A tree with $$$n$$$ nodes fell from the sky along with an initially empty set $$$S$$$. Ecstatic by this unlikely event, you do the following $$$n - 1$$$ times:

let $$$x$$$ be the leaf with maximum index.
add $$$x$$$ into $$$S$$$ (note that if $$$x$$$ is already in $$$S$$$ then nothing changes).
select any leaf other than $$$x$$$ and remove it from the tree.

Determine the number of distinct sets $$$S$$$ you can make. As the number could be ginormous, output it modulo $$$998\,244\,353$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each testcase contains an integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the size of the tree.

Then $$$n - 1$$$ lines follow, each of which contain two integers $$$u$$$ and $$$v$$$ ($$$1 \le u,v \le n, u \ne v$$$), which describe a pair of vertices connected by an edge. It is guaranteed that the given graph is a tree.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

Output the number of distinct sets that can be obtained modulo $$$998\,244\,353$$$.

Note

For the first testcase, there is only one possible order: $$$1$$$, making the set $$$\{2\}$$$

For the third testcase, the tree looks as follows:

$\text{[math]}$

you can make the sets:

$$$\{3, 6, 7\}$$$ by removing in the order $$$1, 2, 3, 4, 5, 6$$$
$$$\{3, 4, 6, 7\}$$$ by removing in the order $$$2, 1, 3, 4, 5, 6$$$
$$$\{3, 4, 5, 6, 7\}$$$ by removing in the order $$$2, 3, 1, 4, 5, 6$$$

It can be proven that these are the only sets obtainable.

Deconstruction Tree

Examples