import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import log,gcd

input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

N = int(input())
A = li()
B = li()

stack = [(A[0],B[0])]
for i in range(1,N):
    a,b = A[i],B[i]
    while stack:
        pa,pb = stack[-1]
        if pa*b >= a*pb:
            stack.pop()
            a,b = pa+a,pb+b
        else:
            break
    stack.append((a,b))

res = 0
for a,b in stack:
    if a <= b:
        res += a + b
    else:
        res += 2 * (a*b)**.5

print(res)