AT_arc206_b [ARC206B] Slime Swap

$ N $ slimes are arranged in a line. The size of the $ i $ -th slime from the left is $ P_i $ , and its color is $ C_i $ . Here, the sizes of the slimes are distinct. A sequence of slimes is called a good sequence when it satisfies the following condition: - By repeatedly performing the operation of swapping the positions of two adjacent slimes of **different colors**, it is possible to arrange the slimes in ascending order of size. To make the sequence of slimes a good sequence, you can perform the following operation any number of times (possibly zero): - Choose a slime, and change the color of the slime to any integer between $ 1 $ and $ N $ , inclusive. This operation costs $ x $ , where $ x $ is the color of the slime immediately before this operation. Find the minimum total cost required to make the sequence of slimes a good sequence.

The input is given from Standard Input in the following format: > $ N $ $ P_1 $ $ \ldots $ $ P_N $ $ C_1 $ $ \ldots $ $ C_N $

Output the answer.

### Sample Explanation 1 Change the color of the $ 3 $ -rd slime to $ 2 $ . Then, by swapping the $ 1 $ -st and $ 2 $ -nd slimes, and swapping the $ 2 $ -nd and $ 3 $ -rd slimes, it is possible to arrange the slimes in ascending order of size, making it a good sequence. The required cost is $ 1 $ , since the color of the $ 3 $ -rd slime immediately before the operation was $ 1 $ . ### Constraints - All input values are integers. - $ 1 \leq N \leq 2\times 10^5 $ - $ 1\leq P_i \leq N $ - $ 1\leq C_i \leq N $ - $ P $ is a permutation of $ (1,\ldots,N) $ .