def read_data():
    M = int(input())
    S = [int(input()) ** 2 for i in range(2**M)]
    return M, S

def solve(M, S):
    N = 2**M
    p = [1.0] * N
    for m in range(0, M-1):
        np = [0.0] * N
        for i in range(N):
            pi = p[i]
            Si = S[i]
            start = ((i >> m) ^ 1) << m
            for j in range(start, start + (1 << m)):
                np[i] += pi * p[j] * Si / (Si + S[j])
        p = np
    p0 = p[0]
    S0 = S[0]
    ans = p0 * sum(p[j] * S0 /(S0 + S[j]) for j in range(N//2, N))
    return ans

M, S = read_data()
print(solve(M, S))