mod = 998244353


def main():
    import sys
    from math import sqrt
    input = sys.stdin.readline

    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))

    st = [(1.0, 0, 0, 0)]
    for a, b in zip(A, B):
        x_new = sqrt(a / b)
        if x_new >= st[-1][0]:
            st.append((x_new, a, b, a / x_new + b * x_new))
        else:
            sa = a
            sb = b
            while st:
                x_old, aa, bb, c = st.pop()
                sa += aa
                sb += bb
                x_new = sqrt(sa / sb)
                if not st:
                    if x_new <= 1:
                        st.append((1.0, sa, sb, sa + sb))
                    else:
                        st.append((x_new, sa, sb, sa / x_new + sb * x_new))
                    break
                else:
                    if x_new >= st[-1][0]:
                        st.append((x_new, sa, sb, sa / x_new + sb * x_new))
                        break
    ans = 0
    for _, _, _, y in st:
        ans += y
    print(ans)


if __name__ == '__main__':
    main()