B'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 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: <= ft( sum_{p in s_n} f_p(k) right) textrm{mod} 998 ,244 ,353 The first line contains one integer n (1 <= n <= 5000) . Print n integers, the i -th of them should be equal to <= ft( sum_{p in s_n} f_p(i) right) textrm{mod} 998 ,244 ,353 . 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] } . '...