[i])/(1-q[i]*u);
        }
        return ret;
    };
    long double ok=0.0;
    long double ng=1;
    const long double eps=1e-10;
    auto pred=[&](long double x)->bool
    {
        return f(x)>x;
    };
    long double u=binary_search(ok,ng,eps,pred);
    vector<long double> ul(n);
    long double ans=0;
    for(int i=0;i<n;i++)
    {
        long double ui=(1-q[i])/(1-q[i]*u);
        ul[i]=ui;
        int a; cin>>a;
        ans+=a*log(ui);
    }
    cout<<ans<<endl;
}};