#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 n, int m){
	return (double)S[n]*S[n] / (double)(S[n]*S[n] + S[m]*S[m]);
}

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

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

	return 0;
}