#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <numeric>
#include <functional>
#include <cmath>
#include <queue>
#include <stack>

#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)
#define NUM 1100
typedef long long ll;

using namespace std;


int inputValue(){
    int a;
    cin >> a;
    return a;
};

void inputArray(int * p, int a){
    rep(i, a){
        cin >> p[i];
    }
};

void inputVector(vector<int> * p, int a){
    rep(i, a){
        int input;
        cin >> input;
        p -> push_back(input);
    }
}

template <typename T>
void output(T a, int precision) {
    if(precision > 0){
        cout << setprecision(precision)  << a << "\n";
    }
    else{
        cout << a << "\n";
    }
}

int power(int n, int m){
    int ret = 1;
    rep(i, m){
        ret *= n;
    }
    return ret;
}

// a = 01011, b = 01000 d = 5 -> ret = d - 3 = 1
int digit(int a, int b, int d){
    int num = 0;
    int c = 1 << (d - 1);
    rep(i, d){
        if ((c & a) == (c & b)) {
            c = c >> 1;
            num++;
        }
        else{
            break;
        }
    }
    return d - num;
}



double P[NUM] = {0};
double dp[NUM][11] = {1};

int main(int argc, const char * argv[]) {
    
    // source code
    int M = inputValue();
    int N = power(2,M);
    rep(i, N){
        cin >> P[i];
    }
    
    rep(i, N){
        dp[i][0] = 1;
    }
    
    repd(i, 1, M + 1){
        rep(j, N){
            double temp = 0.0;
            rep(k, N){
                if (digit(j, k, M) == i && j != k) {
                    temp += dp[k][i - 1] * P[j] * P[j] / (P[j] * P[j] + P[k] * P[k]);
                }
            }
            dp[j][i] = dp[j][i - 1] * temp;
        }
    }
    
    output(dp[0][M], 10);
    
    return 0;
}