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.*; import java.util.*;
public class CF1444B{
  static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        
    } 
    
    static int MOD=998244353;
    static int[] rk, p,siz;
    public static void main(String[] args){
        FastReader br=new FastReader();
        int N=br.nextInt(); 
        long[] fac=new long[2*N+1]; fac[0]=1;
        for (int i = 1; i <= 2*N; i++) {
            fac[i]=(fac[i-1]*i)%MOD;
        }
        int[] a=new int[2*N];
        for (int i = 0; i < 2*N; i++) {
            a[i]=br.nextInt();
        }
        Arrays.sort(a);
        long sum=0;
        for (int i = N; i < 2*N; i++) {
            sum+=a[i];
        }
        for (int i = 0; i < N; i++) {
            sum-=a[i];
        }
        sum%=MOD;
        sum*=fac[2*N]; sum%=MOD;
        sum*=inv(fac[N],MOD); sum%=MOD;
        sum*=inv(fac[N],MOD); sum%=MOD;
        System.out.println(sum);
    }
    public static long inv(long a, long b){//Computes modular inverse of a mod b
        //Assume b>a and gcd(a,b)=1, 
        if(a==1)return 1;
        long q=b/a;
        long r=b-q*a;
        long y=-inv(r,a);
        return ((b*y+1)/a)+b;
        
    }
    
    
}
//Debugging:
//Are you sure your algorithm is correct?
//Bounds: long
//Special cases: n=0,1?
//Make sure you remove your debugging code before you submit!