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 $1 \le i <N$, $|p_i - p_{i+1}| \le 2$
输入解释
The first line contains one integer $T$ denoting the number of tests.
For each test, there is one line containing three integers $N, x, y$.
* $1 \le T \le 5000$
* $2 \le N \le 10^5$
* $1 \le x < y \le N$
输出解释
For each test, output one integer in a single line indicating the answer modulo $998244353$.