### Problem Statement

For a sequence $X=(X_1,X_2\ldots,X_N)$ of length $N$ consisting of positive integers, we define $f(X)$ as follows:

-   A tree with $N$ vertices is said to be good if and only if the degree of the $i$-th $(1 \leq i \leq N)$ vertex is $X_i$. If a good tree exists, $f(X)$ is the maximum diameter of a good tree; if it doesn't, $f(X)=0$.

Here, the distance between two vertices is the minimum number of edges that must be traversed to travel from one vertex to the other, and the diameter of a tree is the maximum distance between two vertices.

Find the sum, modulo $998244353$, of $f(X)$ over all possible sequences $X$ of length $N$ consisting of positive integers. We can prove that the sum of $f(X)$ is a finite value.

Given $T$ test cases, find the answer for each of them.

### Input

The input is given from Standard Input in the following format, where $\mathrm{test}_i$ denotes the $i$\-th test case:

```
$T$
$\mathrm{test}_1$
$\mathrm{test}_2$
$\vdots$
$\mathrm{test}_T$
```

Each test case is given in the following format:

```
$N$
```

### Output

Print $T$ lines.

The $i$\-th $(1\leq i \leq T)$ line should contain the answer to the $i$\-th test case.

### Constraints

-   $1\leq T \leq 2\times 10^5$
-   $2 \leq N \leq 10^6$
-   All values in the input are integers.

1
6
110
8052
9758476
421903645
377386885
881422708
120024839
351256142

If N=3,
for example,

• when X=(1,1,1), there is no tree with three vertices whose degrees are 1,1, and 11, so f(X)=0.
• When X=(2,1,1), the only possible tree is illustrated below. The diameter of this tree is 2, so f(X)=2

For X=(2,1,1),(1,2,1),(1,1,2), we have f(X)=2; for other X, we have f(X)=0. Thus, the answer is 6.