CF1266G.Permutation Concatenation

普及/提高-

通过率：0%

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题目描述

Let $n$ be an integer. Consider all permutations on integers $1$ to $n$ in lexicographic order, and concatenate them into one big sequence $P$ . For example, if $n = 3$ , then $P = [1, 2, 3, 1, 3, 2, 2, 1, 3, 2, 3, 1, 3, 1, 2, 3, 2, 1]$ . The length of this sequence is $n \cdot n!$ .

Let $1 \leq i \leq j \leq n \cdot n!$ be a pair of indices. We call the sequence $(P_i, P_{i+1}, \dots, P_{j-1}, P_j)$ a subarray of $P$ .

You are given $n$ . Find the number of distinct subarrays of $P$ . Since this number may be large, output it modulo $998244353$ (a prime number).

输入格式

The only line contains one integer $n$ ( $1 \leq n \leq 10^6$ ), as described in the problem statement.

输出格式

Output a single integer — the number of distinct subarrays, modulo $998244353$ .

输入输出样例

输入#1
```
2
```
输出#1
```
8
```
输入#2
```
10
```
输出#2
```
19210869
```

说明/提示

In the first example, the sequence $P = [1, 2, 2, 1]$ . It has eight distinct subarrays: $[1]$ , $[2]$ , $[1, 2]$ , $[2, 1]$ , $[2, 2]$ , $[1, 2, 2]$ , $[2, 2, 1]$ and $[1, 2, 2, 1]$ .

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