Codeforces Round 930 (Div. 1) |
---|
Finished |
You are given a permutation $$$p$$$ of length $$$n$$$.
Please count the number of permutations $$$q$$$ of length $$$n$$$ which satisfy the following:
Since the answer may be large, output the answer modulo $$$998\,244\,353$$$.
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.
The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$).
The second line of each test case contains $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \le p_i \le n$$$). It is guaranteed that $$$p$$$ is a permutation.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, print a single integer — the answer modulo $$$998\,244\,353$$$.
622 131 2 333 1 242 4 1 353 5 1 4 2156 13 2 8 7 11 1 3 9 15 4 5 12 10 14
1 3 2 4 18 424488915
In the first test case, $$$p = [2, 1]$$$. The only suitable $$$q$$$ is $$$[1, 2]$$$. Indeed, we need to satisfy the inequality $$$q_1 \neq p_1$$$. It only holds for $$$q = [1, 2]$$$.
In the second test case, $$$p = [1, 2, 3]$$$. So $$$q$$$ has to satisfy two inequalities: $$$q_1 \neq p_1$$$ and $$$\max(q_1, q_2) \neq \max(1, 2) = 2$$$. One can prove that this only holds for the following $$$3$$$ permutations:
Name |
---|