#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <queue>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <ctime>

using namespace std;

inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x) {ostringstream sout;sout<<x;return sout.str();}

typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef tuple<int, int, int> TIII;
typedef long long LL;
typedef unsigned long long ULL;

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)

#define MP make_pair
#define MT make_tuple
#define SZ(a) int((a).size())
#define EACH(i,c) for(auto i: c)
#define SORT(c) sort((c).begin(),(c).end())

#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()

const double EPS = 1e-10;
const double PI  = acos(-1.0);

#define dump(x)  cerr << #x << " = " << (x) << endl;
#define dump2(x, y)  cerr << #x << " = " << (x) << "," << #y << " = " << (y) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	int M;
	cin >> M;
	VI S(1 << M);
	REP(i, 1 << M){
		int tmp;
		cin >> tmp;
		S[i] = tmp * tmp;
	}

	vector<vector<double>> dp(M + 1, vector<double>((1 << M), 0));
	REP(i, 1 << M){
		dp[0][i] = 1.0 * S[i];
		if(i % 2 == 0) dp[0][i] /= (S[i] + S[i + 1]);
		else dp[0][i] /= (S[i - 1] + S[i]);
	}
	cout << endl;
	FOR(i, 1, M){
		REP(j, 1 << M){
			FOR(k, i / (1 << (i + 1)) + (1 << i), i / (1 << (i + 1)) + (1 << (i + 1))){
				if(j == k) continue;
				dp[i][j] += 1.0 * S[j] / (S[j] + S[k]) * dp[i - 1][k] * dp[i - 1][j];
			}
		}
	}
	/*
	REP(i, M) {
		REP(j, 1 << M){
			cout << dp[i][j] << " ";
		}
		cout << endl;
	}
	*/

	cout << dp[M - 1][0] << endl;

	return 0;
}