CF1172A 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.