#include <bits/stdc++.h> using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep2(i, x, n) for (int i = x; i <= n; i++) #define rep3(i, x, n) for (int i = x; i >= n; i--) #define each(e, v) for (auto &e : v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair<int, int>; using pil = pair<int, ll>; using pli = pair<ll, int>; using pll = pair<ll, ll>; template <typename T> bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template <typename T> bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template <typename T> int flg(T x, int i) { return (x >> i) & 1; } template <typename T> void print(const vector<T> &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template <typename T> void printn(const vector<T> &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template <typename T> int lb(const vector<T> &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template <typename T> int ub(const vector<T> &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template <typename T> void rearrange(vector<T> &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template <typename T> vector<int> id_sort(const vector<T> &v, bool greater = false) { int n = v.size(); vector<int> ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template <typename S, typename T> pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) { return make_pair(p.first + q.first, p.second + q.second); } template <typename S, typename T> pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) { return make_pair(p.first - q.first, p.second - q.second); } template <typename S, typename T> istream &operator>>(istream &is, pair<S, T> &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template <typename S, typename T> ostream &operator<<(ostream &os, const pair<S, T> &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; const int MOD = 1000000007; // const int MOD = 998244353; using ld = long double; int main() { int N; cin >> N; vector<ld> p(N), q(N); rep(i, N) cin >> p[i]; rep(i, N) cin >> q[i]; ld EPS = 1e-9; ld L = 0.0, R = 1.0 - EPS; rep(_, 100) { ld M = (L + R) * 0.5; ld x = 0; rep(i, N) x += p[i] * (1 - q[i]) / (1 - q[i] * M); (x >= M ? L : R) = M; } ld S = L; ld ans = 0; rep(i, N) { int A; cin >> A; ld r = (1 - q[i]) / (1 - q[i] * S); ans += log(r) * A; } cout << ans << '\n'; }