Problem Background

First, you do not need to know anything about virtual trees to solve this problem.

— Even though this is the first problem in the repository with "virtual tree" in its name.

Problem Description

Jq姐姐有一棵以结点 $1$ 为根的树。定义一棵树的点集 $S$ 的非空子集 $s$ 是好的，当且仅当它满足 $\forall i,j \in s, \text{LCA}(i,j) \in s$。What is $\text{LCA}$?

为了让树的形态更加可爱，jq 姐姐打算修剪掉某个以节点 $i$ 为根的子树（也就是在原树里将节点 $i$ 及其子树内节点及其相连的边均删除）。

她有若干个修剪方案但从未实施，你需要求出每种方案实施后这棵树的好的非空子集数量。由于答案可能会很大，请输出其对 $998244353$ 取模的结果。

Input Format

The first line contains an integer $n$ ($n \leq 5 \times 10^5$), representing the number of nodes in the tree.

From the second to the $n$-th line, each line contains two integers $u_i, v_i$, indicating an edge from $u_i$ to $v_i$.

The $(n+1)$-th line contains an integer $m$ ($m \leq 5 \times 10^5$), representing the number of pruning schemes.

The next line contains $m$ integers $q_i$, indicating that the subtree rooted at $q_i$ will be pruned.

Output Format

Output $m$ lines, each containing an integer $k$ representing the number of good non-empty subsets of the original tree after removing the subtree rooted at $q_i$.

Sample Input and Output

Sample Input #1

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

Sample Output #1

3
13

Sample Input #2

10
1 2
2 3
2 4
1 5
5 6
5 7
7 8
7 10
1 9
3
5 2 8

Sample Output #2

21
66
201

Notes

Explanation of Sample 1: After removing the subtree rooted at node $2$, all $3$ non-empty subsets of the original tree satisfy the property. After removing the subtree rooted at node $5$, out of the $15$ non-empty subsets of the original tree, $\{3,4\}$ and $\{1,3,4\}$ do not satisfy the property.

For the first $10\%$ of the data, $n, m \leq 20$.

For the first $30\%$ of the data, $n, m \leq 2000$.

For $100\%$ of the data, $1 \leq n, m \leq 5 \times 10^5$, $q \in [1, n]$.

见题面 Input 部分

见题面 Output 部分