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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

/**
 * Accomplished using the EduTools plugin by JetBrains https://plugins.jetbrains.com/plugin/10081-edutools
 */

public class Main {
   public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      Integer[] ar = new Integer[n+n];
      for (int i = 0; i < n + n; i++) {
         ar[i] = sc.nextInt();
      }
      Arrays.sort(ar);
      long sum = 0;
      for (int i = 0; i < n; i++) {
         sum += ar[n+n-i-1] - ar[i];
      }
//System.out.println(sum);
      int p =  998244353;
      long ncr = Modular.nCrModPFermat(n+n, n, p);
      System.out.println(((sum % p) * (ncr))%p);
   }
}
class Modular {
   public static long power(long x, long y, long p) {
      long res = 1;
      x = x % p;
      while (y>0) {
         if ((y&1)==1) {
            res = (res*x) % p;
         }
         y = y >> 1;
         x = ( x * x ) % p;
      }
      return res;
   }
   public static long monInverse( long n, long p) {
      return power(n, p-2, p);
   }
   public static long nCrModPFermat( int n, int r, int p) {
      long[] fac = new long[n+1];
      fac[0] = 1;
      for (int i = 0; i < n; i++) {
         fac[i+1] = (fac[i]*(i+1))%p;
      }
long x = monInverse(fac[r], p);
long y = monInverse(fac[n-r], p);
//System.out.println(fac[n]);
      return (((fac[n]*x)% p) * ( y%p) ) % p;
   }
}