A11318 | Prefix Max Set Counting

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 10^5$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 10^6$ ) — the number of vertices.

The following next $n-1$ lines contain two integers $u$ and $v$ ( $1 \leq u, v \leq n$ , $u \neq v$ ) — denoting an edge between nodes $u$ and $v$ . It is guaranteed that the given edges form a tree.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$ .

For each test case, output the number of distinct values of $f(a)$ modulo $998\,244\,353$ that you can get.

In the first test case, the only valid pre-order is $a=[1]$ . So the only possible value of $f(a)$ is $[1]$ .

In the second test case, the only valid pre-order is $a=[1,2]$ . So the only possible value $f(a)$ is $[1,2]$ .

In the third test case, the two valid pre-orders are $a=[1,2,3]$ and $a=[1,3,2]$ . So the possible values of $f(a)$ are $[1,2,3]$ and $[1,3]$ .

In the fifth test case, the possible values of $f(a)$ are:

- $[1,5]$ ;
- $[1,2,5]$ ;
- $[1,3,5]$ ;
- $[1,4,5]$ ;
- $[1,2,3,5]$ ;
- $[1,2,4,5]$ ;
- $[1,3,4,5]$ ;
- $[1,2,3,4,5]$ .