Kirill and Company

Description:

Input:

The first line of input data contains an integer $$$t$$$ ($$$1 \le t \le 10^3$$$) — the number of test cases in the test.

The first line of the test case contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 10^4$$$, $$$n-1 \le m \le min (10^4, $$$$$$ \frac{n \cdot (n - 1)}{2} $$$$$$)$$$) — the number of vertices and edges, respectively.

The next $$$m$$$ lines of the test case contain a description of the edges, two integers each $$$u$$$ and $$$v$$$ ($$$1 \le u, v \le n$$$, $$$u \ne v$$$) — indexes of vertices connected by an edge. It is guaranteed that there is at most one edge between any pair of vertices (i.e. no multiple edges in the graph).

Then follows line containing the number $$$f$$$ ($$$1 \le f \le 10^4$$$) — the number of Kirill's friends.

The next line of the test case contains $$$f$$$ integers: $$$h_1, h_2, \dots, h_f$$$ ($$$2 \le h_i \le n$$$) — the vertices in which they live. Some vertices may be repeated.

The next line of the set contains the number $$$k$$$ ($$$1 \le k \le min(6, f)$$$) — the number of friends without cars.

The last line of each test case contains $$$k$$$ integers: $$$p_1, p_2, \dots, p_k$$$ ($$$1 \le p_i \le f$$$, $$$p_i < p_{i+1}$$$) — indexes of friends without cars.

It is guaranteed that the sum of $$$n$$$ over all cases does not exceed $$$10^4$$$, as well as the sums of $$$m$$$ and $$$f$$$.

Output:

Output $$$t$$$ lines, each of which contains the answer to the corresponding test case. As an answer, output a single integer — the minimum possible number of friends who will have to walk.

Sample Input:

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

Sample Output:

2
1
1

Sample Input:

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

Sample Output:

3
1
0

Note:

The first test case of the first example is explained in the statement.

In the second test case of the first example, two friends with cars live at vertex $$$5$$$, one can give a ride to friends from vertices $$$2$$$ and $$$3$$$, and the second from vertex $$$4$$$, only a friend from vertex $$$6$$$ will have to walk.