Consider that Simons is given an array (a) of size (m). Simons must operate on the array exactly once as follows: First, he has to select an integer (k) and choose (k) pairs of integers (l_1,r_1,l_2,r_2,\ldots,l_k,r_k), such that: (l_i\le r_i) for each (1\le i\le k), (l_1=1), (r_k=m), and (r_i+1=l_{i+1}) for each (i) from (1) to (k-1). (l_i\le r_i) for each (1\le i\le k), (l_1=1), (r_k=m), and (r_i+1=l_{i+1}) for each (i) from (1) to (k-1). Then, he reverses each subarray (a_{l_i},a_{l_i+1},\ldots, a_{r_i}) independently. After this, the array will become (a_{r_1},a_{r_1-1},\ldots,a_{l_1},a_{r_2},\ldots,a_{l_{k-1}},a_{r_{k}},a_{r_k-1},\ldots,a_{l_k}). You are given an array (T) of size (n). Count the number of arrays (S) such that Simons can transform (S) to (T), modulo (998\,244\,353). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 8000)). The description of the test cases follows. The first line contains an integer (n) ((1\le n\le 8000)) — the length of (T). The second line contains (n) integers (T_1,T_2,\ldots,T_n) ((1\le T_i\le 8000)) — the elements of (T). It is guaranteed that the sum of (n) over all test cases does not exceed (8000). For each test case, output a single integer — the number of arrays (S), modulo (998\,244\,353). In the first test case, we can see only the following arrays can be transformed to (T): For (S=2,1,1,1), Simons will choose (1,3) and (4,4). Thus, the array will become (1,1,2,1), equal to (T). For (S=1,2,1,1), Simons will choose (1,4). For (S=1,1,2,1), Simons will choose (1,2), (3,3), and (4,4). For (S=1,1,1,2), Simons will choose (1,2) and (3,4). In the second test case, we can see only the following array