CF2210B Simply Sitting on Chairs

There are $ n $ chairs in a row, initially all unmarked. You are given a permutation $ p $ $ ^{\text{∗}} $ of length $ n $ . Now, you play a game. You visit each chair sequentially, starting from the $ 1 $ -st chair. At the $ i $ -th chair, you can do the following: - If the $ i $ -th chair is already marked, then you end the game immediately without sitting on it. - Otherwise, you can choose to sit on the chair or skip it and move to the next chair. - If you choose to sit on the chair, then after standing up, you mark the $ p_i $ -th chair and move to the next chair. If all the $ n $ chairs are visited, the game ends.Your task is to determine the maximum number of chairs that you can sit on. $ ^{\text{∗}} $ A permutation of length $ n $ is an array consisting of $ n $ distinct integers from $ 1 $ to $ n $ in arbitrary order. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation ( $ 2 $ appears twice in the array), and $ [1,3,4] $ is also not a permutation ( $ n=3 $ but there is $ 4 $ in the array).

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 2\cdot 10^5 $ ) — the number of chairs. The second line of each test case contains $ n $ distinct integers $ p_1, p_2,\ldots,p_{n} $ — the permutation $ p $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot10^5 $ .

Output a single integer — the maximum number of chairs you can sit on.

In the first test case, you can proceed as follows: 1. You visit the $ 1 $ -st chair, sit on it, and mark the $ 3 $ -rd chair. 2. You visit the $ 2 $ -nd chair, sit on it, and mark the $ 2 $ -nd chair. 3. You visit the $ 3 $ -rd chair. Since it is marked, you end the game. Therefore, using this sequence, you can sit on a total of $ 2 $ chairs. It can be shown that the maximum number of chairs using any sequence of moves is $ 2 $ .In the second test case, you can proceed as follows: 1. You visit the $ 1 $ -st chair, sit on it, and mark the $ 4 $ -th chair. 2. You visit the $ 2 $ -nd chair and skip it. 3. You visit the $ 3 $ -rd chair, sit on it, and mark the $ 2 $ -nd chair. 4. You visit the $ 4 $ -th chair. Since it is marked, you end the game. Therefore, using this sequence, you can sit on a total of $ 2 $ chairs. It can be shown that the maximum number of chairs using any sequence of moves is $ 2 $ .