#include<iostream>
#include<sstream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<string>
#include<vector>
#include<cmath>
#include<set>
#include<map>
#include<stack>
#include<queue>
#include<numeric>
#include<functional>
#include<complex>

using namespace std;
#define BET(a,b,c) ((a)<=(b)&&(b)<(c))
#define FOR(i,n) for(int i=0,i##_end=(int(n));i<i##_end;i++)
#define SZ(x) (int)(x.size())
#define ALL(x) (x).begin(),(x).end()
#define MP make_pair
#define FOR_EACH(it,v) for(__typeof(v.begin()) it=v.begin(),it_end=v.end() ; it != it_end ; it++)
typedef vector<int> VI;
typedef vector<VI> VVI;

int M;
long long S[1024];

double memo[1024][11];

double win(int p, int q){
    return 1.0 * S[p] * S[p] / (1.0 * S[p] * S[p] + 1.0 * S[q] * S[q]);
}

double dfs(int pos, int M){
    if(M == 0) return 1.0;
    double& ret = memo[pos][M];
    if(!std::isnan(ret)) return ret;
    double val = 0;
    int r = 1<<M;
    int s = pos / r * r;
    if(pos % r < r / 2) s += r / 2;
    FOR(i,r / 2) {
        val += dfs(s + i, M - 1) * win(pos, s + i);
    }
    val *= dfs(pos, M - 1);
    return ret = val;
}

int main()
{
    cin>>M;
    FOR(i,1<<M) scanf("%lld",&S[i]);
    memset(memo , -1 , sizeof(memo));
    printf("%.10f\n", dfs(0, M));
    return 0;
}