Problem Statement

Detective Cordelia has been asked by an old gentleman to search for his lost glasses.
The old gentleman's mansion has $n$ rooms, numbered from $1$ to $n$. It is known that the probability that the glasses were lost in the $i$-th room is $\frac{p_i}{1000}$.
Also, the rooms are very messy, so even if the glasses are in a room, searching it once does not necessarily mean they will be found.
When the glasses are in the $i$-th room, the probability of finding them by searching that room once is $\frac{q_i}{100}$, regardless of how many times that room has been searched in the past.

Cordelia wants to find the glasses while searching rooms as few times as possible, because she is going to attend Marine's live concert.
To help Cordelia, minimize the expected number of times rooms are searched until the glasses are found.

Input

$n$
$p_1\ p_2\ \dots\ p_n$
$q_1\ q_2\ \dots\ q_n$

The first line gives the number of rooms.
The second line gives $n$ integers. Each is the probability that the glasses were lost in the corresponding room, multiplied by 1000.
The third line gives $n$ integers. Each is the probability of finding the glasses by searching the corresponding room once, multiplied by 100.
$1 \leq n \leq 1000$
$0 \leq p_i \leq 1000$
$1 \leq q_i \leq 100$
$\sum_{i = 1}^n p_i = 1000$

Output

Output the minimum expected number of times Cordelia searches rooms until she finds the glasses. A relative or absolute error of up to 0.001 is allowed.
Print a newline at the end.

Sample

1
1000
50

2.0

10
100 100 100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100 100 100

5.5

10
64 201 4 30 232 64 197 7 102 99
28 43 94 52 24 33 97 55 36 89

12.277056