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.util.*;
import java.io.*;

public class Sol{

public static void main(String []args){

int t=1;

while(t-->0){
 mod=998244353;
 int n=ni();
 long s1=0l;long s2=0l;Long a[]=new Long[2*n];
 for(int i=0;i<2*n;i++){a[i]=nl();}
 Arrays.sort(a);
 for(int i=0;i<n;i++)s1+=a[i];
 for(int i=n;i<2*n;i++)s2+=a[i];
 long s=s2-s1;s%=mod;
 
 long i=1l;
 long ans=1l;
 while(i<2*n){ans*=i;ans%=mod;i++;i++;}
 
 i=1l;
 while(i<=n){ans*=2l;ans%=mod;i++;}
  
 ans*=s;ans%=mod;

 long denominator=1l;i=1l;
 while(i<=n){denominator*=i;i++;denominator%=mod;}
 //out.println(denominator+" "+n);
 denominator=power(denominator,mod-2,mod);
 ans*=denominator;ans%=mod;
 out.println(ans);

}out.close();}

static ArrayList<Pair> factors(long n){
 ArrayList<Pair> a=new ArrayList<>();
 for(int i=2;i*i<=n;i++){boolean entered=false;int t=0;while(n%i==0){n/=i;t++;entered=true;}if(entered)a.add(new Pair(i,t));}

 if(n>1){a.add(new Pair((int)n,1l));}
 return a;
}

 static long mod=1000000007;

 public static long power(long x, long y , long p)
    {
        //0^0 = 1
        long res = 1L;
        x = x%p;
        while(y > 0)
        {
            if((y&1)==1)
                res = (res*x)%p;
            y >>= 1;
            x = (x*x)%p;
        }
        return res;
    }

//implements Comparable<Pair>

static class Pair implements Comparable<Pair>{
        int id;long value;
        public Pair(int id,long value) {
         
          this.id=id;
          this.value=value;
        }
        @Override
        public int compareTo(Pair p){return Long.compare(value,p.value);}
       
   }
static InputStream inputStream = System.in;
static OutputStream outputStream = System.out;
static FastReader in=new FastReader(inputStream);
static PrintWriter out=new PrintWriter(outputStream);

static class FastReader 
{ 
  BufferedReader br; 
  StringTokenizer st; 
 
  public FastReader(InputStream in) 
  { 
      br = new BufferedReader(new
               InputStreamReader(System.in)); 
  } 
 
  public String next() 
  { 
      while (st == null || !st.hasMoreElements()) 
      { 
          try
          { 
              st = new StringTokenizer(br.readLine()); 
          } 
          catch (IOException  e) 
          { 
              e.printStackTrace(); 
          } 
      } 
      return st.nextToken(); 
  } 
 
  public int nextInt() 
  { 
      return Integer.parseInt(next()); 
  } 
 
  public long nextLong() 
  { 
      return Long.parseLong(next()); 
  } 
 
 public  double nextDouble() 
  { 
      return Double.parseDouble(next()); 
  } 
 
 
  String nextLine() 
  { 
      String str = ""; 
      try
      { 
          str = br.readLine(); 
      } 
      catch (IOException e) 
      { 
          e.printStackTrace(); 
      } 
      return str; 
  } 
}
static int ni(){return in.nextInt();}
static long nl(){return in.nextLong();}
static String ns(){return in.nextLine();}
static int[] na(int n){int a[]=new int[n];for(int i=0;i<n;i++){a[i]=ni();} return a;}

}