#int(input())
#map(int, input().split())
#list(map(int, input().split()))

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

ans = 0
x = 0


def time(x, a, b):
    return a / (1 + x) + b * (1 + x)

def sake(a, b):
    return max(0, (a/b)**0.5-1)

ans = 0

c = []
sa = sum(A)
sb = sum(B)

a = 0
b = 0
k = 0

u = [0] * N

for i in range(N):
    t = sake(sa, sb)
    a += A[i]
    b += B[i]
    nt = sake(a, b)
    if nt <= t:
        for j in range(k, i+1):
            u[j] = nt
        sa -= a
        sb -= b
        a = 0
        b = 0
        k = i+1

for i in range(N):
    ans += time(u[i], A[i], B[i])

print(ans)