CF1444B.Divide and Sum

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 $f(p, q) = \sum_{i = 1}^n |x_i - y_i|$.

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 $998244353$.

给你一个长度为 $2n$ 的数组 $a$。考虑将数组 $a$ 划分为两个长度均为 $n$ 的子序列 $p$ 和 $q$（数组 $a$ 中的每个元素必须且仅属于其中一个子序列：要么在 $p$ 中，要么在 $q$ 中）。

将 $p$ 按非递减顺序排序，将 $q$ 按非递增顺序排序，分别记其排序后的结果为 $x$ 和 $y$。则该划分的代价定义为

$$f(p, q) = \sum_{i = 1}^n |x_i - y_i|。$$

求所有合法划分的 $f(p, q)$ 之和。由于答案可能过大，请输出其对 $998244353$ 取模的结果。

The 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 $a$.

第一行包含一个整数 $n$（$1 \leq n \leq 150\,000$）。

第二行包含 $2n$ 个整数 $a_1, a_2, \ldots, a_{2n}$（$1 \leq a_i \leq 10^9$）—— 数组 $a$ 的元素。

Print one integer — the answer to the problem, modulo $998244353$.

输出一个整数——该问题的答案对 $998244353$ 取模的结果。

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 $p$).

如果子序列 $p$ 所包含元素的下标集合不同，则称这两个数组划分是不同的。

在第一个例子中，数组 $a$ 有两种正确的划分方式：

1. $p = [1]$, $q = [4]$，此时 $x = [1]$, $y = [4]$, $f(p, q) = |1 - 4| = 3$；
2. $p = [4]$, $q = [1]$，此时 $x = [4]$, $y = [1]$, $f(p, q) = |4 - 1| = 3$。

在第二个例子中，数组 $a$ 有六种有效的划分方式：

1. $p = [2, 1]$, $q = [2, 1]$（在原数组中下标为 $1$ 和 $2$ 的元素被选入子序列 $p$）；
2. $p = [2, 2]$, $q = [1, 1]$；
3. $p = [2, 1]$, $q = [1, 2]$（在子序列 $p$ 中选取了原数组中下标为 $1$ 和 $4$ 的元素）；
4. $p = [1, 2]$, $q = [2, 1]$；
5. $p = [1, 1]$, $q = [2, 2]$；
6. $p = [2, 1]$, $q = [2, 1]$（在子序列 $p$ 中选取了原数组中下标为 $3$ 和 $4$ 的元素）。