Double Deck

You are playing a new card game. Each of the two decks has $N \cdot K$ cards, labeled with integers from $1$ to $N$. Each label appears exactly $K$ times in each deck.

The rules are simple. You shuffle both decks and place them face up in front of you, so you always see the top card of each deck. If the top cards match, you take both and get one point. If they do not match, you must discard one of the two cards. Your goal is to score as many points as possible.

You have just finished a round. Given the layout of both decks, find the maximum score you could have gotten.

The first line contains two integers $N$ and $K$ ($1 \leq N \leq 10^4$, $1 \leq K \leq 15$). The second and third lines each contain $N \cdot K$ integers $x_i$ ($1 \leq x_i \leq N$), which describe the layout of the decks. $x_1$ is the top card, $x_2$ is the next card, and so on. No integer appears more than $K$ times in either line.

Print one integer, the maximum possible score.