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.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Problem_D {
	static final int MOD = 998244353;

	public static void shuffle(int[] A) {
		for (int i = 0; i < A.length; i++) {
			int j = (int) (i * Math.random());
			int tmp = A[i];
			A[i] = A[j];
			A[j] = tmp;
		}
	}

	public static long C(int a, int b) {
		long x = 1;
		for (int i = a; i > b; i--) {
			x = x * i % MOD;
		}
		long y = 1;
		for (int i = b; i > 1; i--) {
			y = y * i % MOD;
		}
		return x * pow(y, MOD - 2) % MOD;
	}

	public static long pow(long x, int y) {
		long ret = 1;
		while (y > 0) {
			if (y % 2 == 1) {
				ret = ret * x % MOD;
			}
			x = x * x % MOD;
			y >>= 1;
		}
		return ret;
	}

	public static void main(String[] args) {
		InputReader in = new InputReader();

		int N = in.nextInt();
		int[] A = new int[2 * N];
		for (int i = 0; i < A.length; i++) {
			A[i] = in.nextInt();
		}
		shuffle(A);
		Arrays.sort(A);
		long ans = 0;
		for (int i = 0; i < N; i++) {
			ans -= A[i];
		}
		for (int i = N; i < 2 * N; i++) {
			ans += A[i];
		}
		ans %= MOD;
		ans *= C(2 * N, N);
		ans %= MOD;

		System.out.println(ans);
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer st;

		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(nextLine());
			}
			return st.nextToken();
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}

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