Description

Input

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 $10^6$.

Output

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

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

1
1
2
1
8
6

Note

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:

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