AT_abc465_e [ABC465E] Digit Circus

Find, modulo $ 998244353 $ , the number of integers $ x $ with $ 1 \leq x \leq N $ that satisfy **exactly one** of the following three conditions. - $ x $ is a multiple of $ 3 $ . - The decimal representation of $ x $ contains `3`. - Exactly three different digits are used in the decimal representation of $ x $ . Here, the decimal representation of an integer should not have unnecessary leading `0`s.

The input is given from Standard Input in the following format: > $ N $

Output the answer.

### Sample Explanation 1 Among the integers from $ 1 $ to $ 45 $ , there are $ 19 $ integers satisfying exactly one of the conditions in the problem statement, as follows. - There are $ 10 $ integers satisfying only the first condition: $ 6, 9, 12, 15, 18, 21, 24, 27, 42, 45 $ . - There are $ 9 $ integers satisfying only the second condition: $ 13, 23, 31, 32, 34, 35, 37, 38, 43 $ . - There are no integers satisfying only the third condition. ### Sample Explanation 2 Below are examples of applicable integers. - Integers satisfying only the first condition include $ 555 $ and $ 1011 $ . - Integers satisfying only the second condition include $ 343 $ and $ 553 $ . - Integers satisfying only the third condition include $ 1012 $ and $ 704 $ . ### Sample Explanation 3 There are no applicable integers. ### Constraints - $ N $ is an integer. - $ 1 \leq N < 10^{500} $