B'Initially, we had one array, which was a permutation of size n (an array of size n where each integer from 1 to n appears exactly once). We performed q operations. During the i -th operation, we did the following: For example, suppose the initial array was [6, 3, 4, 1, 2, 5] , and we performed the following operations: You are given two integers n and q , and two sequences [l_1, l_2, ... , l_q] and [r_1, r_2, ... , r_q] . A permutation of size n is called valid if we can perform q operations and produce the given sequences [l_1, l_2, ... , l_q] and [r_1, r_2, ... , r_q] . Calculate the number of valid permutations. The first line contains two integers n and q ( 1 <= q < n <= 3 cdot 10^5 ). The second line contains q integers l_1, l_2, ... , l_q ( 1 <= l_i <= n ). The third line contains q integers r_1, r_2, ... , r_q ( 1 <= r_i <= n ). Additional constraint on the input: there exists at least one permutation which can produce the given sequences [l_1, l_2, ... , l_q] and [r_1, r_2, ... , r_q] . Print one integer -- the number of valid permutations, taken modulo 998244353 . '...