#include <bits/stdc++.h>
using namespace std;
template <typename T>
void rd(T& x) {
  int f = 0, c;
  while (!isdigit(c = getchar())) f ^= !(c ^ 45);
  x = (c & 15);
  while (isdigit(c = getchar())) x = x * 10 + (c & 15);
  if (f) x = -x;
}
template <typename T>
void pt(T x, int c = -1) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) pt(x / 10);
  putchar(x % 10 + 48);
  if (c != -1) putchar(c);
}
const int P = 998244353;
int ad(int k1, int k2) { return k1 += k2 - P, k1 += k1 >> 31 & P; }
int su(int k1, int k2) { return k1 -= k2, k1 += k1 >> 31 & P; }
int mu(int k1, int k2) { return 1LL * k1 * k2 % P; }
void uad(int& k1, int k2) { k1 += k2 - P, k1 += k1 >> 31 & P; }
void usu(int& k1, int k2) { k1 -= k2, k1 += k1 >> 31 & P; }
template <typename... T>
int ad(int k1, T... k2) {
  return ad(k1, ad(k2...));
}
template <typename... T>
int su(int k1, T... k2) {
  return su(k1, ad(k2...));
}
template <typename... T>
int mu(int k1, T... k2) {
  return mu(k1, mu(k2...));
}
template <typename... T>
void uad(int& k1, T... k2) {
  return uad(k1, ad(k2...));
}
template <typename... T>
void usu(int& k1, T... k2) {
  return usu(k1, ad(k2...));
}
int po(int k1, int k2) {
  int k3 = 1;
  for (; k2; k2 >>= 1, k1 = mu(k1, k1))
    if (k2 & 1) k3 = mu(k3, k1);
  return k3;
}
void NTT(vector<int>& a, int g, int lim) {
  a.resize(lim);
  for (int i = 0, j = 0; i < lim; ++i) {
    if (i < j) swap(a[i], a[j]);
    for (int k = lim >> 1; (j ^= k) < k; k >>= 1)
      ;
  }
  vector<int> w(lim >> 1);
  w[0] = 1;
  for (int i = 1; i < lim; i <<= 1) {
    int wn = po(g, (P - 1) / (i << 1));
    for (int j = (i >> 1) - 1; j > 0; --j) w[j << 1] = w[j];
    for (int j = 1; j < i; j += 2) w[j] = mu(w[j - 1], wn);
    for (int j = 0; j < lim; j += i << 1)
      for (int k = 0; k < i; ++k) {
        int x = a[j + k], y = mu(a[i + j + k], w[k]);
        a[j + k] = ad(x, y), a[i + j + k] = su(x, y);
      }
  }
  if (g == 332748118)
    for (int i = 0, I = po(lim, P - 2); i < (int)a.size(); ++i)
      a[i] = mu(a[i], I);
}
vector<int> operator*(vector<int> a, vector<int> b) {
  if (((int)(a).size()) <= 50 && ((int)(b).size()) <= 50) {
    vector<int> c(((int)(a).size()) + ((int)(b).size()) - 1);
    for (int i = (0); i <= (((int)(a).size()) - 1); ++i)
      for (int j = (0); j <= (((int)(b).size()) - 1); ++j)
        uad(c[i + j], mu(a[i], b[j]));
    return c;
  }
  int need = (int)a.size() + b.size() - 1, lim = 1;
  while (lim <= need) lim <<= 1;
  NTT(a, 3, lim), NTT(b, 3, lim);
  for (int i = 0; i < lim; ++i) a[i] = mu(a[i], b[i]);
  NTT(a, 332748118, lim);
  return a.resize(need), a;
}
vector<int> operator+(vector<int> a, vector<int> b) {
  if (a.size() < b.size()) {
    for (int i = 0; i < (int)a.size(); ++i) (b[i] += a[i]) %= P;
    return b;
  } else {
    for (int i = 0; i < (int)b.size(); ++i) (a[i] += b[i]) %= P;
    return a;
  }
}
vector<int> pinv(const vector<int>& a, int n = -1) {
  if (n == -1) n = a.size();
  if (n == 1) return vector<int>(1, po(a[0], P - 2));
  vector<int> b = pinv(a, (n + 1) >> 1),
              tmp = vector<int>(a.begin(), a.begin() + n);
  int lim = 1;
  while (lim <= n * 2 - 2) lim <<= 1;
  NTT(b, 3, lim), NTT(tmp, 3, lim);
  for (int i = 0; i < lim; ++i) b[i] = mu(su(2, mu(b[i], tmp[i])), b[i]);
  NTT(b, 332748118, lim);
  return b.resize(n), b;
}
vector<int> pdao(const vector<int>& a) {
  vector<int> b((int)a.size() - 1);
  for (int i = 1; i < (int)a.size(); ++i) b[i - 1] = mu(a[i], i);
  return b;
}
vector<int> pji(const vector<int>& a) {
  vector<int> b((int)a.size() + 1);
  for (int i = 0; i < (int)a.size(); ++i) b[i + 1] = mu(a[i], po(i + 1, P - 2));
  return b;
