#include <iostream>
#include <vector>
#include <cmath>
#include <map>
#include <set>
#include <iomanip>
#include <queue>
#include <algorithm>
#include <numeric>
#include <deque>
#include <complex>

using namespace std;

int main(){

    long long M, N, vs, v;
    long double P, tot;
    cin >> M;
    N = 1LL<<M;
    vector<vector<long double>> dp(M+1, vector<long double>(N));

    for (int i=0; i<N; i++) dp[0][i] = 1.0;
    vector<long double> S(N);
    for (int i=0; i<N; i++) cin >> S[i];

    for (int i=1; i<=M; i++){
        for (int j=0; j<N; j++){
            tot = 0.0;
            vs = j/(1<<i) * (1<<i) + (1<<(i-1)) - (1<<(i-1) & j);
            for (int k=0; k<(1<<(i-1)); k++){
                v = vs+k;
                P = S[j]*S[j]/(S[v]*S[v]+S[j]*S[j]);
                tot += P * dp[i-1][v];
            }
            dp[i][j] = dp[i-1][j] * tot;
        }
    }

    cout << setprecision(18) << dp[M][0] << endl;

    return 0;
}