Score : $250$ points

问题陈述

有 $N$ 个编号为 $1$ 到 $N$ 的盒子和 $N$ 个编号为 $1$ 到 $N$ 的物品。物品 $i$ $(1 \leq i \leq N)$ 位于盒子 $A_i$ 并且重量为 $W_i$。

你可以重复执行选择一个物品并将其移动到另一个盒子的操作，次数可以是零次或多次。如果被移动的物品重量为 $w$，则该操作的成本为 $w$。

找出使每个盒子恰好包含一个物品所需的最小总成本。

以上为大语言模型 kimi 翻译，仅供参考。

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.

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.

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.

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