}
vector<int> pln(const vector<int>& a) {
  vector<int> b(pdao(a) * pinv(a));
  b.resize((int)a.size() - 1);
  return pji(b);
}
vector<int> pexp(const vector<int>& a, int n = -1) {
  if (n == -1) n = a.size();
  if (n == 1) return vector<int>(1, 1);
  vector<int> b = pexp(a, (n + 1) >> 1), c(b);
  c.resize(n), c = pln(c), --c[0];
  for (int i = 0; i < n; ++i) c[i] = su(a[i], c[i]);
  vector<int> d(b * c);
  return d.resize(n), d;
}
const int N = 300005;
int n, m, K, pre[N], nex[N], num[N], tot[N];
struct ufs {
  int fa[N], bad[N];
  ufs() {
    for (int i = (1); i <= (N - 1); ++i) fa[i] = i, bad[i] = 0;
  }
  int fd(int k1) { return fa[k1] == k1 ? k1 : fa[k1] = fd(fa[k1]); }
  void mer(int k1, int k2) {
    k1 = fd(k1), k2 = fd(k2);
    if (k1 == k2) return;
    bad[k1] = bad[k1] | bad[k2];
    fa[k2] = k1;
  }
} o;
int main() {
  rd(n), rd(m), rd(K);
  for (int i = (1); i <= (n); ++i) {
    int sz;
    rd(sz);
    for (int j = (1); j <= (sz); ++j) {
      rd(num[j]);
    }
    for (int j = (1); j <= (sz - 1); ++j) {
      if (nex[num[j]] != 0 && nex[num[j]] != num[j + 1]) {
        o.bad[o.fd(num[j])] = 1;
      }
      nex[num[j]] = num[j + 1];
      if (pre[num[j + 1]] != 0 && pre[num[j + 1]] != num[j]) {
        o.bad[o.fd(num[j])] = 1;
      }
      pre[num[j + 1]] = num[j];
      o.mer(num[j], num[j + 1]);
    }
  }
  for (int i = (1); i <= (K); ++i) {
    ++tot[o.fd(i)];
  }
  vector<int> v;
  static int vis[N];
  int tim = 0;
  auto chk = [&](int k1) {
    ++tim;
    while (k1) {
      if (vis[k1] == tim) return 0;
      vis[k1] = tim;
      k1 = nex[k1];
    }
    return 1;
  };
  for (int i = (1); i <= (K); ++i)
    if (o.fd(i) == i) {
      if (!o.bad[i] && chk(i)) {
        v.push_back(tot[i]);
      }
    }
  vector<int> res(m + 1);
  uad(res[0], 1);
  for (auto x : v) {
    if (x <= m) usu(res[x], 1);
  }
  res = pinv(res);
  printf("%d\n", res[m]);
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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>
void rd(T& x) {
  int f = 0, c;
  while (!isdigit(c = getchar())) f ^= !(c ^ 45);
  x = (c & 15);
  while (isdigit(c = getchar())) x = x * 10 + (c & 15);
  if (f) x = -x;
}
template <typename T>
void pt(T x, int c = -1) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) pt(x / 10);
  putchar(x % 10 + 48);
  if (c != -1) putchar(c);
}
const int P = 998244353;
int ad(int k1, int k2) { return k1 += k2 - P, k1 += k1 >> 31 & P; }
int su(int k1, int k2) { return k1 -= k2, k1 += k1 >> 31 & P; }
int mu(int k1, int k2) { return 1LL * k1 * k2 % P; }
void uad(int& k1, int k2) { k1 += k2 - P, k1 += k1 >> 31 & P; }
void usu(int& k1, int k2) { k1 -= k2, k1 += k1 >> 31 & P; }
template <typename... T>
int ad(int k1, T... k2) {
  return ad(k1, ad(k2...));
}
template <typename... T>
int su(int k1, T... k2) {
  return su(k1, ad(k2...));
}
template <typename... T>
int mu(int k1, T... k2) {
  return mu(k1, mu(k2...));
}
template <typename... T>
void uad(int& k1, T... k2) {
  return uad(k1, ad(k2...));
}
template <typename... T>
void usu(int& k1, T... k2) {
  return usu(k1, ad(k2...));
}
int po(int k1, int k2) {
  int k3 = 1;
  for (; k2; k2 >>= 1, k1 = mu(k1, k1))
    if (k2 & 1) k3 = mu(k3, k1);
  return k3;
}
void NTT(vector<int>& a, int g, int lim) {
  a.resize(lim);
  for (int i = 0, j = 0; i < lim; ++i) {
    if (i < j) swap(a[i], a[j]);
    for (int k = lim >> 1; (j ^= k) < k; k >>= 1)
      ;
  }
  vector<int> w(lim >> 1);
  w[0] = 1;
  for (int i = 1; i < lim; i <<= 1) {
    int wn = po(g, (P - 1) / (i << 1));
    for (int j = (i >> 1) - 1; j > 0; --j) w[j << 1] = w[j];
    for (int j = 1; j < i; j += 2) w[j] = mu(w[j - 1], wn);
