Problem Description

$\textit{Pang}$ believes that one cannot make an omelet without breaking eggs.

For a subset $A$ of $\{1,2,\ldots,n\}$, we calculate the score of $A$ as follows:

• Initialize the score as $0$.
• For any $i\in A$, add $a_i$ to the score.
• For any pair of integers $(i, j)$ satisfying $i\ge 2$, $j\ge 2$, $i\in A$ and $j\in A$, if there exists positive integer $k > 1$ such that $i^k=j$, subtract $b_j$ from the score.

Find the maximum possible score over the choice of $A$.

Input Format

The first line contains a single integer $n$ $(1\le n\le 100000)$.

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ $(1\le a_i\le 1000000000)$.

The third line contains $n$ integers $b_1,b_2,\ldots,b_n$ $(1\le b_i\le 1000000000)$.

Output Format

Print a single integer $x$ --- the maximum possible score.

4
1 1 1 2
1 1 1 1

4

4
1 1 1 1
1 1 1 2

3