Another Meme Problem
Description
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 $998244353$.
Input
The only line of the input contains one integer $n$ ($1 \le n < 10^{100}$).
Output
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 $998244353$.
Samples
42
150
3141592653589793238462643383279
459925407