description: A subarray of array a from index l to the index r is the array [a_l, a_{l+1}, ..., 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, ..., 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.
  
  Input
  
  The first line contains three integers n, m and k (1 ≤ n, m, k ≤ 3 ⋅ 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 ≤ c_i ≤ 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: ∑_{i=1}^n c_i ≤ 3 ⋅ 10^5; i. e., the number of elements in the given arrays in total does not exceed 3 ⋅ 10^5.
  
  Output
  
  Print one integer — the number of different arrays a you can build, taken modulo 998244353.
  
  Examples
  
  Input
  
  
  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
solution: #include <bits/stdc++.h>
  using namespace std;
  void read(int& x) {
    static char c;
    int f = 0;
    while (!isdigit(c = getchar()))
      if (c == '-') f = 1;
    x = c ^ 48;
    while (isdigit(c = getchar())) x = (x * 10) + (c ^ 48);
    if (f) x = -x;
  }
  void read(long long& x) {
    static char c;
    int f = 0;
    while (!isdigit(c = getchar()))
      if (c == '-') f = 1;
    x = c ^ 48;
    while (isdigit(c = getchar())) x = (x * 10) + (c ^ 48);
    if (f) x = -x;
  }
  void read(unsigned int& x) {
    static char c;
    while (!isdigit(c = getchar()))
      ;
    x = c ^ 48;
    while (isdigit(c = getchar())) x = (x * 10) + (c ^ 48);
  }
  void read(unsigned long long& x) {
    static char c;
    while (!isdigit(c = getchar()))
      ;
    x = c ^ 48;
    while (isdigit(c = getchar())) x = (x * 10) + (c ^ 48);
  }
  void chkmax(int& x, int y) {
    if (y > x) x = y;
  }
  void chkmin(int& x, int y) {
    if (y < x) x = y;
  }
  void chkmax(long long& x, long long y) {
    if (y > x) x = y;
  }
  void chkmin(long long& x, long long y) {
    if (y < x) x = y;
  }
  void chkmax(unsigned int& x, unsigned int y) {
    if (y > x) x = y;
  }
  void chkmin(unsigned int& x, unsigned int y) {
    if (y < x) x = y;
  }
  void chkmax(unsigned long long& x, unsigned long long y) {
    if (y > x) x = y;
  }
  void chkmin(unsigned long long& x, unsigned long long y) {
    if (y < x) x = y;
  }
  const int Mod = 998244353;
  void Add(int& x, int y) { (x += y) >= Mod ? x -= Mod : x; }
  void Del(int& x, int y) { (x -= y) < 0 ? x += Mod : x; }
  const int N = 3e5 + 10;
  const pair<int, int> I = make_pair(0, 0);
  int n, m, k;
  int in[N], out[N];
  set<pair<int, int> > S;
  int _len[N], B[N], F[N];
  vector<int> Trans;
  int fat[N], siz[N], vis[N];
  void Init() {
    for (int i = 1; i <= k; ++i) fat[i] = i, siz[i] = 1;
  }
  int getf(int now) { return now == fat[now] ? now : fat[now] = getf(fat[now]); }
  void Merge(int u, int v) {
    u = getf(u), v = getf(v);
    if (u != v)
      fat[u] = v, siz[v] += siz[u], vis[v] |= vis[u];
    else
      vis[u] = 1;
  }
  void Work() {
    read(n), read(m), read(k), Init();
    for (int i = 1; i <= n; ++i) {
      int c, pre = 0, now;
      read(c);
      for (int p = 0; p < c; ++p) {
        read(now);
        if (p)
          if (S.find(make_pair(pre, now)) == S.end())
            Merge(pre, now), ++in[pre], ++out[now], S.insert(make_pair(pre, now));
        pre = now;
      }
    }
    for (int i = 1; i <= k; ++i)
      if (in[i] > 1 || out[i] > 1) vis[getf(i)] = 1;
    for (int i = 1; i <= k; ++i)
      if (fat[i] == i && !vis[i]) ++B[siz[i]];
    for (int i = 1; i <= m; ++i)
      if (B[i]) Trans.push_back(i);
    F[0] = 1;
    for (int i = 1; i <= m; ++i)
      for (int v : Trans)
        if (v <= i) Add(F[i], 1ll * F[i - v] * B[v] % Mod);
    printf("%d\n", F[m]);
  }
  int main() { Work(); }
  