$$$n$$$ people gathered to hold a jury meeting of the upcoming competition, the $$$i$$$-th member of the jury came up with $$$a_i$$$ tasks, which they want to share with each other.
First, the jury decides on the order which they will follow while describing the tasks. Let that be a permutation $$$p$$$ of numbers from $$$1$$$ to $$$n$$$ (an array of size $$$n$$$ where each integer from $$$1$$$ to $$$n$$$ occurs exactly once).
Then the discussion goes as follows:
A permutation $$$p$$$ is nice if none of the jury members tell two or more of their own tasks in a row.
Count the number of nice permutations. The answer may be really large, so print it modulo $$$998\,244\,353$$$.
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.
The first line of the test case contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — number of jury members.
The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the number of problems that the $$$i$$$-th member of the jury came up with.
The sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, print one integer — the number of nice permutations, taken modulo $$$998\,244\,353$$$.
4 2 1 2 3 5 5 5 4 1 3 3 7 6 3 4 2 1 3 3
1 6 0 540
Explanation of the first test case from the example:
There are two possible permutations, $$$p = [1, 2]$$$ and $$$p = [2, 1]$$$. For $$$p = [1, 2]$$$, the process is the following:
So, the second jury member has told two tasks in a row (in succession), so the permutation is not nice.
For $$$p = [2, 1]$$$, the process is the following:
So, this permutation is nice.
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