Free Figurines

A matryoshka set is $n$ wooden figurines numbered 1 to $n$ in increasing order of size. A figurine can be placed directly inside a larger figurine, and at most one figurine sits directly inside another figurine, whatever the sizes involved.

If figurine $a$ is directly inside figurine $b$, then $b$ is the parent of $a$. A figurine with no parent is free. Writing down the parent of every figurine describes the configuration of the whole set.

Two moves are allowed:

• Place a free figurine inside a larger figurine that is free and currently empty.
• Open a free figurine that is not empty and take out the figurine directly inside it.

You are given an initial configuration and a target configuration. Find the smallest number of moves that turns the initial configuration into the target configuration.

The first line contains an integer $n$ ($1 \le n \le 100000$), the number of figurines.

The second line contains $n$ integers $p_1, p_2, \dots, p_n$ ($0 \le p_k \le n$) describing the initial configuration. $p_k$ is 0 if figurine $k$ is free, and the parent of figurine $k$ otherwise.

The third line contains $n$ integers $q_1, q_2, \dots, q_n$ ($0 \le q_k \le n$) describing the target configuration in the same format.

Both configurations are valid: every figurine is smaller than its parent, and no two figurines have the same parent.

Print one integer, the smallest number of moves.