#include <bits/stdc++.h>
using namespace std;
const long long mod = 998244353;
const int maxi = 3e5 + 100;
int n, m, k;
set<int> alfabet;
vector<vector<int> > a;
vector<int> g[maxi];
set<int> liter[maxi];
set<int> zbior;
int odw[maxi];
set<int> zak;
map<int, int> dl;
int odwslo[maxi];
vector<pair<int, int> > eds;
set<int> wych[maxi], wcho[maxi];
map<pair<int, int>, bool> odweds;
void dfszakslow(int w);
void dfszakliter(int w) {
  if (zak.find(w) != zak.end()) {
    return;
  }
  zak.insert(w);
  for (auto xd : liter[w]) {
    if (!odwslo[xd]) {
      dfszakslow(xd);
    }
  }
}
void dfszakslow(int w) {
  if (odwslo[w]) {
    return;
  }
  odwslo[w] = 1;
  for (auto xd : a[w]) {
    dfszakliter(xd);
  }
}
bool dfs(int w) {
  zbior.insert(w);
  odw[w] = 1;
  bool ans = true;
  if (zak.find(w) != zak.end()) {
    ans = false;
  }
  for (auto xd : g[w]) {
    if (odweds[eds[xd]]) {
      continue;
    }
    odweds[eds[xd]] = true;
    int x = eds[xd].first;
    if (x == w) {
      x = eds[xd].second;
    }
    if (odw[x]) {
      ans = false;
    }
    bool dx = dfs(x);
    ans &= dx;
  }
  return ans;
}
int main() {
  scanf("%d%d%d", &n, &m, &k);
  vector<int> zleslowa;
  for (int i = 0; i < n; ++i) {
    int c;
    scanf("%d", &c);
    vector<int> v;
    set<int> sv;
    multiset<int> mv;
    for (int j = 0; j < c; ++j) {
      int x;
      scanf("%d", &x);
      alfabet.insert(x);
      v.push_back(x);
      liter[x].insert(i);
      sv.insert(x);
      mv.insert(x);
    }
    a.push_back(v);
    bool flf = false;
    for (int j = 1; j < c; ++j) {
      eds.push_back({v[j - 1], v[j]});
      g[v[j]].push_back(eds.size() - 1);
      g[v[j - 1]].push_back(eds.size() - 1);
      wcho[v[j]].insert(v[j - 1]);
      wych[v[j - 1]].insert(v[j]);
      if (wcho[v[j]].size() > 1 || wych[v[j - 1]].size() > 1) {
        flf = true;
      }
    }
    if (sv.size() != mv.size() || flf) {
      zleslowa.push_back(i);
    }
  }
  for (auto xd : zleslowa) {
    dfszakslow(xd);
  }
  for (int i = 1; i <= k; ++i) {
    if (odw[i]) {
      continue;
    }
    zbior.clear();
    bool fla = dfs(i);
    if (fla) {
      ++dl[zbior.size()];
    }
  }
  vector<long long> dp(m + 1, 0);
  dp[0] = 1;
  for (int i = 1; i <= m; ++i) {
    for (auto xd : dl) {
      if (xd.first > i) {
        break;
      }
      dp[i] += dp[i - xd.first] * xd.second;
      dp[i] %= mod;
    }
  }
  printf("%lld\n", dp[m]);
}

### 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>
using namespace std;
const long long mod = 998244353;
const int maxi = 3e5 + 100;
int n, m, k;
set<int> alfabet;
vector<vector<int> > a;
vector<int> g[maxi];
set<int> liter[maxi];
set<int> zbior;
int odw[maxi];
set<int> zak;
map<int, int> dl;
int odwslo[maxi];
vector<pair<int, int> > eds;
set<int> wych[maxi], wcho[maxi];
map<pair<int, int>, bool> odweds;
void dfszakslow(int w);
void dfszakliter(int w) {
  if (zak.find(w) != zak.end()) {
    return;
  }
  zak.insert(w);
  for (auto xd : liter[w]) {
    if (!odwslo[xd]) {
      dfszakslow(xd);
    }
  }
}
void dfszakslow(int w) {
  if (odwslo[w]) {
    return;
  }
  odwslo[w] = 1;
  for (auto xd : a[w]) {
    dfszakliter(xd);
  }
}
bool dfs(int w) {
  zbior.insert(w);
  odw[w] = 1;
  bool ans = true;
  if (zak.find(w) != zak.end()) {
    ans = false;
  }
  for (auto xd : g[w]) {
    if (odweds[eds[xd]]) {
      continue;
    }
    odweds[eds[xd]] = true;
    int x = eds[xd].first;
    if (x == w) {
      x = eds[xd].second;
    }
    if (odw[x]) {
      ans = false;
    }
    bool dx = dfs(x);
    ans &= dx;
  }
  return ans;
}
int main() {
  scanf("%d%d%d", &n, &m, &k);
  vector<int> zleslowa;
  for (int i = 0; i < n; ++i) {
    int c;
    scanf("%d", &c);
    vector<int> v;
    set<int> sv;
    multiset<int> mv;
    for (int j = 0; j < c; ++j) {
      int x;
      scanf("%d", &x);
      alfabet.insert(x);
      v.push_back(x);
      liter[x].insert(i);
      sv.insert(x);
      mv.insert(x);
    }
    a.push_back(v);
    bool flf = false;
    for (int j = 1; j < c; ++j) {
      eds.push_back({v[j - 1], v[j]});
      g[v[j]].push_back(eds.size() - 1);
      g[v[j - 1]].push_back(eds.size() - 1);
      wcho[v[j]].insert(v[j - 1]);
      wych[v[j - 1]].insert(v[j]);
      if (wcho[v[j]].size() > 1 || wych[v[j - 1]].size() > 1) {
        flf = true;
      }
    }
    if (sv.size() != mv.size() || flf) {
      zleslowa.push_back(i);
    }
  }
  for (auto xd : zleslowa) {
    dfszakslow(xd);
  }
  for (int i = 1; i <= k; ++i) {
    if (odw[i]) {
      continue;
    }
    zbior.clear();
    bool fla = dfs(i);
    if (fla) {
      ++dl[zbior.size()];
    }
  }
  vector<long long> dp(m + 1, 0);
  dp[0] = 1;
  for (int i = 1; i <= m; ++i) {
    for (auto xd : dl) {
      if (xd.first > i) {
        break;
      }
      dp[i] += dp[i - xd.first] * xd.second;
      dp[i] %= mod;
    }
  }
  printf("%lld\n", dp[m]);
}

```