#include <bits/stdc++.h>

#define show(x) cout << #x << " = " << x << endl

using namespace std;
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v)
{
    os << "sz=" << v.size() << "\n[";
    for (const auto& p : v) {
        os << p << ",";
    }
    os << "]\n";
    return os;
}

template <typename S, typename T>
ostream& operator<<(ostream& os, const pair<S, T>& p)
{
    os << "(" << p.first << "," << p.second
       << ")";
    return os;
}


constexpr ll MOD = 1e9 + 7;

template <typename T>
constexpr T INF = numeric_limits<T>::max() / 100;

int main()
{
    int M;
    cin >> M;
    const int num = 1 << M;
    vector<int> S(num);
    for (ll i = 0; i < num; i++) {
        cin >> S[i];
    }

    vector<long double> rate(num, 0.0);
    vector<long double> prev_rate(num, 1.0);
    for (int m = 1; m <= M; m++) {
        const int block_size = 1 << m;
        for (int i = 0; i < num; i++) {
            const int block = i / block_size;
            const bool mini_block = (i % block_size) / (block_size / 2);
            long double sum = 0;
            if (mini_block == 0) {
                for (int j = block_size / 2; j < block_size; j++) {
                    const int p = block * block_size + j;
                    if (p == i) {
                        continue;
                    }
                    sum += prev_rate[i] * prev_rate[p] * (static_cast<long double>(S[i] * S[i]) / (S[i] * S[i] + S[p] * S[p]));
                }
            } else {
                for (int j = 0; j < (block_size / 2); j++) {
                    const int p = block * block_size + j;
                    if (p == i) {
                        continue;
                    }
                    sum += prev_rate[i] * prev_rate[p] * (static_cast<long double>(S[i] * S[i]) / (S[i] * S[i] + S[p] * S[p]));
                }
            }
            rate[i] = sum;
        }
        for (int i = 0; i < num; i++) {
            prev_rate[i] = rate[i];
        }
    }
    cout << fixed << setprecision(10) << rate[0] << endl;
    return 0;
}