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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.*;

public class DivideAndSum {
	private static final FastReader fs = new FastReader();
	private static final PrintWriter out = new PrintWriter(System.out);
	private static final long mod = 998244353;

	private static void solve() {
		int n = fs.nextInt();
		long[] a = fs.readlongarray(2*n);
		cf.sortLongArray(a);
		long smallSum = 0,bigSum = 0;
		for(int i = 0; i<n; i++)
			smallSum += a[i];
		for(int i = n; i<2*n; i++)
			bigSum += a[i];
		long ans = cf.sub(bigSum, smallSum, mod);
		long nFactorial = 1,twoNFactorial = 1;
		for(int i = 2; i<=2*n; i++) {
			if(i <= n)
				nFactorial = cf.mul(nFactorial, i*1l, mod);
			twoNFactorial = cf.mul(twoNFactorial, i*1l, mod);
		}
		long inverse = cf.power(nFactorial, mod-2, mod);
		long partition = cf.mul(twoNFactorial, cf.mul(inverse, inverse, mod), mod);
		ans = cf.mul(ans, partition, mod);
		out.println(ans);
	}

	public static void main(String[] args) {
		Thread t = new Thread(null, null, "", 1 << 28) {
			public void run() {
				int test_case = 1;
				//test_case = fs.nextInt();
				for (int cs = 1; cs <= test_case; cs++) {
					solve();
				}
				out.close();
			}
		};
		t.start();
		try {
			t.join();
		} catch (InterruptedException e) {
			e.printStackTrace();
		}
	}

	private static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			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 nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		int[] readintarray(int n) {
			int res[] = new int[n];
			for (int i = 0; i < n; i++)
				res[i] = nextInt();
			return res;
		}

		long[] readlongarray(int n) {
			long res[] = new long[n];
			for (int i = 0; i < n; i++)
				res[i] = nextLong();
			return res;
		}
	}

	private static class cf {
		public static long power(long base, long exponent) {
			long res = 1;
			while (exponent > 0) {
				if (exponent % 2 == 1)
					res *= base;
				exponent >>= 1;
				base *= base;
			}
			return res;
		}

		public static long mul(long a, long b, long mod) {
			return (a % mod * b % mod) % mod;
		}

		public static long add(long a, long b, long mod) {
			return (a % mod + b % mod) % mod;
		}

		public static long sub(long a, long b, long mod) {
			return ((a % mod - b % mod) % mod + mod) % mod;
		}

		public static long power(long base, long exponent, long mod) {
			long res = 1;
			base %= mod;
			while (exponent > 0) {
				if (exponent % 2 == 1)
					res = mul(res, base, mod);
				exponent >>= 1;
				base = mul(base, base, mod);
			}
			return res;
		}

		public static void sortIntArray(int[] a) {
			ArrayList<Integer> tmp = new ArrayList<>();
			for (int x : a)
				tmp.add(x);
			Collections.sort(tmp);
			for (int i = 0; i < tmp.size(); i++)
				a[i] = tmp.get(i);
		}

		public static void sortLongArray(long[] a) {
			ArrayList<Long> tmp = new ArrayList<>();
			for (long x : a)
				tmp.add(x);
			Collections.sort(tmp);
			for (int i = 0; i < tmp.size(); i++)
				a[i] = tmp.get(i);
		}

		public static <T extends Comparable<T>> void sort(T[] a) {
			ArrayList<T> tmp = new ArrayList<>();
			for (T x : a)
				tmp.add(x);
			Collections.sort(tmp);
			for (int i = 0; i < tmp.size(); i++)
				a[i] = tmp.get(i);
		}

		public static class pair<T1 extends Comparable<T1>, T2 extends Comparable<T2>>
				implements Comparable<pair<T1, T2>> {
			T1 ff;
			T2 ss;

			public pair(T1 ff, T2 ss) {
				this.ff = ff;
				this.ss = ss;
			}

			public int compareTo(pair<T1, T2> o) {
				if (ff == o.ff)
					return ss.compareTo(o.ss);
				return ff.compareTo(o.ff);
			}
		}
	}
}