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 a <= b:
        if not q:
            break
        else:
            x,y = q.pop()
            a += x
            b += y
    if a <= b:
        ans += a+b
    else:
        q.append((a,b))

x = y = 0.0
for a,b in q:
    if x*b >= a*y:
        x += a
        y += b
    else:
        ans += 2*((x*y)**0.5)
        x = a
        y = b
ans += 2*((x*y)**0.5)
print(ans)