Nauuo and Cards

Description:

Input:

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 $$$b_{1..n}$$$.

Output:

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

Sample Input:

3
0 2 0
3 0 1

Sample Output:

2

Sample Input:

3
0 2 0
1 0 3

Sample Output:

4

Sample Input:

11
0 0 0 5 0 0 0 4 0 0 11
9 2 6 0 8 1 7 0 3 0 10

Sample Output:

18

Note:

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.