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
// author: erray
#include <bits/stdc++.h>
 
using namespace std;

template<typename A, typename B> string to_string(const pair<A, B>& p);
template<typename A, typename B, typename C> string to_string(const tuple<A, B, C>& t);
template<typename A, typename B, typename C, typename D> string to_string(const tuple<A, B, C, D>& t);

string to_string(const string& s) {
  return '"' + s + '"';
}

string to_string(const char& c) {
  return string("'") + c + "'";
}

string to_string(const char *c) {
  return to_string(string(c));
}

string to_string(const bool& b) {
  return (b ? "true" : "false");
}

string to_string(const vector<bool>& v) {
  string res = "{";
  for (int i = 0; i < (int) v.size(); ++i) {
    if (i > 0) {
      res += ", ";
    }
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template<size_t T> string to_string(const bitset<T>& bs) {
  return bs.to_string();
}

template<typename T> string to_string(queue<T> q) {
  string res = "{";
  size_t sz = q.size();
  while (sz--) {
    T cur = q.front();
    q.pop();
    if ((int) res.size() > 1) {
      res += ", ";
    }
    res += to_string(cur);
  }
  res += "}";
  return res;
}

template<typename T, class C> string to_string(priority_queue<T, vector<T>, C> pq) {
  string res = "{";
  while (!pq.empty()) {
    T cur = pq.top();
    pq.pop();
    if ((int) res.size() > 1) {
      res += ", ";
    }
    res += to_string(cur);
  }
  res += "}";
  return res;
}

template<typename T> string to_string(const T& v) {
  string res = "{";
  for (auto &el : v) {
    if ((int) res.size() > 1) {
      res += ", ";
    }
    res += to_string(el);
  }
  res += "}";
  return res;
}

template<typename A, typename B> string to_string(const pair<A, B>& p) {
  return '(' + to_string(p.first) + ", " + to_string(p.second) + ')';
}
template<typename A, typename B, typename C> string to_string(const tuple<A, B, C>& t) {
  return '(' + to_string(get<0>(t)) + ", " + to_string(get<1>(t)) + ", " + to_string(get<2>(t)) + ')';
}
template<typename A, typename B, typename C, typename D> string to_string(const tuple<A, B, C, D>& t) {
  return '(' + to_string(get<0>(t)) + ", " + to_string(get<1>(t)) + ", " + to_string(get<2>(t)) + ", " + to_string(get<3>(t)) + ')';
}

void debug_out(int size, bool first, string name) {
  vector<string> tmp = {name};
  vector<int> tmp2 = {size, first};
  cerr << endl;
}

constexpr int buffer_size = 255;

template<typename Head, typename... Tail> void debug_out(int size, bool first, string name, Head H, Tail... T) {
  string tmp;
  int off = 0;
  while ((!name.empty() && name[0] != ',') || off != 0) {
    tmp += name[0];
    name.erase(name.begin());
    char c = tmp.back();
    if (c == '{' || c == '(') {
      ++off;
    } else if (c == '}' || c == ')'){
      --off;
    }
  }
  if (!name.empty()) {
    name.erase(name.begin());
  }
  if (tmp[0] == ' ') {
    tmp.erase(tmp.begin());
  }

  string buff = to_string(H);
  if ((int) buff.size() + size + (int) tmp.size() > buffer_size - 5 && !first) {
    cerr << '\n';
    size = 0;
  }
  cerr << '[' << tmp << ": " << buff << "] ";
  debug_out(((int) buff.size() + size + (int) tmp.size() + 5) % buffer_size, false, name, T...);
}

#ifdef DEBUG
#define debug(...) cerr << "-> ", debug_out(3, true, string(#__VA_ARGS__), __VA_ARGS__)
#define here cerr << "-> " << __LINE__ << endl
#else
#define debug(...) void(37)
#define here void(37)
#endif


// modular library by tourist
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) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
      "divl %4; \n\t"
      : "=a" (d), "=d" (m)
      : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
    int64_t q = static_cast<int64_t>(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())); }

  template <typename U>
  friend const Modular<U>& abs(const Modular<U>& v) { return v; }

  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 U>
  friend std::istream& operator>>(std::istream& 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 T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  return stream << number();
}

template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
 
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  vector<deque<int>> a(n);
  for (int i = 0; i < n; ++i) {
    int s;
    cin >> s;
    a[i].resize(s);
    for (int j = 0; j < s; ++j) {
      cin >> a[i][j];
      --a[i][j];
    }
  }

  n += k;
  for (int i = 0; i < k; ++i) {
    a.push_back({i});
  }
  
  auto My_assert = [&](bool x) {
    if (!x) {
      cout << 0 << '\n';
      exit(0);
    }
  };

  sort(a.begin(), a.end(), [&](auto x, auto y) {
    return int(x.size()) > int(y.size());
  });

  debug(a, m, k);

  vector<array<int, 2>> pos(k, {-1, -1});
  vector<int> shift(n);
  int cur_ind = -1;
  vector<bool> clear(n);
  for (auto& e : a) {
    ++cur_ind;
    My_assert(int(set<int>(e.begin(), e.end()).size()) == int(e.size()));
    int s = int(e.size());
    int p = 0;
    while (p < s && pos[e[p]][0] == -1) {
      ++p;
    } 
    debug(e, p);

    if (p == s) {
      for (int i = 0; i < s; ++i) {
        pos[e[i]] = {cur_ind, i};
      }
      debug(pos);
      continue; 
    }
    
    clear[cur_ind] = true;

    if (p == 0) {
      while (p < s && pos[e[p]][0] != -1) {
        if (p > 0) {
          My_assert((pos[e[p]][0] == pos[e[p - 1]][0] && pos[e[p]][1] == pos[e[p - 1]][1] + 1));
        }
        ++p;
      } 
      if (p == s) {
        debug(pos);
        continue;
      } 
      int ins = pos[e[0]][0];
      int ins_s = int(a[ins].size());
      debug(ins, ins_s, pos[e[p - 1]][1], shift[ins]);
      My_assert(pos[e[p - 1]][1] + shift[ins] == ins_s - 1);
      for (int i = p; i < s; ++i) {
        a[ins].push_back(e[i]);
        pos[e[i]] = {ins, ins_s + i};
      }
    } else {
      int old_p = p;
      while (p < s && pos[e[p]][0] != -1) {
        if (p > old_p) {
          My_assert((pos[e[p]][0] == pos[e[p - 1]][0] && pos[e[p]][1] == pos[e[p - 1]][1] + 1));
        }
        ++p;
      } 
      My_assert(p == s);
      p = old_p;
      int ins = pos[e[p]][0];
      My_assert(pos[e[p]][1] + shift[ins] == 0);
      shift[ins] += p;
      for (int i = p - 1; i >= 0; --i) {
        a[ins].push_front(e[i]);
        pos[e[i]] = {ins, i - shift[ins]};
      }
    }
    debug(pos);
  }                                 
  
  vector<int> ct(m + 1);
  for (int i = 0; i < n; ++i) {
    if (!clear[i]) {
      ++ct[int(a[i].size())];
    }
  }

  debug(ct);
  vector<Mint> dp(m + 1);
  dp[0] = 1;
  vector<int> add;
  for (int j = 1; j <= m; ++j) {
    if (ct[j] > 0) {
      add.push_back(j);
    }
  }

  for (int i = 1; i <= m; ++i) {
    for (auto e : add) {
      if (i >= e) {
        dp[i] += dp[i - e] * ct[e];
      }
    }
  }

  cout << dp[m] << '\n';
}