#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(n);i++)
#define ALL(A) A.begin(), A.end()

using namespace std;

typedef long long ll;
typedef pair<int, int> P;

int S[1<<10];
double dp[11][1<<10];

double calc_p(int i, int j){
	return (double)S[i]*S[i] / (double)(S[i]*S[i] + S[j]*S[j]);
}  

int main()
{
	memset(S, 0, sizeof(S));
	memset(dp, 0., sizeof(dp));
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int M; cin >> M;
	rep (i, 1<<M) cin >> S[i];
	rep (i, 1<<M) dp[0][i] = 1.;

	for (int k = 1; k <= M; ++k){
		for (int i = 0; i < (1<<M); ++i){
			int l = (i>>k)<<k, r = l + (1<<k);
			if (i >= (l+r) / 2)
				r = (l + r) / 2;
			else
				l = (l + r) / 2;
			double p = 0.;
			for (int j = l; j < r; ++j){
				p += dp[k-1][j] * calc_p(i,j);
			} // end for
			dp[k][i] = p*dp[k-1][i];
		} // end for
	} // end for

	printf("%.8lf\n", dp[M][0]);	
		
	return 0;
}