#include <bits/stdc++.h>
const long long mod = 998244353;
int main() {
  std::ios::sync_with_stdio(false);
  std::cout.tie(0);
  int n, m, k;
  std::cin >> n >> m >> k;
  std::vector<std::vector<int> > a(n, std::vector<int>(0));
  std::set<int> ban;
  std::vector<std::vector<int> > vec;
  for (int i = 0; i < n; i++) {
    int c, x;
    std::cin >> c;
    while (c--) {
      std::cin >> x;
      x--;
      a[i].emplace_back(x);
    }
    std::map<int, int> mp;
    for (auto x : a[i]) mp[x]++;
    bool flag = true;
    for (auto p : mp)
      if (p.second >= 2) {
        ban.insert(p.first);
        flag = false;
      }
    if (not flag) {
      for (auto x : a[i]) ban.insert(x);
    }
  }
  std::vector<std::set<int> > g(k), rg(k);
  for (auto v : a) {
    for (int i = 0; i + 1 < v.size(); i++) {
      g[v[i]].insert(v[i + 1]);
      rg[v[i + 1]].insert(v[i]);
    }
  }
  std::vector<int> in(k, 0), out(k, 0);
  for (int i = 0; i < k; i++) {
    out[i] = g[i].size();
    in[i] = rg[i].size();
  }
  for (int i = 0; i < k; i++) {
    if (in[i] >= 2 || out[i] >= 2) ban.insert(i);
  }
  std::function<int(int)> dfs = [&](int x) {
    if (ban.count(x)) return -(int)1e9;
    if (out[x] == 0) return 1;
    if (out[x] == 1 && in[*g[x].begin()] == 1) {
      return 1 + dfs(*g[x].begin());
    }
    return -(int)1e9;
  };
  std::vector<int> F(k + 1, 0);
  for (int i = 0; i < k; i++)
    if (!ban.count(i)) {
      if (in[i] == 0) {
        int len = dfs(i);
        if (len > 0) F[len]++;
      }
    }
  std::vector<std::pair<int, int> > key;
  for (int i = 0; i <= k; i++)
    if (F[i] > 0) {
      key.emplace_back(i, F[i]);
    }
  std::vector<int> dp(m + 1, 0);
  dp[0] = 1;
  for (int i = 1; i <= m; i++) {
    for (auto [len, w] : key) {
      assert(len >= 1 && len <= k);
      if (len <= i) {
        dp[i] = (dp[i] + 1ll * w * dp[i - len] % mod) % mod;
      }
    }
  }
  std::cout << dp[m] << "\n";
}

### Prompt

Please formulate a Cpp solution to the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
const long long mod = 998244353;
int main() {
  std::ios::sync_with_stdio(false);
  std::cout.tie(0);
  int n, m, k;
  std::cin >> n >> m >> k;
  std::vector<std::vector<int> > a(n, std::vector<int>(0));
  std::set<int> ban;
  std::vector<std::vector<int> > vec;
  for (int i = 0; i < n; i++) {
    int c, x;
    std::cin >> c;
    while (c--) {
      std::cin >> x;
      x--;
      a[i].emplace_back(x);
    }
    std::map<int, int> mp;
    for (auto x : a[i]) mp[x]++;
    bool flag = true;
    for (auto p : mp)
      if (p.second >= 2) {
        ban.insert(p.first);
        flag = false;
      }
    if (not flag) {
      for (auto x : a[i]) ban.insert(x);
    }
  }
  std::vector<std::set<int> > g(k), rg(k);
  for (auto v : a) {
    for (int i = 0; i + 1 < v.size(); i++) {
      g[v[i]].insert(v[i + 1]);
      rg[v[i + 1]].insert(v[i]);
    }
  }
  std::vector<int> in(k, 0), out(k, 0);
  for (int i = 0; i < k; i++) {
    out[i] = g[i].size();
    in[i] = rg[i].size();
  }
  for (int i = 0; i < k; i++) {
    if (in[i] >= 2 || out[i] >= 2) ban.insert(i);
  }
  std::function<int(int)> dfs = [&](int x) {
    if (ban.count(x)) return -(int)1e9;
    if (out[x] == 0) return 1;
    if (out[x] == 1 && in[*g[x].begin()] == 1) {
      return 1 + dfs(*g[x].begin());
    }
    return -(int)1e9;
  };
  std::vector<int> F(k + 1, 0);
  for (int i = 0; i < k; i++)
    if (!ban.count(i)) {
      if (in[i] == 0) {
        int len = dfs(i);
        if (len > 0) F[len]++;
      }
    }
  std::vector<std::pair<int, int> > key;
  for (int i = 0; i <= k; i++)
    if (F[i] > 0) {
      key.emplace_back(i, F[i]);
    }
  std::vector<int> dp(m + 1, 0);
  dp[0] = 1;
  for (int i = 1; i <= m; i++) {
    for (auto [len, w] : key) {
      assert(len >= 1 && len <= k);
      if (len <= i) {
        dp[i] = (dp[i] + 1ll * w * dp[i - len] % mod) % mod;
      }
    }
  }
  std::cout << dp[m] << "\n";
}

```