#include <atcoder/all>
#include <bits/stdc++.h>
using namespace std;
using namespace atcoder;
#define rep(i, n) REP(i, 0, n)
#define REP(i, s, e) for (int i = (s); i < (int)(e); i++)
#define repr(i, n) REPR(i, n, 0)
#define REPR(i, s, e) for (int i = (int)(s - 1); i >= (int)(e); i--)
#define all(r) r.begin(), r.end()
#define rall(r) r.rbegin(), r.rend()

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;

template <typename T, typename U>
T chmax(T& a, const U& b) {
    if (a >= b) return false;
    a = b;
    return true;
}
template <typename T, typename U>
T chmin(T& a, const U& b) {
    if (a <= b) return false;
    a = b;
    return true;
}

void yes_no(bool f, string yes = "Yes", string no = "No") { cout << (f ? yes : no) << "\n"; }

void solve() {
    int m;
    cin >> m;
    int n = 1 << m;
    using D = long double;
    vector<D> s(n);
    rep(i, n) cin >> s[i], s[i] *= s[i];
    vector dp(m + 1, vector<D>(n, 0));
    rep(i, n) dp[0][i] = 1;
    rep(i, m) {
        int x = (1 << (i + 1)), y = (1 << i);
        rep(j, n) rep(k, n) if (j != k) {
            if (j / x == k / x && j / y != k / y) {
                D p = s[j] / (s[j] + s[k]);
                dp[i + 1][j] += dp[i][j] * dp[i][k] * p;
            }
        }
    }
    D ans = dp[m][0];
    cout << fixed << setprecision(15);
    cout << ans << "\n";
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int t = 1;
    // cin >> t;
    rep(ti, t) solve();
    return 0;
}