#include <iostream>
#include <vector>
#include <algorithm>
#include <iomanip>

using namespace std;

int main() {
	int m;
	cin >> m;
	int playerCount = (1 << m);
	vector<double> s(1 + playerCount);
	for (int i = 1; i <= playerCount; ++i) {
		cin >> s[i];
	}
	// [?-th round][?-th player]
	vector<vector<double> > p(1 + m, vector<double>(1 + playerCount));
	fill(p[0].begin(), p[0].end(), 1.0);
	for (int round = 1; round <= m; ++round) {
		for (int k = 1; k <= playerCount; ++k) {
			double sum = 0;
			int game = (k - 1) / (1 << round);
			int previousGame = (k - 1) / (1 << (round - 1));
			for (int m = game * (1 << round) + 1;
				m <= (game + 1) * (1 << round);
				++m) {
				if (m < previousGame * (1 << (round - 1)) + 1
					|| (previousGame + 1) * (1 << (round - 1)) + 1 <= m) {
					double conditional = s[k] * s[k] / (s[k] * s[k] + s[m] * s[m]);
					sum += conditional * p[round - 1][m];
				}
			}
			p[round][k] = p[round - 1][k] * sum;
		}
	}
	cout << fixed << setprecision(12) << p[m][1] << endl;
	return 0;
}