102564: [AtCoder]ABC256 E - Takahashi's Anguish

Problem Statement

There are $N$ people numbered $1$ through $N$.
Takahashi has decided to choose a sequence $P = (P_1, P_2, \dots, P_N)$ that is a permutation of integers from $1$ through $N$, and give a candy to Person $P_1$, Person $P_2$, $\dots$, and Person $P_N$, in this order.
Since Person $i$ dislikes Person $X_i$, if Takahashi gives a candy to Person $X_i$ prior to Person $i$, then Person $i$ gains frustration of $C_i$; otherwise, Person $i$'s frustration is $0$.
Takahashi may arbitrarily choose $P$. What is the minimum possible sum of their frustration?

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq X_i \leq N$
• $X_i \neq i$
• $1 \leq C_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$
$X_1$ $X_2$ $\dots$ $X_N$
$C_1$ $C_2$ $\dots$ $C_N$

Output

Print the answer.

Sample Input 1

3
2 3 2
1 10 100

Sample Output 1

10

If he lets $P = (1, 3, 2)$, only Person $2$ gains a positive amount of frustration, in which case the sum of their frustration is $10$.
Since it is impossible to make the sum of frustration smaller, the answer is $10$.

Sample Input 2

8
7 3 5 5 8 4 1 2
36 49 73 38 30 85 27 45

Sample Output 2

57

问题描述

有N个编号为1到N的人。
Takahashi决定选择一个序列$P = (P_1, P_2, \dots, P_N)$，该序列是1到N的整数的排列，并按照这个顺序将糖果分给Person $P_1$，Person $P_2$，$\dots$，和Person $P_N$。
由于Person $i$不喜欢Person $X_i$，如果Takahashi在分给Person $i$之前先分给Person $X_i$，那么Person $i$的挫败感会增加$C_i$；否则，Person $i$的挫败感为0。
Takahashi可以任意选择$P$。他们挫败感之和的最小可能值是多少？

约束

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq X_i \leq N$
• $X_i \neq i$
• $1 \leq C_i \leq 10^9$
• 输入中的所有值都是整数。

输入

输入从标准输入以以下格式给出：

$N$
$X_1$ $X_2$ $\dots$ $X_N$
$C_1$ $C_2$ $\dots$ $C_N$

输出

输出答案。

样例输入1

3
2 3 2
1 10 100

样例输出1

10

如果他让$P = (1, 3, 2)$，只有Person $2$获得正数挫败感，此时他们的挫败感之和为10。
由于无法使挫败感之和更小，答案为10。

样例输入2

8
7 3 5 5 8 4 1 2
36 49 73 38 30 85 27 45

样例输出2

57