from math import sqrt

def calc(N, A, B):
    AA = [0]
    BB = [0]
    for a, b in zip(A, B):
        AA.append(AA[-1] + a)
        BB.append(BB[-1] + b)
    L = [(0, 0)]
    for i in range(N)[::-1]:
        sa, sb = A[i], B[i]
        while sa * L[-1][1] - sb * L[-1][0] > 0:
            sa += L[-1][0]
            sb += L[-1][1]
            L.pop()
        L.append((sa, sb))
    ans = 0
    for a, b in L[1:]:
        ans += sqrt(a * b) * 2 if a > b else a + b
    return ans

N = int(input())
A = [int(a) for a in input().split()]
B = [int(a) for a in input().split()]
print(calc(N, A, B))