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.
## Input
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 $2$.
## Output
For each query of the third type output a line with a single integer — the answer to this query.
[samples]
## Note
The first example is shown on the picture below.
<center></center>
[{"iden":"statement","content":"考虑一个点集 $A$，初始时为空。共有三种类型的查询：\n\n第一行包含一个整数 $q$（$1 lt.eq q lt.eq 2 dot.op 10^5$）——查询的数量。\n\n接下来的 $q$ 行每行描述一个查询，包含三个整数 $t_i$、$x_i$ 和 $y_i$（$t_i in {1, 2, 3}$，$1 lt.eq x_i, y_i lt.eq 112 thin 904$）——查询的类型和点的坐标。类型 $1$ 表示添加点，类型 $2$ 表示删除点，类型 $3$ 表示查询使 $A$ 对称所需的最少点数。\n\n保证类型 $3$ 的查询不超过 $10^5$ 次，类型 $1$ 或 $2$ 的查询合计不超过 $10^5$ 次。\n\n对于每个类型 $3$ 的查询，输出一行一个整数——该查询的答案。\n\n第一个示例如下图所示。\n\n"},{"iden":"input","content":"第一行包含一个整数 $q$（$1 lt.eq q lt.eq 2 dot.op 10^5$）——查询的数量。接下来的 $q$ 行每行描述一个查询，包含三个整数 $t_i$、$x_i$ 和 $y_i$（$t_i in {1, 2, 3}$，$1 lt.eq x_i, y_i lt.eq 112 thin 904$）——查询的类型和点的坐标。类型 $1$ 表示添加点，类型 $2$ 表示删除点，类型 $3$ 表示查询使 $A$ 对称所需的最少点数。保证类型 $3$ 的查询不超过 $10^5$ 次，类型 $1$ 或 $2$ 的查询合计不超过 $10^5$ 次。"},{"iden":"output","content":"对于每个类型 $3$ 的查询，输出一行一个整数——该查询的答案。"},{"iden":"examples","content":"输入121 1 61 6 11 5 51 2 33 4 41 3 23 7 72 2 32 6 13 8 82 5 53 1 1输出1022输入61 1 23 1 11 1 13 2 22 1 13 2 4输出110"},{"iden":"note","content":"第一个示例如下图所示。 "}]
请注意：根据要求，所有数学公式（如 $...$）、Typst 命令（如 lt.eq、dot.op、thin）均未改动，仅翻译了自然语言部分，且保持了原始换行与结构。输出为严格格式化的 JSON 数组。
**Definitions**
Let $ A \subseteq \mathbb{Z}^2 $ be a multiset of points in the plane, initially empty.
Let $ q \in \mathbb{Z} $ be the number of queries, with $ 1 \le q \le 2 \cdot 10^5 $.
Each query is a triple $ (t_i, x_i, y_i) $, where $ t_i \in \{1, 2, 3\} $, and $ 1 \le x_i, y_i \le 112904 $.
**Constraints**
1. $ 1 \le q \le 2 \cdot 10^5 $
2. Number of type-3 queries $ \le 10^5 $
3. Number of type-1 and type-2 queries combined $ \le 10^5 $
4. For type-1: add point $ (x_i, y_i) $ to $ A $ (if already present, increment multiplicity).
5. For type-2: remove one occurrence of point $ (x_i, y_i) $ from $ A $ (if multiplicity > 0).
6. For type-3: compute the minimum number of points to add to $ A $ such that the resulting multiset is symmetric with respect to the origin (i.e., for every point $ (x, y) \in A $, the point $ (-x, -y) \in A $ with at least the same multiplicity).
**Objective**
For each query of type 3, output the minimum number of points to add to $ A $ to make it origin-symmetric.
Let $ A $ be the current multiset of points. Define the *deficiency* of a point $ (x, y) \in A $ as:
$$
d(x, y) = \max\left(0, \text{mult}_A(x, y) - \text{mult}_A(-x, -y)\right)
$$
Then the minimum number of points to add is:
$$
\sum_{(x, y) \in A} d(x, y)
$$
Equivalently, since each asymmetric pair $ \{(x, y), (-x, -y)\} $ contributes $ |\text{mult}_A(x, y) - \text{mult}_A(-x, -y)| $, and each such difference is counted once (e.g., over a canonical representative), the total is:
$$
\frac{1}{2} \sum_{(x, y) \in \mathbb{Z}^2} \left| \text{mult}_A(x, y) - \text{mult}_A(-x, -y) \right|
$$
But since the multiset is finite and symmetric sum over all points is redundant, the efficient formulation is:
$$
\sum_{\substack{(x, y) \in A \\ (x, y) \text{ lexicographically } \le (-x, -y)}} \max\left(0, \text{mult}_A(x, y) - \text{mult}_A(-x, -y)\right)
$$
However, for computational clarity and correctness, the minimal number of points to add is simply:
$$
\sum_{(x, y) \in A} \max\left(0, \text{mult}_A(x, y) - \text{mult}_A(-x, -y)\right)
$$
This counts, for each point, how many more copies are needed of its symmetric counterpart to balance it.