import sys
readline = sys.stdin.readline
n = int(readline())
*A, = map(int,readline().split())
*B, = map(int,readline().split())

q = []
ans = 0.0
for a,b in zip(A,B):
    while q and a <= b:
        x,y = q.pop()
        a += x
        b += y
    if a <= b:
        ans += a+b
    else:
        q.append((a,b))

qq = []
for a,b in q:
    while qq:
        x,y = qq[-1]
        if b*x >= a*y:
            qq.pop()
            a += x
            b += y
        else:
            break
    qq.append((a,b))

ans = 0.0
for x,y in qq:
    ans += 2*(1.0*x*y)**0.5

print(ans)