from itertools import product


def mix(S, lr, rr):
    lm = lr.keys()
    rm = rr.keys()
    wr = {}
    for l, r in product(lm, rm):
        p = S[l] / (S[l] + S[r])
        wr[l, r] = p
        wr[r, l] = 1 - p

    result = {}
    for l in lm:
        result[l] = lr[l] * sum(wr[l, r] * rr[r] for r in rm)
    for r in rm:
        result[r] = rr[r] * sum(wr[r, l] * lr[l] for l in lm)
    return result


def solve(M, S):
    print(S)
    range_len_s = list(range(len(S)))
    R = [{i: 1.0} for i in range_len_s]
    print(R)
    for i in range(M):
        step = 2 ** i
        print("_______________")
        print(i, step)
        m = list(range(0, len(S), step))
        for j in range(0, len(m), 2):
            lr = R[m[j]]
            rr = R[m[j + 1]]
            print(j, m[j], m[j + 1], lr, rr)
            R[m[j]] = mix(S, lr, rr)

    print(R)
    return R[0][0]


def main():
    M = int(input())
    n = 2 ** M
    S = [int(input()) ** 2 for i in range(n)]

    print(solve(M, S))


if __name__ == '__main__':
    main()