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.BufferedReader;
// import java.io.InputStreamReader;
// import java.io.PrintStream;
import java.io.IOException;
import java.util.Scanner;
import java.lang.Math;
// import java.util.ArrayList;
import java.util.Arrays;
import java.util.ArrayList;

public class Main {
    
    static Scanner io = new Scanner(System.in);
    static long mod = 998244353;
    
    static long factor(long n) {
        long p = 1;
        for (long i = 2; i <= n; i++)
            p = (p * i) % mod;
        
        return p;
    }
    
    static long binpow(long a, long b) {
        if (b <= 0)
            return 1;
        if (b == 1)
            return a;
        
        if (b % 2 == 1) {
            return (binpow(a, b - 1) * a) % mod;
        } else {
            long q = (binpow(a, b / 2));
            return (q * q) % mod;
        }
    }
    
    static long binom(long n) {
        if (n <= 0)
            return 1;
        
        long up = factor(2 * n);
        long down = factor(n);
        down = (down * down) % mod;
        
        return (up * (binpow(down, mod - 2))) % mod;
    }
    
    public static void main(String[] args) throws IOException {
        int n = io.nextInt();
        long[] a = new long[2 * n];
        
        for (int i = 0; i < 2 * n; i++)
            a[i] = io.nextLong();
            
        Arrays.sort(a);
        long sum = 0;
        for (int i = 0; i < n; i++) {
            sum = (sum + Math.abs(a[i] - a[i + n])) % mod;
        }
        
        long ans = (binom(n) * sum) % mod;
        System.out.println(ans);
    }
}
















