1913D · Array Collapse

Problem: You are given an array $[p_1, p_2, \dots, p_n]$, where all elements are distinct.

You can perform several (possibly zero) operations with it. In one operation, you can choose a contiguous subsegment of $p$ and remove all elements from that subsegment, except for the minimum element on that subsegment. For example, if $p = [3, 1, 4, 7, 5, 2, 6]$ and you choose the subsegment from the $3$-rd element to the $6$-th element, the resulting array is $[3, 1, 2, 6]$.

An array $a$ is called reachable if it can be obtained from $p$ using several (maybe zero) aforementioned operations. Calculate the number of reachable arrays, and print it modulo $998244353$.

Input Format: The first line of the input contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Each test case consists of two lines. The first line contains one integer $n$ ($1 \le n \le 3 \cdot 10^5$). The second line contains $n$ distinct integers $p_1, p_2, \dots, p_n$ ($1 \le p_i \le 10^9$).

Additional constraint on the input: the sum of $n$ over all test cases does not exceed $3 \cdot 10^5$.

Output Format: For each test case, print one integer — the number of reachable arrays, taken modulo $998244353$.