P5370 [PKUSC2018] Zhu Dou Di

If you have taken part in NOIP 2015 and PKUWC 2018, you must have a deep impression of a problem called Dou Dizhu. To pay tribute to the classic, we made another card-related problem. In this problem, the hand types are **similar to but not exactly the same as** Dou Dizhu. We call the poker game in this problem Zhu Dou Di. Zhu Dou Di is a poker game played with a total of 54 cards: A to K of spades, hearts, clubs, and diamonds, plus the small joker and the big joker, one each. All other ranks have four copies. In Dou Dizhu, the order of ranks is as follows: $3

For each test case, input one line: a string of length $17$ representing the “×× netizen”’s hand. We use 456789TJQKA2wW to represent each rank of card.

For each test case, output an integer representing the answer: the number of Jiutiao Kelian’s hands that satisfy the condition. The answer may be very large, so output it modulo $998244353$. **Note**: in this problem we ignore suits. If two hands have exactly the same multiset of ranks but different suits, they are still considered the same.

For various reasons, this problem uses bundled testdata. There are $3$ subtasks in total: | Subtask ID | Score | Constraint | | :---: | :--: | :------------: | | 1 | $30$ | Each rank appears at most $2$ times | | 2 | $30$ | Each rank appears at most $3$ times | | 3 | $40$ | Each rank appears at most $4$ times | Time limit: 2s. Memory limit: 512M. Translated by ChatGPT 5