#include <bits/stdc++.h>
using namespace std;
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U &x) {
    value = normalize(x);
  }
  template <typename U>
  static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
  const Type &operator()() const { return value; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }
  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }
  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }
  template <typename U>
  Modular &operator+=(const U &other) {
    return *this += Modular(other);
  }
  template <typename U>
  Modular &operator-=(const U &other) {
    return *this -= Modular(other);
  }
  Modular &operator++() { return *this += 1; }
  Modular &operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, long long>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    long long q = static_cast<long long>(static_cast<long double>(value) *
                                         rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
  Modular &operator/=(const Modular &other) {
    return *this *= Modular(inverse(other.value, mod()));
  }
  friend const Type &abs(const Modular &x) { return x.value; }
  template <typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);
  template <typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);
  template <typename V, typename U>
  friend V &operator>>(V &stream, Modular<U> &number);

 private:
  Type value;
};
template <typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) == rhs;
}
template <typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value < rhs.value;
}
template <typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T>
bool IsZero(const Modular<T> &number) {
  return number() == 0;
}
template <typename T>
string to_string(const Modular<T> &number) {
  return to_string(number());
}
template <typename U, typename T>
U &operator<<(U &stream, const Modular<T> &number) {
  return stream << number();
}
template <typename U, typename T>
U &operator>>(U &stream, Modular<T> &number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
constexpr int md = (int)998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
const int N = 3e5 + 5;
int An, L, alpha;
set<int> e[N];
int indegree[N];
bool vis[N];
bool flag;
int visited;
void dfs(int at) {
  vis[at] = true;
  visited++;
  if (e[at].size() > 1) flag = false;
  for (int to : e[at]) {
    if (vis[to]) {
      flag = false;
      continue;
    }
    if (indegree[to] != 1) {
      flag = false;
    }
    dfs(to);
  }
}
int lengths[N];
vector<pair<int, int>> recs;
Mint dp[N];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> An >> L >> alpha;
  for (int i = 1; i <= An; i++) {
    int c;
    cin >> c;
    vector<int> A(c);
    for (int &a : A) cin >> a;
    for (int j = 0; j < c - 1; j++) {
      int from = A[j];
      int to = A[j + 1];
      if (e[from].find(to) == e[from].end()) {
        e[from].insert(to);
        indegree[to]++;
      }
    }
  }
  for (int i = 1; i <= alpha; i++) {
    if (indegree[i] == 0) {
      assert(vis[i] == false);
      flag = true;
      visited = 0;
      dfs(i);
      if (flag) {
        lengths[visited]++;
      }
    }
  }
  for (int len = 1; len <= alpha; len++) {
    if (lengths[len]) {
      recs.push_back({len, lengths[len]});
    }
  }
  dp[0] = 1;
  for (int i = 1; i <= L; i++) {
    dp[i] = 0;
    for (auto [back, times] : recs) {
      if (i - back >= 0) {
        dp[i] += dp[i - back] * times;
      }
    }
  }
  cout << dp[L] << "\n";
  return 0;
}

### Prompt

Your challenge is to write 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;
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}
template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;
  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U &x) {
    value = normalize(x);
  }
  template <typename U>
  static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }
  const Type &operator()() const { return value; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }
  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod()) value -= mod();
    return *this;
  }
  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0) value += mod();
    return *this;
  }
  template <typename U>
  Modular &operator+=(const U &other) {
    return *this += Modular(other);
  }
  template <typename U>
  Modular &operator-=(const U &other) {
    return *this -= Modular(other);
  }
  Modular &operator++() { return *this += 1; }
  Modular &operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, long long>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    long long q = static_cast<long long>(static_cast<long double>(value) *
                                         rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }
  Modular &operator/=(const Modular &other) {
    return *this *= Modular(inverse(other.value, mod()));
  }
  friend const Type &abs(const Modular &x) { return x.value; }
  template <typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);
  template <typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);
  template <typename V, typename U>
  friend V &operator>>(V &stream, Modular<U> &number);

 private:
  Type value;
};
template <typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) == rhs;
}
template <typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value < rhs.value;
}
template <typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}
template <typename T>
bool IsZero(const Modular<T> &number) {
  return number() == 0;
}
template <typename T>
string to_string(const Modular<T> &number) {
  return to_string(number());
}
template <typename U, typename T>
U &operator<<(U &stream, const Modular<T> &number) {
  return stream << number();
}
template <typename U, typename T>
U &operator>>(U &stream, Modular<T> &number) {
  typename common_type<typename Modular<T>::Type, long long>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
constexpr int md = (int)998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
const int N = 3e5 + 5;
int An, L, alpha;
set<int> e[N];
int indegree[N];
bool vis[N];
bool flag;
int visited;
void dfs(int at) {
  vis[at] = true;
  visited++;
  if (e[at].size() > 1) flag = false;
  for (int to : e[at]) {
    if (vis[to]) {
      flag = false;
      continue;
    }
    if (indegree[to] != 1) {
      flag = false;
    }
    dfs(to);
  }
}
int lengths[N];
vector<pair<int, int>> recs;
Mint dp[N];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> An >> L >> alpha;
  for (int i = 1; i <= An; i++) {
    int c;
    cin >> c;
    vector<int> A(c);
    for (int &a : A) cin >> a;
    for (int j = 0; j < c - 1; j++) {
      int from = A[j];
      int to = A[j + 1];
      if (e[from].find(to) == e[from].end()) {
        e[from].insert(to);
        indegree[to]++;
      }
    }
  }
  for (int i = 1; i <= alpha; i++) {
    if (indegree[i] == 0) {
      assert(vis[i] == false);
      flag = true;
      visited = 0;
      dfs(i);
      if (flag) {
        lengths[visited]++;
      }
    }
  }
  for (int len = 1; len <= alpha; len++) {
    if (lengths[len]) {
      recs.push_back({len, lengths[len]});
    }
  }
  dp[0] = 1;
  for (int i = 1; i <= L; i++) {
    dp[i] = 0;
    for (auto [back, times] : recs) {
      if (i - back >= 0) {
        dp[i] += dp[i - back] * times;
      }
    }
  }
  cout << dp[L] << "\n";
  return 0;
}

```