F. Occurrencestime limit per test7 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputA subarray of array a from index l to the index r is the array [a_l, a_{l+1}, \dots, a_{r}]. The number of occurrences of the array b in the array a is the number of subarrays of a such that they are equal to b.You are given n arrays A_1, A_2, \dots, A_n; the elements of these arrays are integers from 1 to k. You have to build an array a consisting of m integers from 1 to k in such a way that, for every given subarray A_i, the number of occurrences of A_i in the array a is not less than the number of occurrences of each non-empty subarray of A_i in a. Note that if A_i doesn't occur in a, and no subarray of A_i occurs in a, this condition is still met for A_i.Your task is to calculate the number of different arrays a you can build, and print it modulo 998244353.InputThe first line contains three integers n, m and k (1 \le n, m, k \le 3 \cdot 10^5) — the number of the given arrays, the desired length of the array a, and the upper bound on the values in the arrays.Then n lines follow. The i-th line represents the array A_i. The first integer in the i-th line is c_i (1 \le c_i \le m) — the number of elements in A_i; then, c_i integers from 1 to k follow — the elements of the array A_i.Additional constraint on the input: \sum\limits_{i=1}^n c_i \le 3 \cdot 10^5; i. e., the number of elements in the given arrays in total does not exceed 3 \cdot 10^5.OutputPrint one integer — the number of different arrays a you can build, taken modulo 998244353.ExamplesInput
2 4 3
2 1 2
1 3
Output
5
Input
2 4 3
2 1 2
3 3 2 1
Output
0
Input
1 42 1337
2 13 31
Output
721234447

2 4 3
2 1 2
1 3

5 
['combinatorics', 'dfs and similar', 'dp', 'dsu', 'fft', 'graphs', '*2700']