Vertex Deletion

Given a tree with $n$ vertices, you can delete any vertex you like. We call a way of deletion beautiful if, in the remaining part of the tree, every vertex has at least one vertex still connected to it. You need to calculate how many ways of deletion are beautiful.

Two ways of deletion are considered the same if the set of the deleted vertex is the same.

This problem contains multiple test cases.

The first line contains an integer $T$ indicating the number of test cases.

For each test case, the first line contains one integer $n$ ($1 \leq n \leq 10 ^ 5$).

The next $n - 1$ lines each contains two integers $u$ and $v$ ($1 \leq u, v \leq n,u\neq v$), representing an edge (u, v).

It's guaranteed that $\sum{n} \leq 10 ^ 6$.

Output $T$ lines, each line contains an integer indicating the answer.

Since the answer can be very large, you only need to output the answer modulo $998244353$.

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

22

“红旗杯”第十五届东北地区大学生程序设计竞赛