Divisor Set

5000ms

524288K

Description:

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 $$$998244353$$$.

Input:

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 $$$x$$$.

Output:

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

Sample Input:

3
2999999 43 2999957

Sample Output:

Sample Input:

6
2 3 2 3 2 2

Sample Output:

Note:

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

Informação

Provedor Codeforces

Código CF1257G