You are given a tree with $$$n$$$ vertices.
A hero $$$k$$$ times do the following operation:
You are given an initial tree and the a sequence of written numbers. Find the number of ways to make operations such that the written numbers are equal to the given numbers. Due to the answer can be big, find it by modulo $$$998\,244\,353$$$. Two ways are considered different, if on some operation edge or remaining part are selected differently.
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.
Print a single integer — the answer to the problem by modulo $$$998\,244\,353$$$.
3 1 2 2 3 2 2 1
4
7 2 1 3 2 4 1 5 3 6 4 7 4 2 4 2
2
7 1 2 1 3 1 4 2 5 3 6 4 7 1 2
3
7 1 2 1 3 1 4 2 5 3 6 4 7 4 6 5 2 1
24
8 1 2 2 3 3 4 3 5 3 6 3 7 3 8 2 7 4
0
In the first test there are four possible ways to make operations:
In the second test there are two possible ways to make operations:
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