#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>

using namespace std;

void print(vector< vector<double> > &v){
	for(int i=0; i<v.size(); i++){
		for(int j=0; j<v[i].size(); j++){
			cerr << v[i][j] << " ";
		}
		cerr << endl;
	}
}

int main(){
	int m;
	cin >> m;
	int n = 1<<m;
	vector<double> s(n);
	for(int i=0; i<s.size(); i++){
		cin >> s[i];
	}

	vector<vector<double> > pp(n, vector<double>(n));
	for(int i=0; i<n; i++){
		for(int j=0; j<n; j++){
			//iとjが当たってiが勝つ確率
			pp[i][j] = (s[i]*s[i])/((double)s[i]*s[i] + s[j]*s[j]);
		}
	}

	//dp[ i人目 ][ j回戦 ]
	vector< vector<double> > dp(n, vector<double>(m+1, 0.0));
	for(int i=0; i<n; i++) dp[i][0] = 1.0;

	//i回戦
	for(int i=1; i<=m; i++){
		//cerr << i << endl;
		//print(dp);
		//cerr << endl;
		
		int block = 1<<i;
		int pre_block = 1<<(i-1);
		//自分 j
		for(int j=0; j<n; j++){
			int offset = (j/block) * block;
			int pre_offset = (j/pre_block) * pre_block;
			
			for(int k=0; k<block; k++){
				//相手 x
				int x = offset + k;
				if(pre_offset <= x && x < pre_offset+pre_block) continue;
				dp[j][i] += dp[x][i-1] * pp[j][x];
			}
			dp[j][i] *= dp[j][i-1];
		}
	}
	
	//cerr << m << endl;
	//print(dp);
	//cerr << endl;
	
	printf("%.7f\n", dp[0][m]);
	return 0;
}