Problem Description

Find the rank of a given permutation of $1\sim N$ among all permutations of $1\sim N$. Output the result 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

Output one non-negative integer, the answer modulo $998244353$.

3
2 1 3

3

4
1 2 4 3

2

Hint

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

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

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

Translated by ChatGPT 5