import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
import java.util.TreeSet;
public class Main {
//	public static int w;
//	public static int k;
//	public static int n;
//	public static int[][] dp;
//	public static int[] r;
//	public static long[] buy;
//	public static List<double[]> list = new ArrayList<double[]>();
//	public static NodeW[] product;
	public static double[] str;
	public static void main(String[] args) throws NumberFormatException, IOException{

		ContestScanner in = new ContestScanner();
		int m = in.nextInt(); 
		str = new double[1 << m];
//		double[][] league = new double[1 << m][1 << m];
		int entry = 1 << m;
		for(int i=0; i<entry; i++){
			str[i] = in.nextDouble();
			str[i] = str[i]*str[i];
		}
//		for(int i=0; i<entry; i++){
//			for(int j=0; j<entry; j++){
//				league[i][j] = str[i]/(str[i]+str[j]);
//				if(i!=j) System.err.println(i+" beats "+j+":"+league[i][j]);
//			}
//		}
		System.out.println(dfs(0, m));

	}
	
	public static double dfs(int who, int bn){
		double ans = 0;
		if(bn == 1){
			if(who%2 == 0){
				ans = str[who]/(str[who+1]+str[who]);
			}else{
				ans = str[who]/(str[who-1]+str[who]);
			}
		}else{
			int start = who/(1 << (bn-1));
			if(start % 2 == 0){
				start = (start + 1)*(1 << (bn-1));
			}else{
				start = (start - 1)*(1 << (bn-1));
			}
			int max = start + (1 << (bn-1));
			for(int i=start; i<max; i++){
				ans += dfs(i, bn-1)*(str[who]/(str[who]+str[i]));
			}
			ans *= dfs(who, bn-1);
		}
		return ans;
	}
	
}
//class MyComp implements Comparator<int[]>{
//	public int compare(int[] a, int[] b) {
//		return Main.product[a[0]].dist - Main.product[b[0]].dist;
//	}
//}


class Reverse implements Comparator<Integer>{
	public int compare(Integer arg0, Integer arg1) {
		return arg1 - arg0;
	}
}


class NodeW{
	int id;
//	int dist;
	List<NodeW> edge = new ArrayList<NodeW>();
	List<Integer> costList = new ArrayList<Integer>();
	public NodeW(int id) {
		this.id = id;
	}
	public void createEdge(Node node) {
		System.err.println("Don't use this func");
	}
	public void createEdge(NodeW node, int cost) {
		edge.add(node);
		costList.add(cost);
//		node.setDist(dist+1);
	}
//	public void setDist(int dist){
//		this.dist = Math.max(this.dist, dist);
//		for(NodeW node: edge){
//			node.setDist(dist+1);
//		}
//	}
}

class Range<T extends Comparable<T>> implements Comparable<Range<T>>{
	T start;
	T end;
	public Range(T start, T end){
		this.start = start;
		this.end = end;
	}
	public boolean inRange(T val){
		if(start.compareTo(val) <= 0 && end.compareTo(val) >= 0){
			return true;
		}
		return false;
	}
	
	public boolean isCommon(Range<T> range){
		if(inRange(range.start) || inRange(range.end) || range.inRange(start)){
			return true;
		}
		return false;
	}
	
	public Range<T> connect(Range<T> range){
		if(!isCommon(range)) return null;
		Range<T> res = new Range<T>(start.compareTo(range.start) <= 0 ? start : range.start,
				end.compareTo(range.end) >= 0 ? end : range.end);
		return res;
	}
	
	public boolean connectToThis(Range<T> range){
		if(!isCommon(range)) return false;
		start = start.compareTo(range.start) <= 0 ? start : range.start;
		end = end.compareTo(range.end) >= 0 ? end : range.end;
		return true;
	}
	@Override
	public int compareTo(Range<T> range) {
		int res = start.compareTo(range.start);
		if(res == 0) return end.compareTo(range.end);
		return res;
	}
	
	public String toString(){
		return "["+start+","+end+"]";
	}
}

class RangeSet<T extends Comparable<T>>{
	TreeSet<Range<T>> ranges = new TreeSet<Range<T>>();
	public void add(Range<T> range){
		Range<T> con = ranges.floor(range);
		if(con != null){
			if(con.connectToThis(range))
				range = con;
		}
		con = ranges.ceiling(range);
		while(con != null && range.connectToThis(con)){
			ranges.remove(con);
			con = ranges.ceiling(range);
		}
		ranges.add(range);
	}
	
	public String toString(){
		StringBuilder bld = new StringBuilder();
		for(Range<T> r: ranges){
			bld.append(r+"\n");
		}
		return bld.toString();
	}
}


class Node{
	int id;
	List<Node> edge = new ArrayList<Node>();
	public Node(int id){
		this.id = id;
	}
	public void createEdge(Node node){
		edge.add(node);
	}
}

class MyMath{
	public static long fact(long n){
		long res = 1;
		while(n > 0){
			res *= n--;
		}
		return res;
	}
	public static long[][] pascalT(int n){
		long[][] tri = new long[n][];
		for(int i=0; i<n; i++){
			tri[i] = new long[i+1];
			for(int j=0; j<i+1; j++){
				if(j == 0 || j == i){
					tri[i][j] = 1;
				}else{
					tri[i][j] = tri[i-1][j-1] + tri[i-1][j];
				}
			}
		}
		return tri;
	}
}

class ContestScanner{
	private BufferedReader reader;
	private String[] line;
	private int idx;
	public ContestScanner() throws FileNotFoundException{
		reader = new BufferedReader(new InputStreamReader(System.in));
	}
	
	public String nextToken() throws IOException{
		if(line == null || line.length <= idx){
			line = reader.readLine().trim().split(" ");
			idx = 0;
		}
		return line[idx++];
	}
	
	public long nextLong() throws IOException, NumberFormatException{
		return Long.parseLong(nextToken());
	}
	
	public int nextInt() throws NumberFormatException, IOException{
		return (int)nextLong();
	}
	
	public double nextDouble() throws NumberFormatException, IOException{
		return Double.parseDouble(nextToken());
	}
}