import sys

sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
inf = (1 << 63)-1
# inf = (1 << 31)-1
md = 10**9+7
# md = 998244353

n = II()
aa = LI()
bb = LI()

st = []
for a, b in zip(aa[::-1], bb[::-1]):
    cur = max(0, (a/b)**0.5-1)
    while st and cur >= st[-1][-1]:
        pa, pb, pc = st.pop()
        a, b = a+pa, b+pb
        cur = max(0, (a/b)**0.5-1)
    st.append((a, b, cur))

ans = 0
for a, b, c in st:
    ans += a/(1+c)+b*(1+c)

print(ans)