CF1349F1 Slime and Sequences (Easy Version)

Note that the only differences between easy and hard versions are the constraints on $ n $ and the time limit. You can make hacks only if all versions are solved. Slime is interested in sequences. He defined good positive integer sequences $ p $ of length $ n $ as follows: - For each $ k>1 $ that presents in $ p $ , there should be at least one pair of indices $ i,j $ , such that $ 1 \leq i < j \leq n $ , $ p_i = k - 1 $ and $ p_j = k $ . For the given integer $ n $ , the set of all good sequences of length $ n $ is $ s_n $ . For the fixed integer $ k $ and the sequence $ p $ , let $ f_p(k) $ be the number of times that $ k $ appears in $ p $ . For each $ k $ from $ 1 $ to $ n $ , Slime wants to know the following value: $ $$$\left(\sum_{p\in s_n} f_p(k)\right)\ \textrm{mod}\ 998\,244\,353 $ $$$

N/A

N/A

In the first example, $ s=\{[1,1],[1,2]\} $ . In the second example, $ s=\{[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,1,2],[1,2,3]\} $ . In the third example, $ s=\{[1]\} $ .