Let (A_1, A_2, \ldots, A_n) be an array of (n) positive integers. Define array (f(A)) as followed: For each integer (i) from (1) to (n): If there exists integer (j) such that (j \lt i) and (A_j \lt A_i), (f(A)_i=\max\limits_{j \lt i,A_j \lt A_i} j). That is, (f(A)_i) is the index of the rightmost element before (i) whose value is strictly smaller than (A_i). Otherwise (f(A)_i=0). We call the array (P_1,P_2,\ldots,P_n) of non-negative integers a cute array if there exists an array (A) such that (f(A)=P). Given a length (n) array (X) in which (-1\le X_i\le n) holds for all (i) from (1) to (n). Count the numbers of cute arrays (X') formed by replacing the (-1)s in (X) with integers from (0) to (n). As the number can be very large, print it modulo (998\,244\,353). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^3)). The description of the test cases follows. The first line of each test cases contain an integer (n) ((1\le n\le5000)) denoting the length of (X). The second line contain (n) integers (X_1,X_2,\ldots,X_n) ((-1\le X_i\le n)). It is guaranteed that the sum of (n) over all test cases does not exceed (5000). For each test cases, output a single integer denoting the number of arrays (X') such that (X') is a cute array, modulo (998\,244\,353). For the first test case, only (0,0,0) and (0,0,2) are cute arrays among all possible (X'). (0,0,0) is a good cute array because (f(1,1,1)=0,0,0), and (0,0,2) is a good array because (f(1,1,2)=0,0,2). For the second test case, only (0,1,1,0), (0,1,1,1) and (0,1,1,3) are cute arrays among all possible (X').