You are given an integer (n) and an array (a) of length (n-1). For a permutation(^{\text{∗}}) (p) of length (n), define () v_i=\min\left(\max_{1\le j\le i}p_j, \max_{i+1\le j\le n}p_j\right), () where (1\le i\le n-1). In other words, cut the permutation between positions (i) and (i+1), take the maximum element on each side, and let (v_i) be the smaller of these two values. Your task is to count the number of permutations (p) of length (n) such that (v_i=a_i) for each (1\le i\le n-1). Output the answer 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 one integer (n) ((2\le n\le 10^6)) — the length of (p). The second line contains (n-1) integers (a_1,a_2,\ldots,a_{n-1}) ((1\le a_i\le n)) — the elements of (a). It is guaranteed that the sum of (n) over all test cases does not exceed (10^6). For each test case, output one integer — the number of suitable permutations, modulo (998\,244\,353). In the first test case, both permutations (1,2) and (2,1) satisfy (v_1=1). In the second test case, the only suitable permutations are (2,1,3) and (3,1,2). In the third test case, no suitable permutation exists.