B"Pak Chanek is given an array a of n integers. For each i ( 1 <= q i <= q n ), Pak Chanek will write the one-element set {a_i } on a whiteboard. After that, in one operation, Pak Chanek may do the following: After performing zero or more operations, Pak Chanek will construct a multiset M containing the sizes of all sets written on the whiteboard. In other words, each element in M corresponds to the size of a set after the operations. How many distinct ^ dagger multisets M can be created by this process? Since the answer may be large, output it modulo 998 ,244 ,353 . ^ dagger Multisets B and C are different if and only if there exists a value k such that the number of elements with value k in B is different than the number of elements with value k in C . The first line contains a single integer n ( 1 <= n <= 2000 ). The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= q a_i <= q n ). Output the number of distinct multisets M modulo 998 ,244 ,353 . In the first example, the possible multisets M are {1,1,1,1,1,1 } , {1,1,1,1,2 } , {1,1,1,3 } , {1,1,2,2 } , {1,1,4 } , {1,2,3 } , and {2,2,2 } . As an example, let's consider a possible sequence of operations. "...