P6654 [YsOI2020] Zeroing

Ysuperman especially likes playing counting games. ~~Actually, this problem was originally planned to be called “亦旧亦久罢以龄”, but I saw that other problem names are all two characters long, so it would not be good to use such a long name.~~

In his free time, Ysuerpman chooses to kill time with a calculator. He inputs a very long decimal number $S$. How long is it? It has $n$ digits in total. For convenience, let the digit on the $i$-th position from low to high be $S_i$ (the index starts from $1$). Each time, Ysuerpman will choose a **non-zero** digit position and perform “rounding”. Specifically, suppose he performs “rounding” on the $i$-th digit: - If $S_i

A high-precision number $S$.

The number of different plans that make $S$ become $0$, modulo $998244353$.

### Sample Explanation #### Sample Explanation $1$ $\underline5\to \underline10 \to 0$ There is $1$ plan in total. #### Sample Explanation $2$ $\underline{4}5\to\underline{5}\to\underline10\to 0$ $4\underline{5}\to\underline{5}0\to \underline100 \to 0$ There are $2$ plans in total. #### Sample Explanation $3$ $\underline{5}5\to\underline{1}05\to\underline{5}\to\underline{1}0 \to 0$ $\underline{5}5\to10\underline{5}\to\underline{1}10\to \underline10 \to 0$ $\underline{5}5\to10\underline{5}\to1\underline{1}0\to \underline100 \to 0$ $5\underline{5}\to\underline{6}0\to \underline100 \to 0$ There are $4$ plans in total. ### Constraints **This problem uses bundled testdata.** | $\rm{subtask}$ | $n$ | $S_i\in$ | Score | | :------------: | :-------: | :------: | :---: | | $0$ | $\le 6$ | $[0,9]$ | $5$ | | $1$ | $\le 15$ | $[0,9]$ | $13$ | | $2$ | $\le40$ | $[0,4]$ | $5$ | | $3$ | $\le 40$ | $\{9\}$ | $12$ | | $4$ | $\le40$ | $[5,8]$ | $15$ | | $5$ | $\le 40$ | $[0,9]$ | $30$ | | $6$ | $\le 64$ | $[0,9]$ | $20$ | For $100\%$ of the data, $1\le n \le 64$, and $S$ has no leading zeros. ### Hint The time limit for this problem is $1145\ \rm{ms}$. The problem is not hard. Translated by ChatGPT 5