import sys
from collections import defaultdict, Counter, deque
from itertools import permutations, combinations, product, combinations_with_replacement, groupby, accumulate
import operator
from math import sqrt, gcd, factorial
#from math import isqrt, prod, comb  #python3.8用(notpypy)
#from bisect import bisect_left, bisect_right
#from functools import lru_cache, reduce
#from heapq import heappush, heappop, heapify, heappushpop, heapreplace
#import numpy as np
#import networkx as nx
#from networkx.utils import UnionFind
#from numba import njit, b1, i1, i4, i8, f8
#numba例 @njit(i1(i4[:], i8[:, :]),cache=True) 引数i4配列、i8 2次元配列,戻り値i1
#from scipy.sparse import csr_matrix
#from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson, NegativeCycleError, maximum_bipartite_matching, maximum_flow, minimum_spanning_tree
def input(): return sys.stdin.readline().rstrip()
def divceil(n, k): return 1+(n-1)//k  # n/kの切り上げを返す
def yn(hantei, yes='Yes', no='No'): print(yes if hantei else no)

def check(AA,BB):
    if AA <= BB:
        return 1,AA+BB
    else:
        return sqrt(AA/BB),BB*sqrt(AA/BB)*2

def check2(drink,AA,BB):
    r=max(drink,sqrt(AA/BB))
    return r,AA/r+BB*r


def main():
    mod = 10**9+7
    mod2 = 998244353
    n=int(input())
    A=list(map(int, input().split()))
    B=list(map(int, input().split()))
    accA=[0]+list(accumulate(A))
    accB=[0]+list(accumulate(B))
    t,y=check(A[0],B[0])
    stack=[[-1,1,0],[0,t,y]]
    for i in range(1,n):
        while len(stack) > 1:
            index1,drink1,time1=stack[-1]
            index2,drink2,time2=stack[-2]
            if check2(drink1,accA[i+1]-accA[index1+1],accB[i+1]-accB[index1+1])[1] + time1 >= check2(drink2,accA[i+1]-accA[index2+1],accB[i+1]-accB[index2+1])[1] + time2:
                stack.pop()
            else:
                d,t=check2(drink1,accA[i+1]-accA[index1+1],accB[i+1]-accB[index1+1])
                if d>drink1 or i==n-1:
                    stack.append([i,d,time1+t])
                break
        if len(stack)==1:
            index1,drink1,time1=stack[-1]
            d,t=check2(drink1,accA[i+1]-accA[index1+1],accB[i+1]-accB[index1+1])
            stack.append([i,d,time1+t])
    print(stack[-1][2])
        






if __name__ == '__main__':
    main()