Problem Statement

$N$ 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.

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 $(1,\ldots,N)$.

Input

The input is given from Standard Input in the following format:

N
P_1 \ldots P_N
C_1 \ldots C_N

Output

Output the answer.