#include <bits/stdc++.h>  

using namespace std;

//#define int long long
#define FOR(i, j, k) for(int i = j; i < (int)k; ++i)
#define rep(i, j) FOR(i, 0, j)
#define INF (1 << 30)

typedef unsigned long long ull;
typedef pair<int, int> P;
typedef pair<P, int> Pi;

const int MOD = 1e9 + 7;
const int dy[] = {0, 0, 1, -1};
const int dx[] = {1, -1, 0, 0};

template <class T> void chmin(T& a, const T& b) { a = min(a, b); }
template <class T> void chmax(T& a, const T& b) { a = max(a, b); }
template<typename T> T gcd(T a, T b) { return (b == 0 ? a : gcd(b, a % b)); }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

double s[1025];
double dp[12][1025], w[1025][1025];

signed main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int m;
    cin >> m;
    rep(i, (1 << m)) cin >> s[i];
    rep(i, (1 << m)) rep(j, (1 << m)) {
        if(i == j) continue;
        w[i][j] = (s[i] * s[i]) / (s[i] * s[i] + s[j] * s[j]);
    }
    rep(i, 1025) dp[0][i] = 1.0;
    rep(i, m) rep(j, (1 << m)) rep(k, (1 << m)) {
        if((j >> i) != (k >> i) && (j >> (i + 1)) == (k >> (i + 1))) {
            dp[i + 1][j] += dp[i][j] * dp[i][k] * w[j][k];
         }
    }
    printf("%.9f\n", dp[m][0]);
    return 0;
}