Tree Cutting

Description:

Input:

The first line contains a single integer $$$n$$$ ($$$2 \leq n \leq 5000$$$) — the number of vertices.

Each of the next $$$n-1$$$ lines contains two integers $$$s$$$, $$$f$$$ ($$$1 \leq s, f \leq n$$$, $$$s \neq f$$$) — description of edge $$$(s, f)$$$.

Next line contains a single integer $$$k$$$ ($$$1 \leq k \leq \min{(6, n - 1)}$$$) — the number of operations.

Next line contains $$$k$$$ integers $$$s_1, s_2, \ldots, s_k$$$ ($$$n > s_1 > s_2 > \ldots > s_k \geq 1$$$) — written numbers.

Output:

Print a single integer — the answer to the problem by modulo $$$998\,244\,353$$$.

Sample Input:

3
1 2
2 3
2
2 1

Sample Output:

4

Sample Input:

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

Sample Output:

2

Sample Input:

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

Sample Output:

3

Sample Input:

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

Sample Output:

24

Sample Input:

8
1 2
2 3
3 4
3 5
3 6
3 7
3 8
2
7 4

Sample Output:

0

Note:

In the first test there are four possible ways to make operations:

• Remove the edge $$$(1, 2)$$$ and delete vertex $$$1$$$. Remove the edge $$$(2, 3)$$$ and delete vertex $$$2$$$.
• Remove the edge $$$(1, 2)$$$ and delete vertex $$$1$$$. Remove the edge $$$(3, 2)$$$ and delete vertex $$$3$$$.
• Remove the edge $$$(3, 2)$$$ and delete vertex $$$3$$$. Remove the edge $$$(1, 2)$$$ and delete vertex $$$1$$$.
• Remove the edge $$$(3, 2)$$$ and delete vertex $$$3$$$. Remove the edge $$$(2, 1)$$$ and delete vertex $$$2$$$.

In the second test there are two possible ways to make operations:

• Remove the edge $$$(4, 1)$$$ and delete the part with vertex $$$4$$$. Remove the edge $$$(2, 3)$$$ and delete the part with vertex $$$2$$$.
• Remove the edge $$$(4, 1)$$$ and delete the part with vertex $$$4$$$. Remove the edge $$$(3, 2)$$$ and delete the part with vertex $$$3$$$.