F. Strange Set
time limit per test
4 seconds
memory limit per test
32 megabytes
input
standard input
output
standard output

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.

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.

Examples
Input
9
4 7 3 4 5 6 7 8 13
-2 3 -19 5 -6 7 -8 9 1

Output
16

Input
2
42 42
-37 13

Output
0

Input
2
42 42
13 -37

Output
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.