#include <iostream>
#include <iomanip>
#include <vector>

using ldouble = long double;

void solve() {
    int m;
    std::cin >> m;
    int n = 1 << m;

    std::vector<ldouble> ps(1 << m);
    for (auto& p : ps) {
        std::cin >> p;
        p *= p;
    }

    std::vector<ldouble> dp(1 << m, 1);
    for (int i = 1; i <= m; ++i) {
        std::vector<ldouble> ndp(1 << m, 0);

        for (int x = 0; x < n; ++x) {
            for (int y = 0; y < n; ++y) {
                if ((x >> i) != (y >> i) ||
                    ((x >> (i - 1)) & 1) == ((y >> (i - 1)) & 1)) continue;
                ndp[x] += dp[x] * dp[y] * ps[x] / (ps[x] + ps[y]);
            }
        }

        std::swap(dp, ndp);
    }

    std::cout << dp[0] << "\n";
}

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(10);

    solve();

    return 0;
}