There are $N$ balls arranged from left to right. The color of the $i$-th ball from the left is Color $C_i$, and an integer $X_i$ is written on it.

Takahashi wants to rearrange the balls so that the integers written on the balls are non-decreasing from left to right. In other words, his objective is to reach a situation where, for every $1\leq i\leq N-1$, the number written on the $(i+1)$\-th ball from the left is greater than or equal to the number written on the $i$-th ball from the left.

For this, Takahashi can repeat the following operation any number of times (possibly zero):

> Choose an integer $i$ such that $1\leq i\leq N-1$.  
> If the colors of the $i$-th and $(i+1)$-th balls from the left are different, pay a cost of $1$. (No cost is incurred if the colors are the same).  
> Swap the $i$-th and $(i+1)$-th balls from the left.

Find the minimum total cost Takahashi needs to pay to achieve his objective.

Input is given from Standard Input in the following format:

```
$N$
$C_1$ $C_2$ $\ldots$ $C_N$
$X_1$ $X_2$ $\ldots$ $X_N$
```

Print the minimum total cost Takahashi needs to pay to achieve his objective, as an integer.

-   $2 \leq N \leq 3\times 10^5$
-   $1\leq C_i\leq N$
-   $1\leq X_i\leq N$
-   All values in input are integers.

6

Let us represent a ball as (Color,, Integer). The initial situation is (1,3), (5,2), (2,1), (2,2), (1,1). Here is a possible sequence of operations for Takahashi:

• Swap the 1-st ball (Color 1) and 2-nd ball (Color 5). Now the balls are arranged in the order (5,2), (1,3), (2,1), (2,2), (1,1).
• Swap the 2-nd ball (Color 1) and 3-rd ball (Color 2). Now the balls are arranged in the order (5,2), (2,1), (1,3), (2,2), (1,1).
• Swap the 3-rd ball (Color 1) and 4-th ball (Color 2). Now the balls are in the order (5,2), (2,1), (2,2), (1,3), (1,1).
• Swap the 4-th ball (Color 1) and 5-th ball (Color 1). Now the balls are in the order (5,2), (2,1), (2,2), (1,1), (1,3).
• Swap the 3-rd ball (Color 2) and 4-th ball (Color 1). Now the balls are in the order (5,2), (2,1), (1,1), (2,2), (1,3).
• Swap the 1-st ball (Color 5) and 2-nd ball (Color 2). Now the balls are in the order (2,1), (5,2), (1,1), (2,2), (1,3).
• Swap the 2-nd ball (Color 5) and 3-rd ball (Color 1). Now the balls are in the order (2,1), (1,1), (5,2), (2,2), (1,3).

After the last operation, the numbers written on the balls are 1,1,2,2,3 from left to right, which achieves Takahashi's objective.

The 1-st, 2-nd, 3-rd, 5-th, 6-th, and 7-th operations incur a cost of 1 each, for a total of 6, which is the minimum. Note that the 4-th operation does not incur a cost since the balls are both in Color 1.

0

All balls are in the same color, so no cost is incurred in swapping balls.

0

Takahashi's objective is already achieved without any operation.