#include <bits/stdc++.h>

using namespace std;

double dp[11][1050];

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int m;
	cin >> m;
	int n = (1 << m);
	vector<double> s(n);
	for (int i = 0; i < n; i++) {
		cin >> s[i];
		dp[0][i] = 1.0;
	}
	for (int i = 1; i <= m; i++) {
		for (int j = 0; j < n; j++) {
			int c = 1 << (i - 1);
			int k = j ^ c;
			for (int e = k, l = k + c; e < l; e++) {
				double tmp = s[j] * s[j];
				dp[i][j] += dp[i - 1][e] * tmp / (tmp + s[e] * s[e]);
			}
			dp[i][j] *= dp[i - 1][j];
			if (i == m && j == 0) {
				cout << fixed << setprecision(10) << dp[m][0] << endl;
				return 0;
			}			
		}
	}
	return 0;
}