5D. Remove Mountain

You are given a permutation $p_1, p_2, \ldots, p_n$ of integers from $1$ to $n$.

In one operation, you can choose an index $i$ such that $1 < i < |p|$ (where $|p|$ is the current length of the permutation), $p_i > p_{i-1}$ and $p_i > p_{i+1}$, and remove $p_i$ from the sequence. After removing $p_i$, the remaining elements are concatenated without changing their relative order.

Find the number of different subsets of numbers that can remain after applying this operation any number of times (possibly zero). Since the answer can be very large, print it modulo $998244353$.

Constraints

• $1 \le t \le 10^4$
• $2 \le n \le 2 \times 10^5$
• The sum of $n$ over all test cases does not exceed $2 \times 10^5$.