#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int (i) = 0 ; (i) < (int)(n) ; (i)++)
#define REP(i,a,b) for(int (i) = a ; (int)(i) <= (int)(b) ; (i)++)
#define all(n) (n).begin(),(n).end()
typedef long long ll;
typedef vector<int> Vi;
typedef vector<Vi> VVi;
typedef pair<long long,long long> Pii;
typedef vector<Pii> VPii;
typedef complex<double> P;


map< array<int,3> , double> dp;

int S[1024];

double prob(int i,int j){
	return 1. * S[i]*S[i] / (S[i]*S[i]+S[j]*S[j]);
}
double dfs(int l,int r,int who){
	if( r - l == 1 ) return who == l; 
	if( dp.count({l,r,who})) return dp[{l,r,who}];
	
	double ans = 0;
	int m = (l+r) / 2;
	if( l <= who && who < m ){
		double sub = dfs(l,m,who);
		for(int i = m ; i < r ; i++){
			ans += dfs(m,r,i) * prob(who,i);
		}
		ans *= sub;
	}else{
		double sub = dfs(m,r,who);
		for(int i = l ; i < m ; i++){
			ans += dfs(l,m,i) * prob(who,i);
		}
		ans *= sub;
	}
	return dp[{l,r,who}] = ans;
	
}
int main(){
	int M;
	cin >> M;
	rep(i,1<<M) cin >> S[i];
	printf("%.10lf\n",dfs(0,(1<<M),0));
	
}