#line 1 "main.cpp"
#include <bits/stdc++.h>
#line 2 "/home/ubuntu/Library/utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 4 "/home/ubuntu/Library/utils/binary_search_float.hpp"

/**
 * @brief a binary search on floating point numbers / 二分探索 (浮動小数点数)
 */
template <int Iteration = 64, typename UnaryPredicate>
double binsearch_float(double l, double r, UnaryPredicate p) {
    assert (l <= r);
    REP (i, Iteration) {
        double m = (l + r) / 2;
        (p(m) ? r : l) = m;
    }
    return r;
}
#line 4 "main.cpp"
using namespace std;

double solve(int n, const vector<double> & p, const vector<double> & q, const vector<int> & a) {
    auto f = [&](double r) -> double {
        double fr = 0;
        REP (i, n) {
            fr += p[i] * (1 - q[i]) / (1 - q[i] * r);
        }
        return fr;
    };
    double r = binsearch_float(0, 1, [&](double r) { return r >= f(r); });
    double ans = 0;
    REP (i, n) {
        double r_i = (1 - q[i]) / (1 - q[i] * r);
        ans += a[i] * log(r_i);
    }
    return ans;
}

int main() {
    int n; cin >> n;
    vector<double> p(n);
    REP (i, n) {
        cin >> p[i];
    }
    vector<double> q(n);
    REP (i, n) {
        cin >> q[i];
    }
    vector<int> a(n);
    REP (i, n) {
        cin >> a[i];
    }
    auto ans = solve(n, p, q, a);
    cout << setprecision(18) << ans << endl;
    return 0;
}