Solve the programming task below in a Python markdown code block.
Given a sequence A of length N, the weight of this sequence is defined as

\text{weight}(A) = \sum_{i = 1}^{N} i\cdot A_{i}

Given an integer N, we pick a permutation A of [1, 2 \dots N] uniformly at random. What is the expected weight of this permutation?

It can be shown that the answer can be represented as \displaystyle \frac{P}{Q} where P and Q are coprime integers and Q \neq 0 \pmod{998244353}. Print the value of P \cdot Q^{-1} modulo 998244353.

------ Input Format ------ 

- First line of the input contains T, the number of test cases. Then the test cases follow.
- Each test case contains a single integer on a single line N.

------ Output Format ------ 

For each test case, print a single integer, the answer to the test case.

------ Constraints ------ 

$1 ≤ T ≤ 2 \cdot 10^{5}$
$1 ≤ N ≤ 10^{9}$

------ subtasks ------ 

Subtask 1 (100 points): Original constraints

----- Sample Input 1 ------ 
3
1
2
3

----- Sample Output 1 ------ 
1
499122181
12

----- explanation 1 ------ 
- Test case $1$: There is only one permutation of $[1]$ which is $[1]$ and the weight of this permutation is equal to $1$. So, the expected weight is equal to $1$.
- Test case $2$: There are $2$ permutations of $[1, 2]$ namely
- $[1, 2]$ with weight equal to $5$.
- $[2, 1]$ with weight equal to $4$.

So, the expected weight is equal to $\frac{5 + 4}{2!} = \frac{9}{2}$.
- Test case $3:$
There are $6$ permutations of $[1, 2, 3]$ namely
- $[1, 2, 3]$ with weight equal to $14$.
- $[1, 3, 2]$ with weight equal to $13$.
- $[2, 1, 3]$ with weight equal to $13$.
- $[2, 3, 1]$ with weight equal to $11$.
- $[3, 1, 2]$ with weight equal to $11$.
- $[3, 2, 1]$ with weight equal to $10$.

So, the expected weight is equal to $\frac{14 + 13 + 13 + 11 + 11 + 10}{3!} = 12$.