N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))

P = []
Q = []
for a, b in zip(A, B):
    while P and P[-1] * Q[-1] >= a * b:
        a += P.pop()
        b += Q.pop()
    P.append(a)
    Q.append(b)

ans = 0
for p, q in zip(P, Q):
    x = 0
    if p > q:
        x = (p / q) ** .5 - 1
    ans += p / (1 + x)
    ans += q * (1 + x)

print("{:.13f}".format(ans))