Strange Set
Description
Note that the memory limit is unusual.
You are given an integer $n$ and two sequences $a_1, a_2, \dots, a_n$ and $b_1, b_2, \dots, b_n$.
Let's call a set of integers $S$ such that $S \subseteq \{1, 2, 3, \dots, n\}$ strange, if, for every element $i$ of $S$, the following condition is met: for every $j \in [1, i - 1]$, if $a_j$ divides $a_i$, then $j$ is also included in $S$. An empty set is always strange.
The cost of the set $S$ is $\sum\limits_{i \in S} b_i$. You have to calculate the maximum possible cost of a strange set.
The first line contains one integer $n$ ($1 \le n \le 3000$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 100$).
The third line contains $n$ integers $b_1, b_2, \dots, b_n$ ($-10^5 \le b_i \le 10^5$).
Print one integer — the maximum cost of a strange set.
Input
The first line contains one integer $n$ ($1 \le n \le 3000$).
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 100$).
The third line contains $n$ integers $b_1, b_2, \dots, b_n$ ($-10^5 \le b_i \le 10^5$).
Output
Print one integer — the maximum cost of a strange set.
Samples
9
4 7 3 4 5 6 7 8 13
-2 3 -19 5 -6 7 -8 9 1
16
2
42 42
-37 13
0
2
42 42
13 -37
13
Note
The strange set with the maximum cost in the first example is $\{1, 2, 4, 8, 9\}$.
The strange set with the maximum cost in the second example is empty.