Problem Statement

There are N boxes numbered 1 to N and N items numbered 1 to $N. Item i (1 \leq i \leq N)$ is in box A_i and has a weight of W_i.
You can repeatedly perform the operation of choosing an item and moving it to another box zero or more times. If the weight of the item being moved is w, the cost of the operation is w.
Find the minimum total cost required to make each box contain exactly one item.

Input

The input is given from Standard Input in the following format:
N
$A_1 A_2 \ldots A_N$
$W_1 W_2 \ldots W_N$

Output

Print the minimum total cost required to make each box contain exactly one item.

Constraints

• $1 \leq N \leq 10^{5}$
• $1 \leq A_i \leq N (1 \leq i \leq N)$
• $1 \leq W_i \leq 10^{4} (1 \leq i \leq N)$
• All input values are integers.

Sample Input 1

5
2 2 3 3 5
33 40 2 12 16

Sample Output 1

35

With the following two moves, you can make each box contain exactly one item:

• Move item 1 from box 2 to box 1. The cost is 33.
• Move item 3 from box 3 to box 4. The cost is 2.

The total cost of these two moves is 35. It is impossible to make each box contain exactly one item with a cost less than 35, so print 35.

Sample Input 2

12
3 6 7 4 12 4 8 11 11 1 8 11
3925 9785 9752 3587 4013 1117 3937 7045 6437 6208 3391 6309

Sample Output 2

17254

见题面 Input 部分

见题面 Output 部分