CF1799H.Tree Cutting

You are given a tree with $n$ vertices.

A hero $k$ times do the following operation:

• Choose some edge.
• Remove it.
• Take one of the two remaining parts and delete it.
• Write the number of vertices in the remaining part.

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.

你被给定一棵包含 $n$ 个顶点的树。

一位英雄执行 $k$ 次如下操作：

• 选择某条边；
• 删除该边；
• 从剩余的两个连通分量中任选其一并删除；
• 将剩余连通分量中的顶点数写下来。

你被给定初始树以及一个已写出的数字序列。请计算执行上述操作的方式数目，使得所写出的数字序列恰好等于给定序列。由于答案可能很大，请对 $998\,244\,353$ 取模。若在某次操作中所选的边或所保留的连通分量不同，则认为两种方式不同。

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 $s_1, s_2, \ldots, s_k$ ($n \gt s_1 \gt s_2 \gt \ldots \gt s_k \geq 1$) — written numbers.

第一行包含一个整数 $n$（$2 \leq n \leq 5000$）——顶点的数量。

接下来的 $n-1$ 行，每行包含两个整数 $s$、$f$（$1 \leq s, f \leq n$，$s \neq f$）——表示一条边 $(s, f)$。

下一行包含一个整数 $k$（$1 \leq k \leq \min{(6, n - 1)}$）——操作次数。

再下一行包含 $k$ 个整数 $s_1, s_2, \ldots, s_k$（$n \gt s_1 \gt s_2 \gt \ldots \gt s_k \geq 1$）——所写的数字。

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

输出一个整数——该问题的答案对 $998\,244\,353$ 取模的结果。

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 $3$.

在第一个测试中，共有四种可能的操作方式：

• 移除边 $(1, 2)$ 并删除顶点 $1$；移除边 $(2, 3)$ 并删除顶点 $2$。
• 移除边 $(1, 2)$ 并删除顶点 $1$；移除边 $(3, 2)$ 并删除顶点 $3$。
• 移除边 $(3, 2)$ 并删除顶点 $3$；移除边 $(1, 2)$ 并删除顶点 $1$。
• 移除边 $(3, 2)$ 并删除顶点 $3$；移除边 $(2, 1)$ 并删除顶点 $2$。

在第二个测试中，共有两种可能的操作方式：

• 移除边 $(4, 1)$ 并删除包含顶点 $4$ 的连通分量；移除边 $(2, 3)$ 并删除包含顶点 $2$ 的连通分量。
• 移除边 $(4, 1)$ 并删除包含顶点 $4$ 的连通分量；移除边 $(3, 2)$ 并删除包含顶点 $3$ 的连通分量。