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.*;
import java.math.*;
 
 
//Sub_To_Errichto
public class Main {
    //static final long MOD = 1000000007L;
    //static final long MOD2 = 1000000009L;
    static final long MOD = 998244353L;
    static final int INF = 50000000;
    static final int NINF = -500000000;
    

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
        
        int N = sc.ni();
        long[] nums = new long[2*N];
        for (int i = 0; i < 2*N; i++)
        	nums[(i+N)%(2*N)] = sc.nl();
        Arrays.sort(nums);
        long s = 0;
        for (int i = 0; i < N; i++)
        	s -= nums[i];
        for (int i = N; i < 2*N; i++)
        	s += nums[i];
        s %= MOD;
        Combo comb = new Combo(2*N,MOD);
        long ans = (comb.choose(2*N,N)*s)%MOD;
        pw.println(ans);
        pw.close();
    }
    
    static class Combo {
    	//cache factorials
    	long[] facs;
    	long[] invfacs;
    	long MOD;

    	public Combo(int N, long M) {
    		MOD = M;
    		facs = new long[N+1];
    		invfacs = new long[N+1];
    		facs[0] = 1;
    		for (int i = 1; i <= N; i++) {
    			facs[i] = (facs[i-1]*i)%MOD;
    		}
    		invfacs[N] = power(facs[N],MOD-2);
    		for (int i = N-1; i >= 0; i--)
    			invfacs[i] = ((i+1)*invfacs[i+1])%MOD;
    	}

    	public long choose(int n, int k) {
    		if (n<0||k<0||n<k) return 0;
    		long denInv = (invfacs[k]*invfacs[n-k])%MOD;
    		long ans = (facs[n]*denInv)%MOD;
    		return ans;
    	}

    	public long factorial(int n) {
    		return facs[n];
    	}

    	//binary exponentation
    	public long power(long x, long y) {
    		long ans = 1;
    		x %= MOD;
    		while (y > 0) {
    			if((y&1)==1)
    				ans = (ans * x) % MOD;
    			y /= 2;
    			x = (x * x) % MOD;
    		}
    		return ans;
    	}
    }
 
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int ni() {
            return Integer.parseInt(next());
        }
 
        long nl() {
            return Long.parseLong(next());
        }
 
        double nd() {
            return Double.parseDouble(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}