P11029 "DABOI Round 1" A Simple Problem

> Red problems make people "red-hot" (hong wen).

Compute $\prod \limits_{i=1}^{n} \prod\limits_{j=1}^{i} \prod \limits_{k=1}^{j} k^k$ modulo $998244353$.

The input contains $1$ line with $1$ integer, which is $n$.

Output $1$ line with $1$ integer, which is the answer.

**Constraints** - For $20\%$ of the testdata, $n\leq5\times10^2$. - For $50\%$ of the testdata, $n\leq5\times10^3$. - For $100\%$ of the testdata, $1\leq n\leq1.8\times10^6$. Translated by ChatGPT 5