#include <iostream>
#include <cstdio>

#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,j) FOR(i,0,j)

int M;
double S[1024], dp[11][1024];
bool calculated[11][1024];

// indexがstageで勝つ確率(l, rはどこまでか)
double rec(int index, int stage, int l, int r){
    if(stage == M){return 1.0f;}
    if(calculated[stage][index]){return dp[stage][index];}

    int mid = (l+r) / 2;
    double res = 0.0f;
    if(l <= index && index < mid){
        FOR(i, mid, r){
            res += rec(i, stage+1, mid, r) * S[index] / (S[index] + S[i]);
        }
        res *= rec(index, stage+1, l, mid);
    }else{
        FOR(i, l, mid){
            res += rec(i, stage+1, l, mid) * S[index] / (S[index] + S[i]);
        }
        res *= rec(index, stage+1, mid, r);
    }

    calculated[stage][index] = true;
    return dp[stage][index] = res;
}

int main(){
    std::cin >> M;

    REP(i, 1<<M){
        std::cin >> S[i];
        S[i] *= S[i];
    }

    printf("%.8f\n", rec(0, 0, 0, 1<<M));
}