Distinct Neighbours

You are given three positive integers $N, x$, and $y$. Count the number of arrays $P$ of length $N$ such that: - $P_1 = P_N = 1$ - There are exactly $x$ indices $i$ such that $P_i=1$ - There are exactly $y$ indices $i$ such that $P_i=2$ - There are exactly $N-x-y$ indices $i$ such that $P_i=3$ - $P_i \neq P_{i+1}$ for each $1 \leq i \lt N$ Since the answer can be large, output it modulo $998244