Shohag has an array $$$a$$$ of integers. Initially $$$a = [0, 1]$$$. He can repeatedly perform the following operation any number of times:

- Let $$$k$$$ be the number of inversions$$$^{\text{∗}}$$$ in the current array $$$a$$$.
- Insert $$$k$$$ at any position in $$$a$$$, including the beginning or the end.

For example, if $$$a = [4, 6, 2, 4]$$$, then the number of inversions is $$$k = 3$$$. So Shohag can obtain the following arrays after the operation: $$$[\textbf{3}, 4, 6, 2, 4]$$$, $$$[4, \textbf{3}, 6, 2, 4]$$$, $$$[4, 6, \textbf{3}, 2, 4]$$$, $$$[4, 6, 2, \textbf{3}, 4]$$$, and $$$[4, 6, 2, 4, \textbf{3}]$$$.

Given an integer $$$n$$$, help Shohag count, modulo $$$998\,244\,353$$$, the number of distinct arrays of length $$$n$$$ that can be obtained after performing the operations.

Input format:
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first and only line of each test case contains an integer $$$n$$$ ($$$2 \le n \le 10^6$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$.
Output format:
For each test case, output an integer — the number of possible arrays modulo $$$998\,244\,353$$$.
Example Input 0:
4
4
2
7
69

Example Output 0:
5
1
682
325188814

Notes:
In the first test case, the following $$$5$$$ arrays can be obtained (the inserted inversion count is shown in bold):

- $$$[0, 1] \rightarrow [0, \textbf{0}, 1] \rightarrow [0, 0, 1, \textbf{0}]$$$,
- $$$[0, 1] \rightarrow [0, \textbf{0}, 1] \rightarrow [0, 0, \textbf{0}, 1]$$$,
- $$$[0, 1] \rightarrow [0, 1, \textbf{0}] \rightarrow [0, 1, 0, \textbf{1}]$$$,
- $$$[0, 1] \rightarrow [0, 1, \textbf{0}] \rightarrow [0, 1, \textbf{1}, 0]$$$,
- $$$[0, 1] \rightarrow [0, 1, \textbf{0}] \rightarrow [\textbf{1}, 0, 1, 0]$$$.

Example input:
4
4
2
7
69


Example output:
5
1
682
325188814