Define a function $$$f$$$ such that for an array $$$b$$$, $$$f(b)$$$ returns the array of prefix maxima of $$$b$$$. In other words, $$$f(b)$$$ is an array containing only those elements $$$b_i$$$, for which $$$b_i=\max(b_1,b_2,\ldots,b_i)$$$, without changing their order. For example, $$$f([3,10,4,10,15,1])=[3,10,10,15]$$$.

You are given a tree consisting of $$$n$$$ nodes rooted at $$$1$$$.

A permutation$$$^\dagger$$$ $$$p$$$ of is considered a pre-order of the tree if for all $$$i$$$ the following condition holds:

Let $$$k$$$ be the number of proper descendants$$$^\ddagger$$$ of node $$$p_i$$$.
For all $$$x$$$ such that $$$i \lt x \leq i+k$$$, $$$p_x$$$ is a proper descendant of node $$$p_i$$$.

Find the number of distinct values of $$$f(a)$$$ over all possible pre-orders $$$a$$$. Since this value might be large, you only need to find it modulo $$$998\,244\,353$$$.

$$$^\dagger$$$ A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

$$$^\ddagger$$$ Node $$$t$$$ is a proper descendant of node $$$s$$$ if $$$s \neq t$$$ and $$$s$$$ is on the unique simple path from $$$t$$$ to $$$1$$$.

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.

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:

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

Prefix Max Set Counting

Examples