A12605. Nauuo and Cards

Nauuo is a girl who loves playing cards.

One day she was playing cards but found that the cards were mixed with some empty ones.

There are $n$ cards numbered from $1$ to $n$ , and they were mixed with another $n$ empty cards. She piled up the $2n$ cards and drew $n$ of them. The $n$ cards in Nauuo's hands are given. The remaining $n$ cards in the pile are also given in the order from top to bottom.

In one operation she can choose a card in her hands and play it — put it at the bottom of the pile, then draw the top card from the pile.

Nauuo wants to make the $n$ numbered cards piled up in increasing order (the $i$ -th card in the pile from top to bottom is the card $i$ ) as quickly as possible. Can you tell her the minimum number of operations?

The first line contains a single integer $n$ ( $1\le n\le 2\cdot 10^5$ ) — the number of numbered cards.

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $0\le a_i\le n$ ) — the initial cards in Nauuo's hands. $0$ represents an empty card.

The third line contains $n$ integers $b_1,b_2,\ldots,b_n$ ( $0\le b_i\le n$ ) — the initial cards in the pile, given in order from top to bottom. $0$ represents an empty card.

It is guaranteed that each number from $1$ to $n$ appears exactly once, either in $a_{1..n}$ or $b_{1..n}$ .

The output contains a single integer — the minimum number of operations to make the $n$ numbered cards piled up in increasing order.

Example 1

We can play the card $2$ and draw the card $3$ in the first operation. After that, we have $[0,3,0]$ in hands and the cards in the pile are $[0,1,2]$ from top to bottom.

Then, we play the card $3$ in the second operation. The cards in the pile are $[1,2,3]$ , in which the cards are piled up in increasing order.

Example 2

Play an empty card and draw the card $1$ , then play $1$ , $2$ , $3$ in order.