import java.util.Arrays; import java.util.PriorityQueue; import java.util.Scanner; class Main { public static void main(String[] args) { new Main().run(); } void run() { Scanner sc=new Scanner(System.in); int M=sc.nextInt(); double[] S=new double[1<<M]; for(int i=0;i<1<<M;++i)S[i]=sc.nextDouble(); for(int i=0;i<1<<M;++i)S[i]=S[i]*S[i]; double[][] P=new double[1<<M][M+1]; for(int i=0;i<1<<M;++i)P[i][0]=1; for(int i=0;i<M;++i) { for(int a=0;a<1<<M;++a) { for(int b=0;b<1<<M;++b) { if((a>>(i+1))!=(b>>(i+1)))continue; if((a>>i)%2==(b>>i)%2)continue; P[a][i+1]+=P[a][i]*P[b][i]*S[a]/(S[a]+S[b]); } } } System.out.println(P[0][M]); } static void tr(Object... objects) { System.out.println(Arrays.deepToString(objects)); } }