G. Another Meme Problem
dp
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 \(998244353\).