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?

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.

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.

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

见题面 Input 部分

见题面 Output 部分