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()
dq = []
def f(x,y):
    return x[0] * y[1] > x[1] * y[0]

for i in range(n):
    dq.append((a[i],b[i]))
    while len(dq) > 1 and f(dq[-2],dq[-1]):
        x = dq.pop()
        y = dq.pop()
        dq.append((x[0]+y[0],x[1]+y[1]))

ans = 0
for i in dq:
    x = max(i[0]/i[1],1)**0.5
    #print(i[0],i[1])
    ans += i[0] / x + i[1] * x
print(ans)