PROGRAMMING:Hamiltonian Cycle

The "Hamilton cycle problem" is to find a simple cycle that contains every vertex in a graph. Such a cycle is called a "Hamiltonian cycle".
In this problem, you are supposed to tell if a given cycle is a Hamiltonian cycle.
### Input Specification:
Each input file contains one test case. For each case, the first line contains 2 positive integers $$N$$ ($$2< N \le 200$$), the number of vertices, and $$M$$, the number of edges in an undirected graph. Then $$M$$ lines follow, each describes an edge in the format `Vertex1 Vertex2`, where the vertices are numbered from 1 to $$N$$. The next line gives a positive integer $$K$$ which is the number of queries, followed by $$K$$ lines of queries, each in the format:
$$n$$ $$V_ 1$$ $$V_ 2$$ ... $$V_ n$$
where $$n$$ is the number of vertices in the list, and $$V_ i$$'s are the vertices on a path.
### Output Specification:
For each query, print in a line `YES` if the path does form a Hamiltonian cycle, or `NO` if not.
### Sample Input:
```in
6 10
6 2
3 4
1 5
2 5
3 1
4 1
1 6
6 3
1 2
4 5
six
7 5 1 4 3 6 2 5
6 5 1 4 3 6 2
9 6 2 1 6 3 4 5 2 6
4 1 2 5 1
7 6 1 3 4 5 2 6
7 6 1 2 5 4 3 1
```
### Sample Output:
```out
YES
NO
NO
NO
YES
NO
```







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