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 $ .