CF1257G Divisor Set

You 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 $ .

The 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 $ .

Print the maximum possible size of a good subset modulo $ 998244353 $ .

In 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 \} $ .