CF1028F Make Symmetrical

Consider a set of points $ A $ , initially it is empty. There are three types of queries: 1. Insert a point $ (x_i, y_i) $ to $ A $ . It is guaranteed that this point does not belong to $ A $ at this moment. 2. Remove a point $ (x_i, y_i) $ from $ A $ . It is guaranteed that this point belongs to $ A $ at this moment. 3. Given a point $ (x_i, y_i) $ , calculate the minimum number of points required to add to $ A $ to make $ A $ symmetrical with respect to the line containing points $ (0, 0) $ and $ (x_i, y_i) $ . Note that these points are not actually added to $ A $ , i.e. these queries are independent from each other.

The first line contains a single integer $ q $ ( $ 1 \le q \le 2 \cdot 10^5 $ ) — the number of queries. Each of the following $ q $ lines describes a query and contains three integers $ t_i $ , $ x_i $ and $ y_i $ ( $ t_i \in \{1, 2, 3\} $ , $ 1 \le x_i, y_i \le 112\,904 $ ) — the type of the query and the coordinates of the point. Type $ 1 $ is addition of the point, type $ 2 $ is removal of the point, type $ 3 $ is the query to compute the minimum number of points required to make $ A $ symmetrical. It is guaranteed that there are no more than $ 10^5 $ queries of type $ 3 $ and no more than $ 10^5 $ queries having type $ 1 $ or $ 2 $ .

For each query of the third type output a line with a single integer — the answer to this query.

The first example is shown on the picture below.