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 D {

    static int modInverse(int a, int m) 
    { 
        int m0 = m; 
        int y = 0, x = 1; 
  
        if (m == 1) 
            return 0; 
  
        while (a > 1) 
        { 
            // q is quotient 
            int q = a / m; 
  
            int t = m; 
  
            // m is remainder now, process 
            // same as Euclid's algo 
            m = a % m; 
            a = t; 
            t = y; 
  
            // Update x and y 
            y = x - q * y; 
            x = t; 
        } 
  
        // Make x positive 
        if (x < 0) 
            x += m0; 
  
        return x; 
    } 

    public static void main(String args[]) throws Exception{
        BufferedReader br = new BufferedReader (new InputStreamReader(System.in));
        Scanner sc = new Scanner (System.in);
        int T = sc.nextInt();
        // int T  = Integer.parseInt(br.readLine());
        T = T*2;
        int arr[] = new int[T];

        for(int i=0; i<T; i++){
            arr[i] = sc.nextInt();
        }
        long mod= 998244353;
        long sum = 0;
        Arrays.sort(arr, 0, T);
        for(int i=0; i<T/2; i++){
            sum -= arr[i]; 
            sum = sum%mod;
        }
        for(int i=T/2; i<T; i++){
            sum += arr[i]; 
            sum = sum%mod;
        }
        long ans = 1;
        for(int i=T; i>T/2; i--){
            ans =((long)(ans%mod)*(i%mod))%mod;
        }
        for(int i=T/2; i>0; i--){
            ans =((long)(ans%mod)*modInverse(i, (int)mod))%mod;
        }
        System.out.println(((long)ans%mod*(sum%mod))%mod);
    }
}
