B. Divide and Sumtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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) = \sum_{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.InputThe first line contains a single integer n (1 \leq n \leq 150\,000).The second line contains 2n integers a_1, a_2, \ldots, a_{2n} (1 \leq a_i \leq 10^9) — elements of array a.OutputPrint one integer — the answer to the problem, modulo 998244353.ExamplesInput
1
1 4
Output
6Input
2
2 1 2 1
Output
12Input
3
2 2 2 2 2 2
Output
0Input
5
13 8 35 94 9284 34 54 69 123 846
Output
2588544NoteTwo 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:  p = [1], q = [4], then x = [1], y = [4], f(p, q) = |1 - 4| = 3;  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:   p = [2, 1], q = [2, 1] (elements with indices 1 and 2 in the original array are selected in the subsequence p);  p = [2, 2], q = [1, 1];  p = [2, 1], q = [1, 2] (elements with indices 1 and 4 are selected in the subsequence p);  p = [1, 2], q = [2, 1];  p = [1, 1], q = [2, 2];  p = [2, 1], q = [2, 1] (elements with indices 3 and 4 are selected in the subsequence p). 
1
1 4

6
['combinatorics', 'math', 'sortings', '*1900']