Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https://codeforces.com/10years.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

G. Divisor Set

time limit per test

5 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard 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 $$$998244353$$$.

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 $$$998244353$$$.

Examples

Input

3 2999999 43 2999957

Output

3

Input

6 2 3 2 3 2 2

Output

3

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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/26/2020 13:19:33 (e2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|