Score : $400$ points

问题描述

高桥正在玩玩具火车，连接和断开它们。 共有 $N$ 辆玩具火车车厢，编号分别为：车1、车2、……、车$N$。 最初，所有车厢都是分开的。

你将收到 $Q$ 个查询请求，请按照给定顺序处理。查询有三种类型，如下所示：

• 1 x y：将车$y$的前端与车$x$的后端连接起来。
  确保满足以下条件：

  • $x \neq y$
  • 在此查询之前，没有火车连接到车$x$的后端；
  • 在此查询之前，没有火车连接到车$y$的前端；
  • 在此查询之前，车$x$和车$y$属于不同的连通分量。

• 2 x y：将车$y$的前端从车$x$的后端断开连接。
  确保满足以下条件：

  • $x \neq y$；
  • 在此查询之前，车$y$的前端直接连接到车$x$的后端。

• 3 x：打印包含车$x$的连通分量中车厢的编号，从前到后。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi is playing with toy trains, connecting and disconnecting them.
There are $N$ toy train cars, with car numbers: Car $1$, Car $2$, $\ldots$, Car $N$.
Initially, all cars are separated.

You will be given $Q$ queries. Process them in the order they are given. There are three kinds of queries, as follows.

• 1 x y: Connect the front of Car $y$ to the rear of Car $x$.
  It is guaranteed that:

  • $x \neq y$
  • just before this query, no train is connected to the rear of Car $x$;
  • just before this query, no train is connected to the front of Car $y$;
  • just before this query, Car $x$ and Car $y$ belong to different connected components.

• 2 x y: Disconnect the front of Car $y$ from the rear of Car $x$.
  It is guaranteed that:

  • $x \neq y$;
  • just before this query, the front of Car $y$ is directly connected to the rear of Car $x$.

• 3 x: Print the car numbers of the cars belonging to the connected component containing Car $x$, from front to back.

Constraints

• $2 \leq N \leq 10^5$
• $1 \leq Q \leq 10^5$
• $1 \leq x \leq N$
• $1 \leq y \leq N$
• All values in input are integers.
• All queries satisfy the conditions in the Problem Statement.
• The queries of the format 3 x ask to print at most $10^6$ car numbers in total.

Input

Input is given from Standard Input in the following format:

$N$ $Q$

$\mathrm{query}_1$

$\mathrm{query}_2$

$\vdots$

$\mathrm{query}_Q$

The $i$-th query $\mathrm{query}_i$ begins with an integer $c_i$ ($1$, $2$, or $3$) representing the kind of the query, followed by $x$ and $y$ if $c_i = 1$ or $2$, and followed by $x$ if $c_i = 3$.

In short, each query is in one of the following three formats:

$1$ $x$ $y$

$2$ $x$ $y$

$3$ $x$

Output

If a query with $c_i = 3$ asks to print the values $j_1, j_2, \ldots, j_M$, output the following line:

$M$ $j_1$ $j_2$ $\ldots$ $j_M$

Your output should consist of $q$ lines, where $q$ is the number of queries with $c_i = 3$.

The $k$-th line $(1 \leq k \leq q)$ should contain the response to the $k$-th such query.

Sample Input 1

7 14
1 6 3
1 4 1
1 5 2
1 2 7
1 3 5
3 2
3 4
3 6
2 3 5
2 4 1
1 1 5
3 2
3 4
3 6

Sample Output 1

5 6 3 5 2 7
2 4 1
5 6 3 5 2 7
4 1 5 2 7
1 4
2 6 3

The figure below shows the cars when the first $5$ queries are processed.
For example, Car $2$ belongs to the same connected component as Cars $3, 5, 6, 7$, which is different from the connected component containing Cars $1, 4$.

The figure below shows the cars when the first $11$ queries are processed.

update @ 2024/3/10 09:53:22