Given two sequences $s_1{\dots}s_n$ and $w_1{\dots}w_n$. A graph is built with n vertices and n directed edges $(i,s_i)$. Cost to change some $s_i$ is  $w_i$ . Your goal is to make the graph strongly connected with minimum cost.

Input

The first line contains an integer n.

The second line contains n intergers, $s_1{\dots}s_n$.

The third line contains n integers $w_1{\dots}w_n$.

Output

An integer representing the answer.

Constraints

$1 \le n \le 10^5$

$1 \le s_i \le n$

$1 \le w_i \le 10^9$