Problem Description

Determine the rank of a given permutation of $1\sim N$ among all permutations of $1\sim N$. The result should be taken modulo $998244353$.

Input Format

The first line contains a positive integer $N$.

The second line contains $N$ positive integers, representing a permutation of $1\sim N$.

Output Format

A single line containing a non-negative integer, representing the answer modulo $998244353$.

Sample Input and Output

Sample Input #1

3
2 1 3

Sample Output #1

3

Sample Input #2

4
1 2 4 3

Sample Output #2

2

Notes

For $10\%$ of the data, $1 \le N \le 10$.

For $50\%$ of the data, $1 \le N \le 5000$.

For $100\%$ of the data, $1 \le N \le 1000000$.

见题面 Input 部分

见题面 Output 部分