No submission language available for this problem.

Description

Input

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 $a$.

Output

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

Samples

1
1 4

6

2
2 1 2 1

12

3
2 2 2 2 2 2

0

5
13 8 35 94 9284 34 54 69 123 846

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 $p$).