permutation 2

You are given three positive integers $N, x, y$.
Please calculate how many permutations of $1 \sim N$ satisfies the following conditions (We denote the $i$-th number of a permutation by $p_i$):

1. $p_1 = x$

2. $p_N = y$

3. for all $1 \le i <N$, $|p_i - p_{i+1}| \le 2$

The first line contains one integer $T$ denoting the number of tests.

For each test, there is one line containing three integers $N, x, y$.

* $1 \le T \le 5000$

* $2 \le N \le 10^5$

* $1 \le x < y \le N$

For each test, output one integer in a single line indicating the answer modulo $998244353$.

3
4 1 4
4 2 4
100000 514 51144

2
1
253604680

2019 Multi-University Training Contest 5