B'The prime factorization of a positive integer m is the unique way to write it as displaystyle m=p_1^{e_1} cdot p_2^{e_2} cdot ldots cdot p_k^{e_k} , where p_1, p_2, ldots, p_k are prime numbers, p_1 < p_2 < ldots < p_k and e_1, e_2, ldots, e_k are positive integers. For each positive integer m , f(m) is defined as the multiset of all numbers in its prime factorization, that is f(m)= {p_1,e_1,p_2,e_2, ldots,p_k,e_k } . For example, f(24)= {2,3,3,1 } , f(5)= {1,5 } and f(1)= { } . You are given a list consisting of 2n integers a_1, a_2, ldots, a_{2n} . Count how many positive integers m satisfy that f(m)= {a_1, a_2, ldots, a_{2n} } . Since this value may be large, print it modulo 998 ,244 ,353 . The first line contains one integer n ( 1 <= n <= 2022 ). The second line contains 2n integers a_1, a_2, ldots, a_{2n} ( 1 <= a_i <= 10^6 ) -- the given list. Print one integer, the number of positive integers m satisfying f(m)= {a_1, a_2, ldots, a_{2n} } modulo 998 ,244 ,353 . In the first sample, the two values of m such that f(m)= {1,2,3,3 } are m=24 and m=54 . Their prime factorizations are 24=2^3 cdot 3^1 and 54=2^1 cdot 3^3 . In the second sample, the five values of m such that f(m)= {2,2,3,5 } are 200, 225, 288, 500 and 972 . In the third sample, there is no value of m such that f(m)= {1,4 } . Neither 1^4 nor 4^1 are prime factorizations because 1 and 4 are not primes. '...