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1 초 | 512 MB | 11 | 4 | 4 | 36.364% |
In 2020, there are $C$ programming contests held in Indonesia, numbered from $1$ to $C$. Each contest has zero or more tasks written for the contest. There are $A$ task authors who can write tasks for these contests, numbered from $1$ to $A$. The $i$th task author only likes the set of contests $L_i \subseteq \{1, 2, \dots , C\}$, and only wants to write tasks for contests in $L_i$. Each task author cannot write more than one task for the same contest.
There are also $T$ topics in programming contest tasks, numbered from $1$ to $T$. For example, topic 1 might be about graph tasks, topic 2 might be about string tasks, and so on. Each task has exactly one topic. The $i$th task author is familiar with the set of topics $F_i \subseteq \{1, 2, \dots , T\}$, and only wants to write tasks about topics in $F_i$. Each task author cannot write more than one task about the same topic.
Additionally, each contest also has a syllabus. The $j$th contest syllabus contains the set of topics $S_j \subseteq \{1, 2, \dots , T\}$, and the topic for the tasks written for the contest must be in $S_j$. Each contest cannot have more than one task for the same topic.
You are a programming contest enthusiast in Indonesia. Surprisingly, you observed the following:
You want to find the maximum total number of tasks that can be written across all contests.
Input begins with a line containing three integers: $A C T$ ($1 \le A, C, T \le 50 000$) representing the number of task authors, contests, and topics, respectively.
The next $A$ lines each begins with an integer: $|L_i|$ ($0 \le |L_i| \le 2$) representing the number of contests that the $i$th task author likes, followed by $|L_i|$ integers: $L_i[x]$ ($1 \le L_i[x] \le C$) representing the liked contests. It is guaranteed that the values in $L_i$ are distinct. It is also guaranteed that for all $1 \le j \le C$, the value $j$ only appears at most twice in $\bigcup_{i=1}^{A}{L_i}$.
The next A lines each begins with an integer: $|F_i|$ ($0 \le |F_i| \le 2$) representing the number of topics that the $i$th task author is familiar with, followed by $|F_i|$ integers: $F_i[y]$ ($1 \le F_i[y] \le T$) representing the familiarized topics. It is guaranteed that the values in $F_i$ are distinct. It is also guaranteed that for all $1 \le k \le T$, the value $k$ only appears at most twice in $\bigcup_{i=1}^{A}{F_i}$.
The next $C$ lines each begins with an integer: $|S_j|$ ($0 \le |S_j| \le 2$) representing the number of topics in the $j$th contest syllabus, followed by $|S_j|$ integers: $S_j[z]$ ($1 \le S_j[z] \le T$) representing the topics in the syllabus. It is guaranteed that the values in $S_j$ are distinct. It is also guaranteed that for all $1 \le k \le T$, the value $k$ only appears at most twice in $\bigcup_{j=1}^{C}{S_j}$.
Output in a line an integer representing the maximum total number of tasks that can be written across all contests.
2 3 2 2 1 2 2 2 3 1 1 1 1 1 1 1 1 1 2
2
There are at most two tasks that can be written:
Note that the 1st task author has written a task about the 1st topic, thus they cannot write a task for the 2nd contest about the same topic.
This example can be illustrated by the following figure, with $A_i$ represents the $i$th task author, $C_j$ represents the $j$th contest, $T_k$ represents the $k$th topic, thick lines represent the first task, and the dashed lines represent the second task.