You are given an integer x represented as a product of n its prime divisors p_1 ⋅ p_2, ⋅ … ⋅ 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 ∈ D, b ∈ D such that a ≠ 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 ≤ n ≤ 2 ⋅ 10^5) — the number of prime divisors in representation of x.

The second line contains n integers p_1, p_2, ..., p_n (2 ≤ p_i ≤ 3 ⋅ 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 ⋅ 43 ⋅ 2999957 and one of the maximum good subsets is \{ 43, 2999957, 2999999 \}.

In the second sample, x = 2 ⋅ 3 ⋅ 2 ⋅ 3 ⋅ 2 ⋅ 2 = 144 and one of the maximum good subsets is \{ 9, 12, 16 \}.
import java.util.*;
import java.io.*;
public class EdA {

	public static void main(String[] args) throws Exception{
		long num = 998244353;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		int n = Integer.parseInt(bf.readLine());
 		Map<Integer, Integer> map = new HashMap<Integer, Integer>();
 		StringTokenizer st = new StringTokenizer(bf.readLine());
 		for(int j = 0;j<n;j++){
 			int number = Integer.parseInt(st.nextToken());
 			if (!map.containsKey(number))
 				map.put(number,  1);
 			else
 				map.put(number, map.get(number)+1);
 		}
 		ArrayList<Integer> array = new ArrayList<Integer>();
 		for(int j : map.keySet()){
 			array.add(map.get(j));
 		}
 		Collections.sort(array);
 		
 		long ans = ((map.size() - map.size()*(map.size()-1)/2) %num+num)%num;
 		for(int j =0;j<array.size();j++){
 			ans+= (array.size()-1-j)*array.get(j);
 			ans%= num;
 		}
 		
 		
 		out.println(ans);
	 		
 		out.close();
 		
 		
 		
 	}
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is

 		
 		
 		
 		
	


