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 $i < x \leq i+k$, $p_x$ 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.

见题面 Input 部分

见题面 Output 部分

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:

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