G. Divisor Settime limit per test5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given an integer x represented as a product of n its prime divisors p_1 \cdot p_2, \cdot \ldots \cdot p_n. Let S be the set of all positive integer divisors of x (including 1 and x itself).We call a set of integers D good if (and only if) there is no pair a \in D, b \in D such that a \ne b and a divides b.Find a good subset of S with maximum possible size. Since the answer can be large, print the size of the subset modulo 998244353.InputThe first line contains the single integer n (1 \le n \le 2 \cdot 10^5) — the number of prime divisors in representation of x.The second line contains n integers p_1, p_2, \dots, p_n (2 \le p_i \le 3 \cdot 10^6) — the prime factorization of x.OutputPrint the maximum possible size of a good subset modulo 998244353.ExamplesInput
3
2999999 43 2999957
Output
3
Input
6
2 3 2 3 2 2
Output
3
NoteIn the first sample, x = 2999999 \cdot 43 \cdot 2999957 and one of the maximum good subsets is \{ 43, 2999957, 2999999 \}.In the second sample, x = 2 \cdot 3 \cdot 2 \cdot 3 \cdot 2 \cdot 2 = 144 and one of the maximum good subsets is \{ 9, 12, 16 \}.
3
2999999 43 2999957

3 
['divide and conquer', 'fft', 'greedy', 'math', 'number theory', '*2600']