CF2245F Familiar?

Note the unusual memory limit. Consider the following pseudocode that processes a permutation $ p $ of length $ n $ $ ^{\text{∗}} $ : ``` function mystery(p): n = length of p st = an empty stack count = an array of length n filled with 0s for i from 1 to n: while st is not empty and p[i] < top of st: pop from st count[i] = count[i] + 1 push p[i] into st return count ``` You are given an array $ a $ of length $ n $ . Your task is to count the number of permutations $ p $ of length $ n $ such that, if $ b $ is the array returned by mystery(p), the condition $ a_i = b_i $ holds for all $ i $ ( $ 1 \le i \le n $ ) where $ a_i \neq -1 $ . Since the answer can be very large, output it modulo $ 998\,244\,353 $ . $ ^{\text{∗}} $ A permutation of length $ n $ is an array consisting of $ n $ distinct integers from $ 1 $ to $ n $ in arbitrary order. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation ( $ 2 $ appears twice in the array), and $ [1,3,4] $ is also not a permutation ( $ n=3 $ but there is $ 4 $ in the array).

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 an integer $ n $ ( $ 1 \le n \le 500 $ ), representing the length of $ a $ . The second line contains $ n $ integers $ a_1,a_2,\ldots,a_n $ ( $ -1 \le a_i \le n $ ), representing the elements in $ a $ . It is guaranteed that the sum of $ n^3 $ over all test cases does not exceed $ 500^3 $ .

For each test case, output an integer representing the number of permutations, modulo $ 998\,244\,353 $ .

In the first and second test cases, the only valid permutation is $ [1] $ . In the fourth test case, the valid permutations are $ [1,2,4,3] $ , $ [3,4,2,1] $ , and $ [1,4,3,2] $ . In the fifth test case, all permutations of length $ 6 $ are valid.