문제

Bessie has a special function $f(x)$ that takes as input an integer in $[1, N]$ and returns an integer in $[1, N]$ ($1 \le N \le 2 \cdot 10^5$). Her function $f(x)$ is defined by $N$ integers $a_1 \ldots a_N$ where $f(x) = a_x$ ($1 \le a_i \le N$).

Bessie wants this function to be idempotent. In other words, it should satisfy $f(f(x)) = f(x)$ for all integers $x \in [1, N]$.

For a cost of $c_i$, Bessie can change the value of $a_i$ to any integer in $[1, N]$ ($1 \le c_i \le 10^9$). Determine the minimum total cost Bessie needs to make $f(x)$ idempotent.

입력

The first line contains $N$.

The second line contains $N$ space-separated integers $a_1,a_2,\dots,a_N$.

The third line contains $N$ space-separated integers $c_1,c_2,\dots,c_N$.

출력

Output the minimum total cost Bessie needs to make $f(x)$ idempotent.

예제 입력 1

5
2 4 4 5 3
1 1 1 1 1

예제 출력 1

3

예제 입력 2

8
1 2 5 5 3 3 4 4
9 9 2 5 9 9 9 9

예제 출력 2

7

점수

Subtasks:

Input 3: $N\le 20$Inputs 4-9: $a_i\ge i$Inputs 10-15: All $a_i$ are distinct.Inputs 16-21: No additional constraints.

Additionally, in each of the last three subtasks, the first half of tests will satisfy $c_i=1$ for all $i$.