[COCI2017-2018#6] Alkemija

一共存在 $N$ 种元素，现在你只拥有其中的 $M$ 个。现在给你 $K$ 个式子，每个式子都有两排，第一排为他所需要的元素，第二排为他所可以获得的元素。你的元素是无限的，问你最后最多可以获得哪些元素？

In ancient times, when alchemists were searching for gold, the world was familiar with a total of ​N distinct substances, denoted with 1 to ​N​. During many years of hard work, searching for the secret formula, alchemists discovered a series of interesting regularities - ​alchemical reactions ​. In one reaction, it’s possible to transform substance set { $X_1$​,$X_2$​, …, $X_L$​} to another substance set {$Y_1$​, $Y_2$​, …, ​$Y_R$​}. For example, the substance set {1, 4, 5} might react once and create the new substance set {2, 6}. Joško is a modern alchemist and has ​M distinct substances denoted with ​$A_1$​, $A_2$​, …, ​$A_M$​. He has an unlimited quantity of each substance from that set. Joško wants to know which substances he can create using a list of reactions of ancient alchemists, so he’s asking you to help him solve this problem.

The first line of input contains two integers N and M (1 ≤ M ≤ N ≤ 100 000), the numbers from the task. The second line of input contains M integers $A_i$ (1 ≤ $A_i$ ≤ N), labels of the substances Joško has in the beginning. The third line of input contains the integer K (1 ≤ K ≤ 100 000), the number of known reactions. The following 3·K lines contain a list of reactions. Each reaction is described with 3 lines in the following way: - The first line contains the integers L and R (1 ≤ L, R ≤ N). - The second line contains L distinct integers $X_i$ (1 ≤ $X_i$ ≤ N). - The third line contains R distinct integers $Y_i$ (1 ≤ $Y_i$ ≤ N). - This describes the reaction with which the substance set {$X_1$, $X_2$, …, $X_L$} transforms into substance set {$Y_1$, $Y_2$, …, $Y_R$}. The sum of all L values won’t exceed 100 000. The sum of all R values won’t exceed 100 000.

The first line of output must contain the integer X, the number of obtainable substances. The second line of output must contain X distinct integers $B_i$, sorted ascendingly, that represent the labels of the obtainable substances.

4 2
1 2
2
2 1
1 2
3
2 1
1 3
4

4
1 2 3 4

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

5
1 2 4 5 6

In test cases worth 60% of total points, it will hold: - N, K ≤ 500. - The sum of all L values and the sum of all R values won’t exceed 500. **Clarification of the first test case:** There are 2 reactions. The first reaction transforms substance set {1, 2} into substance set {3}. The second reaction transforms substance set {1, 3} into substance set {4}. Joško initially has substances from the set {1, 2}. Using the first reaction, Joško can obtain substance 3, after which he has substances from the set {1, 2, 3}. After that, using the second reaction, he can also obtain substance 4. **Clarification of the second test case:** Joško initially has substances from the set {1, 4, 5}. Using the second reaction, it is possible to obtain substance 6, after which it is possible to apply the third reaction, giving substance 2. The first reaction is impossible to apply because Joško doesn’t have substance 3.