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). 
//Created by:Coding_lover(11/8/2020, 3:18:38 PM)
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;
import java.util.Arrays;

public class D680 {

	static long mod=998244353;
	static boolean LOCAL = System.getProperty("ONLINE_JUDGE")==null;
	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		//int T=fs.nextInt();
		int T=1;
		for (int tt=0; tt<T; tt++) {
			int n=fs.nextInt();
			int[] arr=new int[2*n];
			for(int i=0;i<2*n;i++){
				arr[i]=fs.nextInt();
			}
			sort(arr);
			int[] p1=new int[n]; //non decreasing
			int[] p2=new int[n]; //non increasing
			for(int i=0;i<n;i++){
				p1[i]=arr[i];
			}
			int j=0;
			for(int i=2*n-1;i>=n;i--){
				p2[j]=arr[i];
				j++;
			}
			long ans=0;
			for(int i=0;i<n;i++){
				ans=(ans+Math.abs(p2[i]-p1[i])%mod)%mod;
			}
			long mul=nCr(2*n,n);
			dbg(mul);
			ans=((ans%mod)*(mul%mod))%mod;
			System.out.println(ans);
		}
	}
	static void dbg(Object... o){if(LOCAL)System.err.println(Arrays.deepToString(o));}
	static long fact(int a){
		long tmp=1;
		for(int i=a;i>0;i--){
			tmp=(tmp*i)%mod;
		}
		return tmp;
	}
 	static long nCr(int n,int r){
		long num1=fact(n);
		long dnum1=fact(r);
		long dnum2=fact(n-r);
		long inv_dnum1=ModInv.modInverse(dnum1,mod);
		long inv_dnum2=ModInv.modInverse(dnum2,mod);
		long res=1;
		res=(res*num1)%mod;
		res=(res%mod*inv_dnum1%mod)%mod;
		res=(res*inv_dnum2)%mod;
		return res;
	}
	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	static class ModInv{
		static long modInverse(long a, long m)
    	{
	        long m0 = m;
	        long y = 0, x = 1;

	        if (m == 1)
	            return 0;

	        while (a > 1) {
	            // q is quotient
	            long q = a / m;

	            long 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;
	    }
	}

	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}


}
