#include <string>
#include <vector>
#include <cmath>
#include <ctime>
#include <iostream>
#include <cstdio>
#include <set>
#include <map>
#include <queue>
#include <sstream>
#include <algorithm>
#include <numeric>
#include <cstring>
using namespace std;
typedef long long ll;

int S[(1<<10)+10];
double dp[12][(1<<10)+10];

double prob(int A, int B){
    return 1.0 * A * A / (A * A + B * B);
}

int main(){
    int M;
    cin >> M;
    
    int N = 1 << M;
    for(int i=0;i<N;i++)cin >> S[i];
    for(int i=0;i<N;i++)dp[0][i] = 1;
    
    int len = 2;
    int half = 1;
    
    for(int i=0;i<M;i++){
        for(int j=0;j<N;j+=len){
            int as = j;
            int at = as + half;
            int bs = at;
            int bt = bs + half;
            
            for(int a=as;a<at;a++)for(int b=bs;b<bt;b++){
                dp[i+1][a] += prob(S[a], S[b]) * dp[i][a] * dp[i][b];
                dp[i+1][b] += prob(S[b], S[a]) * dp[i][a] * dp[i][b];
            }
        }
        
        len <<= 1;
        half <<= 1;
    }
    
    printf("%.10f\n", dp[M][0]);
    return 0;
}