B'Koxia and Mahiru are playing a game with three arrays a , b , and c of length n . Each element of a , b and c is an integer between 1 and n inclusive. The game consists of n rounds. In the i -th round, they perform the following moves: Let d_i be the integer Mahiru chose in the i -th round. If d is a permutation ^ dagger , Koxia wins. Otherwise, Mahiru wins. Currently, only the arrays a and b have been chosen. As an avid supporter of Koxia, you want to choose an array c such that Koxia will win. Count the number of such c , modulo 998 ,244 ,353 . Note that Koxia and Mahiru both play optimally. ^ dagger 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 consists of multiple test cases. The first line contains a single integer t ( 1 <= q t <= q 2 cdot 10^4 ) -- the number of test cases. The description of test cases follows. The first line of each test case contains a single integer n ( 1 <= q n <= q {10}^5 ) -- the size of the arrays. The second line of each test case contains n integers a_1, a_2, ... , a_n ( 1 <= q a_i <= q n ). The third line of each test case contains n integers b_1, b_2, ... , b_n ( 1 <= q b_i <= q n ). It is guaranteed that the sum of n over all test cases does not exceed {10}^5 . Output a single integer -- the number of c makes Koxia win, modulo 998 ,244 ,353 . In the first test case, there are 6 possible arrays c that make Koxia win -- [1, 2, 3] , [1, 3, 2] , [2, 2, 3] , [2, 3, 2] , [3, 2, 3] , [3, 3, 2'...