import sys
input = lambda :sys.stdin.readline()[:-1]
ni = lambda :int(input())
na = lambda :list(map(int,input().split()))
yes = lambda :print("yes");Yes = lambda :print("Yes");YES = lambda : print("YES")
no = lambda :print("no");No = lambda :print("No");NO = lambda : print("NO")
#####################################################################
n = ni()
a = na()
b = na()
ans = 0
i = 0
while i < n:
    r = i
    A = 0
    B = 0
    while r < n and a[r] * b[i] <= a[i] * b[r]:
        A += a[r]
        B += b[r]
        r += 1
    x1 = max(A / B, 1)**0.5
    ans += A/x1 + B * x1
    i = r
print(ans)