The Most Beautiful Christmas Tree

Hyeona is preparing a Christmas tree and wants the tree she made to be the most beautiful in the world.

Hyeona's tree $T$ has $n$ vertices and $n-1$ edges, and it has a root $r$. Hyeona also has $n$ ornaments, one for each vertex. Every ornament has a unique beauty value. There is a 1st most beautiful ornament, a 2nd most beautiful ornament, up to an $n$-th most beautiful ornament. No two ornaments have the same beauty value.

The tree $T$ is called beautiful if the ornaments placed on the vertices satisfy the following condition.

• For every parent-child pair formed with $r$ as the root, the ornament on the child vertex is more beautiful (has a larger beauty value) than the ornament on the parent vertex.

Here, vertex $u$ is the parent of vertex $v$ if the two vertices are adjacent and the distance from $r$ to $u$ is smaller than the distance from $r$ to $v$. The distance between two vertices $u$ and $v$ is the minimum number of edges on a path from $u$ to $v$.

Find the number of ways to place ornaments on the vertices so that $T$ is beautiful, modulo $998\,244\,353$. $998\,244\,353$ is a prime. Every vertex must receive an ornament. Changing the root of the tree, find this count $Q$ times.

The first line contains the number of vertices $n$.

The next $n-1$ lines each contain two integers $u$ and $v$, separated by a space, meaning that an edge connects vertices $u$ and $v$.

The next line contains the number of queries $Q$.

Each of the next $Q$ lines contains one integer $r$. This is a query asking for the answer when the root of the tree is $r$.

For each query, print the answer. Separate consecutive answers with a newline.

• $2 \leq n \leq 200\,000$
• $1 \leq u, v \leq n$, $u \neq v$
• $1 \leq Q \leq 200\,000$
• $1 \leq r \leq n$
• The given graph is always a tree.