#include "bits/stdc++.h"
using namespace std;
#define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i))
#define rep(i,j) FOR(i,0,j)
#define each(x,y) for(auto &(x):(y))
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define debug(x) cout<<#x<<": "<<(x)<<endl
#define smax(x,y) (x)=max((x),(y))
#define smin(x,y) (x)=min((x),(y))
#define MEM(x,y) memset((x),(y),sizeof (x))
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vll;

const int MA = 1 << 10;
int M, N;
double S[MA], p[MA][MA], dp[11][MA];

double f(int win, int l, int r, int k){
    double &res = dp[win][k];
    if(res > -1)return res;
    if(win == 0){
        assert(l + 1 == r);
        return res = 1;
    }
    int m = (l + r) / 2;
    res = 0;
    if(k < m){
        FOR(i, m, r) res += f(win - 1, l, m, k)*f(win - 1, m, r, i)*p[k][i];
    } else{
        FOR(i, l, m) res += f(win - 1, l, m, i)*f(win - 1, m, r, k)*p[k][i];
    }
    return res;
}

int main(){
    cin >> M;
    N = 1 << M;
    rep(i, N)cin >> S[i];
    rep(i, N)rep(j, N)p[i][j] = (S[i] * S[i]) / (S[i] * S[i] + S[j] * S[j]);
    rep(i, M + 1)rep(j, N)dp[i][j] = -2;
    double ans = f(M, 0, N, 0);
    printf("%0.10f\n", ans);
}