#include <bits/stdc++.h>
template <class t>
inline void read(t &s) {
  s = 0;
  register long long f = 1;
  register char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) s = (s << 3) + (s << 1) + (c ^ 48), c = getchar();
  ;
  s *= f;
}
template <class t, class... A>
inline void read(t &x, A &...a) {
  read(x);
  read(a...);
}
template <class t>
inline void write(t x) {
  if (x < 0) putchar('-'), x = -x;
  static long long buf[21], top = 0;
  while (x) buf[++top] = x % 10, x /= 10;
  if (!top) buf[++top] = 0;
  while (top) putchar(buf[top--] ^ '0');
}
inline void setIn(std::string s) {
  freopen(s.c_str(), "r", stdin);
  return;
}
inline void setOut(std::string s) {
  freopen(s.c_str(), "w", stdout);
  return;
}
inline void setIO(std::string s = "") {
  setIn(s + ".in");
  setOut(s + ".out");
  return;
}
template <class t>
inline bool ckmin(t &x, t y) {
  if (x > y) {
    x = y;
    return 1;
  }
  return 0;
}
template <class t>
inline bool ckmax(t &x, t y) {
  if (x < y) {
    x = y;
    return 1;
  }
  return 0;
}
inline long long lowbit(long long x) { return x & (-x); }
const long long MaxN = 3e5 + 50;
const long long p = 998244353;
std::map<long long, long long> F[MaxN];
long long n, m, K;
long long f[MaxN], ideg[MaxN], odeg[MaxN];
std::vector<long long> nd[MaxN];
inline long long getf(long long x) { return f[x] == x ? x : f[x] = getf(f[x]); }
inline void merge(long long x, long long y) {
  long long a = getf(x), b = getf(y);
  if (a != b) f[b] = a;
}
inline void add(long long x, long long y) {
  if (!F[x].count(y)) F[x][y], ++odeg[x], ++ideg[y], merge(x, y);
}
long long g[MaxN];
signed main(void) {
  read(n, m, K);
  for (long long i = 1; i <= K; ++i) f[i] = i;
  while (n--) {
    long long x, y, lst = 0;
    read(x);
    while (x--) {
      read(y);
      if (lst) add(lst, y);
      lst = y;
    }
  }
  for (long long i = 1; i <= K; ++i) nd[getf(i)].push_back(i);
  for (long long i = 1; i <= K; ++i)
    if (getf(i) == i) {
      long long c0 = 0, c2 = 0, C0 = 0, C2 = 0;
      for (auto j : nd[i]) {
        if (!ideg[j])
          ++c0;
        else if (ideg[j] >= 2)
          ++c2;
        if (!odeg[j])
          ++C0;
        else if (odeg[j] >= 2)
          ++C2;
      }
      if (!c2 && c0 == 1 && !C2 && C0 == 1) ++g[(long long)nd[i].size()];
    }
  std::vector<std::pair<long long, long long> > G;
  for (long long i = 1; i <= K; ++i)
    if (g[i]) G.push_back(std::make_pair(i, g[i]));
  std::memset(f, 0, sizeof f), f[0] = 1;
  for (long long i = 0; i < m; ++i)
    for (auto j : G)
      if (i + j.first <= m) (f[i + j.first] += f[i] * j.second) %= p;
  write(f[m]), putchar('\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>
template <class t>
inline void read(t &s) {
  s = 0;
  register long long f = 1;
  register char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) s = (s << 3) + (s << 1) + (c ^ 48), c = getchar();
  ;
  s *= f;
}
template <class t, class... A>
inline void read(t &x, A &...a) {
  read(x);
  read(a...);
}
template <class t>
inline void write(t x) {
  if (x < 0) putchar('-'), x = -x;
  static long long buf[21], top = 0;
  while (x) buf[++top] = x % 10, x /= 10;
  if (!top) buf[++top] = 0;
  while (top) putchar(buf[top--] ^ '0');
}
inline void setIn(std::string s) {
  freopen(s.c_str(), "r", stdin);
  return;
}
inline void setOut(std::string s) {
  freopen(s.c_str(), "w", stdout);
  return;
}
inline void setIO(std::string s = "") {
  setIn(s + ".in");
  setOut(s + ".out");
  return;
}
template <class t>
inline bool ckmin(t &x, t y) {
  if (x > y) {
    x = y;
    return 1;
  }
  return 0;
}
template <class t>
inline bool ckmax(t &x, t y) {
  if (x < y) {
    x = y;
    return 1;
  }
  return 0;
}
inline long long lowbit(long long x) { return x & (-x); }
const long long MaxN = 3e5 + 50;
const long long p = 998244353;
std::map<long long, long long> F[MaxN];
long long n, m, K;
long long f[MaxN], ideg[MaxN], odeg[MaxN];
std::vector<long long> nd[MaxN];
inline long long getf(long long x) { return f[x] == x ? x : f[x] = getf(f[x]); }
inline void merge(long long x, long long y) {
  long long a = getf(x), b = getf(y);
  if (a != b) f[b] = a;
}
inline void add(long long x, long long y) {
  if (!F[x].count(y)) F[x][y], ++odeg[x], ++ideg[y], merge(x, y);
}
long long g[MaxN];
signed main(void) {
  read(n, m, K);
  for (long long i = 1; i <= K; ++i) f[i] = i;
  while (n--) {
    long long x, y, lst = 0;
    read(x);
    while (x--) {
      read(y);
      if (lst) add(lst, y);
      lst = y;
    }
  }
  for (long long i = 1; i <= K; ++i) nd[getf(i)].push_back(i);
  for (long long i = 1; i <= K; ++i)
    if (getf(i) == i) {
      long long c0 = 0, c2 = 0, C0 = 0, C2 = 0;
      for (auto j : nd[i]) {
        if (!ideg[j])
          ++c0;
        else if (ideg[j] >= 2)
          ++c2;
        if (!odeg[j])
          ++C0;
        else if (odeg[j] >= 2)
          ++C2;
      }
      if (!c2 && c0 == 1 && !C2 && C0 == 1) ++g[(long long)nd[i].size()];
    }
  std::vector<std::pair<long long, long long> > G;
  for (long long i = 1; i <= K; ++i)
    if (g[i]) G.push_back(std::make_pair(i, g[i]));
  std::memset(f, 0, sizeof f), f[0] = 1;
  for (long long i = 0; i < m; ++i)
    for (auto j : G)
      if (i + j.first <= m) (f[i + j.first] += f[i] * j.second) %= p;
  write(f[m]), putchar('\n');
  return 0;
}

```