#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#include <set>
#include <map>
#include <queue>
#include <iostream>
#include <sstream>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <cctype>
#include <cassert>
#include <limits>
#include <functional>
#define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i))
#define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i))
#if defined(_MSC_VER) || __cplusplus > 199711L
#define aut(r,v) auto r = (v)
#else
#define aut(r,v) __typeof(v) r = (v)
#endif
#define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it)
#define all(o) (o).begin(), (o).end()
#define pb(x) push_back(x)
#define mp(x,y) make_pair((x),(y))
#define mset(m,v) memset(m,v,sizeof(m))
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
using namespace std;
typedef vector<int> vi; typedef pair<int,int> pii; typedef vector<pair<int,int> > vpii; typedef long long ll;
template<typename T, typename U> inline void amin(T &x, U y) { if(y < x) x = y; }
template<typename T, typename U> inline void amax(T &x, U y) { if(x < y) x = y; }

int main() {
	int M;
	while(~scanf("%d", &M)) {
		vector<int> S(1 << M);
		for(int i = 0; i < 1 << M; ++ i)
			scanf("%d", &S[i]);
		vector<vector<double> > dp, ndp;
		ndp.assign(1 << M, vector<double>(1));
		rep(i, 1 << M)
			ndp[i][0] = 1;
		for(int i = M - 1; i >= 0; -- i) {
			dp.swap(ndp);
			ndp.assign(1 << i, vector<double>(1 << (M - i)));
			int m = M - i - 1, n = 1 << m;
			rep(j, 1 << i) {
				rep(k, n) rep(l, n) {
					int s = S[(j << 1 | 0) << m | k];
					int t = S[(j << 1 | 1) << m | l];
					double x = dp[j << 1 | 0][k] * dp[j << 1 | 1][l];
					double p = (s * s) * 1. / (s * s + t * t);
					double q = 1 - p;
					ndp[j][0 + k] += p * x;
					ndp[j][n + l] += q * x;
				}
			}
		}
		double ans = ndp[0][0];
		printf("%.10f\n", ans);
	}
	return 0;
}