F. Make Symmetrical
time limit per test
6 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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.

Examples
Input
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
Output
1022
Input
61 1 23 1 11 1 13 2 22 1 13 2 4
Output
110
Note

The first example is shown on the picture below.