#include <algorithm>
#include <cstdio>
#include <functional>
#include <iostream>
#include <cstring>
#include <climits>
#include <cmath>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
using namespace std;
 
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> i_i;
typedef pair<ll, int> ll_i;
typedef pair<double, int> d_i;
typedef pair<ll, ll> ll_ll;
typedef pair<double, double> d_d;
struct edge { int u, v; ll w; };
 
double calc(int x, int y) {
	return (double)x * x / (x * x + y * y);
}
 
int main() {
	int K; cin >> K;
	int n = 1 << K;
	vector<int> R(n);
	for (int i = 0; i < n; i++) cin >> R[i];
	vector< vector<double> > dp(K + 1);
	dp[0].assign(n, 1);
	for (int k = 1; k <= K; k++) {
		dp[k].assign(n, 0);
		int m = 1 << (k - 1);
		for (int i = 0; i < n; i++)
			for (int j = m * ((i / m) ^ 1); j < m * ((i / m) ^ 1) + m; j++)
				dp[k][i] += dp[k - 1][i] * dp[k - 1][j] * calc(R[i], R[j]);
	}
	printf("%.10f\n", dp[K][0]);
}