P5367 [Template] Cantor Expansion

Find the rank of a given permutation of $1\sim N$ among all permutations of $1\sim N$. Output the result modulo $998244353$.

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

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

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