Problem Description

Little C likes drawing on a drawing board. He performs $n$ operations. Each operation can be one of the following three types:

• 1 k b means Little C draws a line with equation $y = kx + b$.
• 2 k b means Little C asks you: the line $y = kx + b$ has exactly one common point with how many drawn lines?
• 3 k b means Little C erases all lines that have at least one common point with the line $y = kx + b$.

Note: Two overlapping (coincident) lines have infinitely many intersection points.

Note: During queries, coincident lines should be counted separately.

Input Format

The first line contains an integer $n$.

The next $n$ lines each contain three integers $1/2/3, k, b$, representing one operation.

Output Format

For each 2 k b operation, output the number of lines that satisfy the requirement.

6
1 1 0
1 -1 0
2 2 1
3 1 3
2 2 1
2 1 1

2
1
0

10
1 1 0
1 1 0
2 1 1
2 1 0
2 2 5
3 1 0
2 2 5
1 2 3
1 3 4
2 3 5

0
0
2
0
1

Hint

[Sample 1 Explanation]

In the 1st operation, draw the line $y = x$.

In the 2nd operation, draw the line $y = -x$.

In the 3rd operation, you can see that the line $y = 2x + 1$ intersects the previous two lines.

In the 4th operation, erase all lines that intersect $y = x + 3$; the line $y = -x$ is erased.

In the 5th operation, $y = 2x + 1$ obviously intersects $y = x$.

In the 6th operation, $y = x + 1$ has the same slope as $y = x$, so they are parallel and do not intersect.

[Constraints]

For $100\%$ of the testdata, $1 \le n \le 10^5$, $1 \le |k| \le 10^5$, $0 \le |b| \le 10^5$.

Hint: This problem uses bundled tests.

$$\def\r{\cr\hline} \def\None{\text{None}} \def\arraystretch{1.5} \begin{array}{c|c|c} \textbf{Subtask} & \textbf{Sp. Constraints} & \textbf{Score}\r \textsf1& n \le 5000 & 27 \r \textsf2& \vert k\vert,\vert b\vert \le 50 & 21 \r \textsf3& No type 3 operations & 13 \r \textsf4& The $i$-th operation satisfies $k = i$ & 14 \r \textsf5& No special constraints & 25 \r \end{array}$$

The hack test points added after the contest will be placed into subtask 6.

Source

Item	People
idea	船酱魔王 (Chuánjiàng Mówáng)
data
check	EstasTonne
solution	船酱魔王 (Chuánjiàng Mówáng)

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