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.Random;
import java.util.StringTokenizer;

public final class D {

    private static final int MOD = 998244353;

    private static class Combinations {
        long[] factorial;
        long[] facInverse;
        long[] inverse;

        Combinations(int n) {
            final int MAX = n + 2;
            factorial = new long[MAX];
            facInverse = new long[MAX];
            inverse = new long[MAX];
            factorial[0] = factorial[1] = 1;
            facInverse[0] = facInverse[1] = 1;
            inverse[1] = 1;
            for (int i = 2; i < MAX; i++) {
                factorial[i] = factorial[i - 1] * i % MOD;
                final long inv = inverse[i] = MOD - inverse[MOD % i] * (MOD / i) % MOD;
                facInverse[i] = facInverse[i - 1] * inv % MOD;
            }
        }

        long ncr(int n, int r) {
            if (n < r) { return 0; }
            if (n < 0 || r < 0) { return 0; }
            return factorial[n] * (facInverse[r] * facInverse[n - r] % MOD) % MOD;
        }

        long modpow(long a, long n) {
            long res = 1;
            while (n > 0) {
                if (n % 2 == 1) {
                    res = res * a % MOD;
                }
                a = a * a % MOD;
                n /= 2;
            }
            return res;
        }
    }

    public static void main(String[] args) {
        final FastScanner fs = new FastScanner();
        final int n = fs.nextInt();
        final int[] arr = fs.nextIntArray(2 * n);
        final Combinations comb = new Combinations((int) 3e5);
        long leftSum = 0;
        long rightSum = 0;
        Utils.shuffleSort(arr);
        for (int i = 0; i < n; i++) {
            leftSum = (leftSum + arr[i]) % MOD;
        }
        for (int i = n; i < 2 * n; i++) {
            rightSum = (rightSum + arr[i]) % MOD;
        }
        long diff = rightSum - leftSum;
        if (diff < 0) {
            diff += MOD;
        }
        final long c = comb.ncr(2 * n, n);
        System.out.println((diff * c) % MOD);
    }

    static final class Utils {
        public static void shuffleSort(int[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffleSort(long[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffle(int[] x) {
            final Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                final int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void shuffle(long[] x) {
            final Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                final int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void swap(int[] x, int i, int j) {
            final int t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

        public static void swap(long[] x, int i, int j) {
            final long t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

        private Utils() {}
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        private String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    //noinspection CallToPrintStackTrace
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        int[] nextIntArray(int n) {
            final int[] a = new int[n];
            for (int i = 0; i < n; i++) { a[i] = nextInt(); }
            return a;
        }

        long[] nextLongArray(int n) {
            final long[] a = new long[n];
            for (int i = 0; i < n; i++) { a[i] = nextLong(); }
            return a;
        }
    }
}
