Given three integers (n, m, k), as well as (k) arrays of integers of lengths (l_1, l_2, \dots, l_k) respectively. We denote the element at position (j) in array number (i) as (a_{i,j}). In each array, all elements are distinct (but may repeat in different arrays). We call an array (b) of length (k) beautiful if for each (i) from (1) to (k), the element (b_i) is equal to one of the elements of the array (a_i). We call an array (c) perfect if every beautiful array (b) can be obtained from array (c) by deleting several (possibly zero) elements without changing their order. In other words, array (c) is perfect if every beautiful array (b) is a subsequence of it. Your task is to count the number of perfect arrays (c) of length (n) containing only integers from (1) to (m). The first line contains three integers (n, m, k) ((2 \le n \le 2 \cdot 10^5); (5 \le m \le 10^8); (2 \le k \le n)). The second line contains (k) integers (l_1, l_2, \dots, l_k) ((1 \le l_i \le 5)). The following (k) lines contain the (i)-th line with (l_i) distinct integers (a_{i,1}, a_{i,2}, \dots, a_{i,l_i}) ((1 \le a_{i,j} \le m)). Additional constraint on the input: the sum of (l_i) does not exceed (n). Print one integer — the number of perfect arrays of length (n) such that they contain only integers from (1) to (m). Since the answer may be very large, output it modulo (998244353). In the first example, there are two beautiful arrays: (4, 1, 4) and (4, 1, 3). Only two arrays of length (4) contain both of these arrays as subsequences: (4, 1, 4, 3) and (4, 1, 3, 4). In the second example, there is only one beautiful array: (5, 2). There are (13) arrays of length (3) with integers from (1) to (5) that contain it as a subsequence.