CF1194G.Another Meme Problem

Let's call a fraction $\frac{x}{y}$ good if there exists at least one another fraction $\frac{x'}{y'}$ such that $\frac{x}{y} = \frac{x'}{y'}$ , $1 \le x', y' \le 9$ , the digit denoting $x'$ is contained in the decimal representation of $x$ , and the digit denoting $y'$ is contained in the decimal representation of $y$ . For example, $\frac{26}{13}$ is a good fraction, because $\frac{26}{13} = \frac{2}{1}$ .

You are given an integer number $n$ . Please calculate the number of good fractions $\frac{x}{y}$ such that $1 \le x \le n$ and $1 \le y \le n$ . The answer may be really large, so print it modulo $998244353$ .

The only line of the input contains one integer $n$ ( $1 \le n < 10^{100}$ ).

Print the number of good fractions $\frac{x}{y}$ such that $1 \le x \le n$ and $1 \le y \le n$ . The answer may be really large, so print it modulo $998244353$ .