A12979. 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 $\{ 9, 12, 16 \}$ .