We call two permutations $$$p_1, p_2, \dots, p_n$$$ and $$$q_1, q_2, \dots, q_n$$$ equivalent if and only if for every pair $$$(i, j)$$$ ($$$1\leq i \leq j \leq n$$$), the indices of the minimum element of $$$p_i, p_{i+1}, \dots, p_j$$$ and $$$q_i, q_{i+1}, \dots, q_j$$$ are the same.

Given $$$x$$$ and $$$y$$$, consider the set of all permutations $$$p$$$ of $$$\{1, 2, \ldots, n\}$$$ such that $$$p_x = y$$$. Find the maximum number of permutations you can pick from this set such that no two are equivalent. Output this number modulo $$$998244353$$$.

The problem is too easy, so output the answer for every $$$y = 1, 2, \dots, n$$$.