write a go solution for Description:
The prime factorization of a positive integer m is the unique way to write it as displaystylem=p_1^e_1*p_2^e_2*ldots*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.

Input Format:
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.

Output Format:
Print one integer, the number of positive integers m satisfying f(m)=a_1,a_2,ldots,a_2n modulo 998,244,353.

Note:
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*3^1 and 54=2^1*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.. Output only the code with no comments, explanation, or additional text.