CFR Cluj

Task

Because time means money, and students don't have either, much like CFR Cluj's trophy cabinet, this problem will not have a story:

You have to process $q$ queries of the following types:

• 1 x y: Activate point $(x,y)$. It is guaranteed that an already active point with the same $x$ or $y$ coordinate does not exist.
• 2 x y: Deactivate point $(x,y)$. It is guaranteed that point $(x,y)$ is active at the moment.
• 3 x y: Draw open line segments ( segments which do not contain their endpoints) from point $(x,y)$, which is active at the moment, to all the other active points, and then print the maximum total number of intersections of a "plus" with these drawn segments (if more than one intersection occurs at the same point, all of them are counted separately). A "plus" centered in $(x_0,y_0)$, where $x_0,y_0 \in \mathbb{R}$, is a shape formed from the two lines with equations $x=x_0$ and $y=y_0$.

Observation: The open line segments drawn in queries of type $3$ are deleted after printing the answer (i.e. they do not persist through queries).

Input data

The first line contains an integer, the number of queries $q$.

The next $q$ lines will each contain three integers $t$, $x$ and $y$ - the parameters of the queries.

Output data

For each query of type $3$, print the maximum number of intersections of a "plus" with the drawn open line segments.

Constraints and clarifications

• $2 \le q \le 5 \cdot 10^5$
• $1 \le t \le 3$
• $-10^9 \le x,y \le 10^9$
• It is guaranteed that there is at least one query of type $3$.
• It is guaranteed that for queries of type $1$, there does not exist any active point with the same $x$ or $y$ coordinate.
• It is guaranteed that for queries of type $2$ and $3$, the point $(x,y)$ is active.

Example 1

stdin

17
1 0 0
1 1 1
1 -1 -1
3 0 0
1 -2 3
1 3 -2
3 0 0
3 -1 -1
2 0 0
1 4 4
3 1 1
2 1 1
1 2 2
3 4 4
3 2 2
3 -2 3
3 3 -2

stdout

2
4
6
4
8
4
7
7

Explanation

Down below there is a graphic for the first example and query $(3,-1,-1)$, illustrating the $6$ intersections:

The active points are: $C(-1,-1)$, $A(0,0)$, $B(1,1)$, $D(-2,3)$, $E(3,-2)$.

A "plus" centered in point $(-0.5,-0.75)$ has $6$ intersections, since:

• Its vertical line intersects the segments $CA$, $CB$ and $CE$.
• Its horizontal line intersects the segments $CA$, $CB$ and $CD$.

Example 2

stdin

4
1 905580697 285643736
2 905580697 285643736
1 687880848 -231766091
3 687880848 -231766091

stdout

0

Example 3

stdin

13
1 0 0
1 1 1
1 -1 -1
1 -2 3
1 3 -2
1 4 4
1 2 2
3 -1 -1
3 1 1
3 4 4
3 2 2
3 -2 3
3 3 -2

stdout

10
6
12
8
11
11