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

const int MAX_M = 10;

int M;
double S[1<<MAX_M], dp[MAX_M+1][1<<MAX_M];
double P[1<<MAX_M][1<<MAX_M];

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

	rep( i, 1<<M ) rep( j, 1<<M )
		P[i][j] = (S[i]*S[i])/(S[i]*S[i]+S[j]*S[j]);

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

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

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

	return 0;
}