#include<cstdio>
#define repi(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,a) repi(i,0,a)

int M;
double S[1024], dp[11][1024];

double calc( int a, int b )
{ return S[a]*S[a]/(S[a]*S[a]+S[b]*S[b]); }

int main()
{
	scanf( "%d", &M );
	rep( i, 1<<M )
		scanf( "%lf", S+i ), dp[0][i]=1.0;

	rep( i, M ) rep( j, 1<<M )
	{
		int lev=1<<i+1, lb=j/lev*lev, ub=lb+lev, mid=lb+ub>>1;

		repi( k, j<mid?mid:lb, j<mid?ub:mid )
			dp[i+1][j]+=dp[i][j]*dp[i][k]*calc(j,k);
	}

	printf( "%.7f\n", dp[M][0] );

	return 0;
}