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.

考虑一个点集 $A$，初始时为空。存在三种类型的查询：

1. 向 $A$ 中插入一个点 $(x_i, y_i)$。保证该点此时不在 $A$ 中。
2. 从 $A$ 中删除一个点 $(x_i, y_i)$。保证该点此时属于 $A$。
3. 给定一个点 $(x_i, y_i)$，计算为使 $A$ 关于过点 $(0, 0)$ 和 $(x_i, y_i)$ 的直线对称，所需向 $A$ 中添加的最少点数。注意：这些点实际上不会被加入 $A$，即此类查询相互独立。

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 $2$.

第一行包含一个整数 $q$（$1 \le q \le 2 \cdot 10^5$），表示查询次数。

接下来的 $q$ 行每行描述一次查询，包含三个整数 $t_i$、$x_i$ 和 $y_i$（其中 $t_i \in \{1, 2, 3\}$，$1 \le x_i, y_i \le 112\,904$），分别表示查询类型及该点的坐标。类型 $1$ 表示添加该点；类型 $2$ 表示删除该点；类型 $3$ 表示查询：为使集合 $A$ 成为中心对称，至少需要添加多少个点。

保证类型 $3$ 的查询总数不超过 $10^5$，且类型 $1$ 或类型 $2$ 的查询总数也不超过 $10^5$。

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

对于每个第三种类型的查询，输出一行，包含一个整数——该查询的答案。

The first example is shown on the picture below.

第一个示例见下图。