You are given an array a of length 2n. Consider a partition of array a into two subsequences p and q of length n each (each element of array a should be in exactly one subsequence: either in p or in q).

Let's sort p in non-decreasing order, and q in non-increasing order, we can denote the sorted versions by x and y, respectively. Then the cost of a partition is defined as f(p, q) = ∑_{i = 1}^n |x_i - y_i|.

Find the sum of f(p, q) over all correct partitions of array a. Since the answer might be too big, print its remainder modulo 998244353.

Input

The first line contains a single integer n (1 ≤ n ≤ 150 000).

The second line contains 2n integers a_1, a_2, …, a_{2n} (1 ≤ a_i ≤ 10^9) — elements of array a.

Output

Print one integer — the answer to the problem, modulo 998244353.

Examples

Input


1
1 4


Output


6

Input


2
2 1 2 1


Output


12

Input


3
2 2 2 2 2 2


Output


0

Input


5
13 8 35 94 9284 34 54 69 123 846


Output


2588544

Note

Two partitions of an array are considered different if the sets of indices of elements included in the subsequence p are different.

In the first example, there are two correct partitions of the array a:

  1. p = [1], q = [4], then x = [1], y = [4], f(p, q) = |1 - 4| = 3; 
  2. p = [4], q = [1], then x = [4], y = [1], f(p, q) = |4 - 1| = 3. 



In the second example, there are six valid partitions of the array a: 

  1. p = [2, 1], q = [2, 1] (elements with indices 1 and 2 in the original array are selected in the subsequence p); 
  2. p = [2, 2], q = [1, 1]; 
  3. p = [2, 1], q = [1, 2] (elements with indices 1 and 4 are selected in the subsequence p); 
  4. p = [1, 2], q = [2, 1]; 
  5. p = [1, 1], q = [2, 2]; 
  6. p = [2, 1], q = [2, 1] (elements with indices 3 and 4 are selected in the subsequence p). 
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.*;
import java.math.*;

/**
 * hecked
 */
public class Main{
    public static void main(String[] args){
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(32768, in, out);
        out.close();
    }
 
static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
    }
static class TaskD{
    long mod = 998244353;
    public long gcd(long a,long b){
        if(a == 0) return b;
        return gcd(b%a,a);
    }
    
    public long n2cn(int n){
        long val1 = 1l,val2 = 1l;
        for(int i=1;i<=n;i++){
            val1=(val1 *i)%mod;
        }
        for(int i=n+1;i<=2*n;i++){
            val2 = (val2 * i)%mod;
        }
        return (val2 % mod * fermat(val1,mod,mod) % mod) % mod;
        
    }
    
    public long fermat(long a,long p,long mod){ // a^(-1) mod(p) = a^(p-2) (mod p) 
        p-=2;
        long res = 1l;
        long temp = p;
        while(temp > 0){
            if(temp % 2 != 0) res = (res * a) % mod;
            a = (a * a) % mod;
            temp>>=1;
        }
        return res % mod;
    }
    public void solve(int testNum,InputReader in,PrintWriter out){
       
           int n = in.nextInt();
           int []arr = new int[2*n];
           int c = 0;
           for(int a : arr){
               arr[c++] = in.nextInt();
           }
           Arrays.sort(arr);
           long result = 0l;
           for(int i=0;i<n;i++){
               int val = (int)Math.abs(arr[i + n] - arr[i]);
               result = (result + (long)val)%mod;
           }
           result = (result * (n2cn(n)) % mod)%mod;
           out.println(result);
       
    }
}
}
