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
#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 = 6e5 + 10;
const pair<int, int> I = make_pair(0, 0);
int n, m, k;
vector<int> A[N];
int tot;
int Buc[N];
pair<int, int> Pos[N];
bool _check(int id, int pos) {
  if (Pos[A[id][pos]] == I) return true;
  int _id = Pos[A[id][pos]].first, _pos = Pos[A[id][pos]].second;
  if (_pos && pos && A[_id][_pos - 1] != A[id][pos - 1]) return false;
  if (_pos != A[_id].size() - 1 && pos != A[id].size() - 1 &&
      A[_id][_pos + 1] != A[id][pos + 1])
    return false;
  return true;
}
int _len[N], B[N], F[N];
vector<int> Trans;
void Work() {
  read(n), read(m), read(k);
  A[n + 1].resize(3), A[n + 1][0] = A[n + 1][1] = A[n + 1][2] = k + 1;
  for (int i = 1; i <= n; ++i) {
    int c, flag = 1;
    read(c), A[i].clear();
    for (int p = 1; p <= c; ++p) {
      int v;
      read(v), A[i].push_back(v);
      if (Buc[v]) flag = 0;
      ++Buc[v];
    }
    for (int v : A[i]) --Buc[v];
    if (!flag) {
      for (int v : A[i]) Pos[v] = make_pair(n + 1, 1);
      continue;
    }
    set<int> comb;
    for (int v : A[i]) {
      if (Pos[v] == I) continue;
      int _id = Pos[v].first, _pos = Pos[v].second;
      comb.insert(_id);
      if (comb.size() > 2) break;
    }
    if (comb.size() > 2) {
      for (int v : A[i]) Pos[v] = make_pair(n + 1, 1);
      continue;
    }
    for (int p = 0; p < c; ++p) {
      flag &= _check(i, p);
      if (!flag) break;
    }
    if (!flag) {
      for (int v : A[i]) Pos[v] = make_pair(n + 1, 1);
      continue;
    }
    if (comb.size() == 0)
      for (int p = 0; p < c; ++p) Pos[A[i][p]] = make_pair(i, p);
    if (comb.size() == 1) {
      int _id = Pos[*A[i].begin()].first | Pos[*(--A[i].end())].first;
      if (Pos[*A[i].begin()] == I) {
        for (int p = 0; p < c; ++p) Pos[A[i][p]] = make_pair(i, p);
        for (int v : A[_id])
          if (Pos[v].first == _id)
            A[i].push_back(v), Pos[v] = make_pair(i, A[i].size() - 1);
        A[_id].clear();
      } else {
        for (int v : A[i])
          if (Pos[v] == I)
            A[_id].push_back(v), Pos[v] = make_pair(_id, A[_id].size() - 1);
        A[i].clear();
      }
    }
    if (comb.size() == 2) {
      int L = Pos[*A[i].begin()].first, R = Pos[*(--A[i].end())].first;
      for (int v : A[i])
        if (Pos[v].first != L)
          A[L].push_back(v), Pos[v] = make_pair(L, A[L].size() - 1);
      for (int v : A[R])
        A[L].push_back(v), Pos[v] = make_pair(L, A[L].size() - 1);
      A[i].clear(), A[R].clear();
    }
  }
  for (int i = 1; i <= k; ++i) _len[Pos[i].first]++;
  for (int i = 1; i <= n; ++i)
    if (_len[i] > 0 && _len[i] <= m) ++B[_len[i]];
  for (int i = 1; i <= k; ++i)
    if (!Pos[i].first) ++B[1];
  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(); }
