You are given two integer arrays (a) and (b) both of length (n). You can choose any subset of indices and swap the elements at those positions (i. e. make a swap((a_i), (b_i)) for each (i) in the subset). A subset of indices is considered good if, after the swapping, both arrays are sorted in non-descending order. Your task is to calculate the number of good subsets. Since the answer can be large, print it modulo (998244353). The first line contains a single integer (t) ((1 \le t \le 500)) — the number of test cases. The first line of each test case contains a single integer (n) ((1 \le n \le 100)). The second line contains (n) integers (a_1, a_2, \dots, a_n) ((1 \le a_i \le 1000)). The third line contains (n) integers (b_1, b_2, \dots, b_n) ((1 \le b_i \le 1000)). Additional constraint on the input: there is at least one good subset. For each test case, print a single integer — the number of good subsets, taken modulo (998244353). In the first example, there are (2) good subsets: {1, 3} and {2} . In the second example, there are (2) good subsets: {1} and {} . In the third example, there are (8) good subsets: {1, 2, 3, 4, 5} , {1, 2, 3} , {1, 2, 4, 5} , {1, 2} , {3, 4, 5} , {3} , {4, 5} and {} .