    for (int j = 0; j < lim; j += i << 1)
      for (int k = 0; k < i; ++k) {
        int x = a[j + k], y = mu(a[i + j + k], w[k]);
        a[j + k] = ad(x, y), a[i + j + k] = su(x, y);
      }
  }
  if (g == 332748118)
    for (int i = 0, I = po(lim, P - 2); i < (int)a.size(); ++i)
      a[i] = mu(a[i], I);
}
vector<int> operator*(vector<int> a, vector<int> b) {
  if (((int)(a).size()) <= 50 && ((int)(b).size()) <= 50) {
    vector<int> c(((int)(a).size()) + ((int)(b).size()) - 1);
    for (int i = (0); i <= (((int)(a).size()) - 1); ++i)
      for (int j = (0); j <= (((int)(b).size()) - 1); ++j)
        uad(c[i + j], mu(a[i], b[j]));
    return c;
  }
  int need = (int)a.size() + b.size() - 1, lim = 1;
  while (lim <= need) lim <<= 1;
  NTT(a, 3, lim), NTT(b, 3, lim);
  for (int i = 0; i < lim; ++i) a[i] = mu(a[i], b[i]);
  NTT(a, 332748118, lim);
  return a.resize(need), a;
}
vector<int> operator+(vector<int> a, vector<int> b) {
  if (a.size() < b.size()) {
    for (int i = 0; i < (int)a.size(); ++i) (b[i] += a[i]) %= P;
    return b;
  } else {
    for (int i = 0; i < (int)b.size(); ++i) (a[i] += b[i]) %= P;
    return a;
  }
}
vector<int> pinv(const vector<int>& a, int n = -1) {
  if (n == -1) n = a.size();
  if (n == 1) return vector<int>(1, po(a[0], P - 2));
  vector<int> b = pinv(a, (n + 1) >> 1),
              tmp = vector<int>(a.begin(), a.begin() + n);
  int lim = 1;
  while (lim <= n * 2 - 2) lim <<= 1;
  NTT(b, 3, lim), NTT(tmp, 3, lim);
  for (int i = 0; i < lim; ++i) b[i] = mu(su(2, mu(b[i], tmp[i])), b[i]);
  NTT(b, 332748118, lim);
  return b.resize(n), b;
}
vector<int> pdao(const vector<int>& a) {
  vector<int> b((int)a.size() - 1);
  for (int i = 1; i < (int)a.size(); ++i) b[i - 1] = mu(a[i], i);
  return b;
}
vector<int> pji(const vector<int>& a) {
  vector<int> b((int)a.size() + 1);
  for (int i = 0; i < (int)a.size(); ++i) b[i + 1] = mu(a[i], po(i + 1, P - 2));
  return b;
}
vector<int> pln(const vector<int>& a) {
  vector<int> b(pdao(a) * pinv(a));
  b.resize((int)a.size() - 1);
  return pji(b);
}
vector<int> pexp(const vector<int>& a, int n = -1) {
  if (n == -1) n = a.size();
  if (n == 1) return vector<int>(1, 1);
  vector<int> b = pexp(a, (n + 1) >> 1), c(b);
  c.resize(n), c = pln(c), --c[0];
  for (int i = 0; i < n; ++i) c[i] = su(a[i], c[i]);
  vector<int> d(b * c);
  return d.resize(n), d;
}
const int N = 300005;
int n, m, K, pre[N], nex[N], num[N], tot[N];
struct ufs {
  int fa[N], bad[N];
  ufs() {
    for (int i = (1); i <= (N - 1); ++i) fa[i] = i, bad[i] = 0;
  }
  int fd(int k1) { return fa[k1] == k1 ? k1 : fa[k1] = fd(fa[k1]); }
  void mer(int k1, int k2) {
    k1 = fd(k1), k2 = fd(k2);
    if (k1 == k2) return;
    bad[k1] = bad[k1] | bad[k2];
    fa[k2] = k1;
  }
} o;
int main() {
  rd(n), rd(m), rd(K);
  for (int i = (1); i <= (n); ++i) {
    int sz;
    rd(sz);
    for (int j = (1); j <= (sz); ++j) {
      rd(num[j]);
    }
    for (int j = (1); j <= (sz - 1); ++j) {
      if (nex[num[j]] != 0 && nex[num[j]] != num[j + 1]) {
        o.bad[o.fd(num[j])] = 1;
      }
      nex[num[j]] = num[j + 1];
      if (pre[num[j + 1]] != 0 && pre[num[j + 1]] != num[j]) {
        o.bad[o.fd(num[j])] = 1;
      }
      pre[num[j + 1]] = num[j];
      o.mer(num[j], num[j + 1]);
    }
  }
  for (int i = (1); i <= (K); ++i) {
    ++tot[o.fd(i)];
  }
  vector<int> v;
  static int vis[N];
  int tim = 0;
  auto chk = [&](int k1) {
    ++tim;
    while (k1) {
      if (vis[k1] == tim) return 0;
      vis[k1] = tim;
      k1 = nex[k1];
    }
    return 1;
  };
  for (int i = (1); i <= (K); ++i)
    if (o.fd(i) == i) {
      if (!o.bad[i] && chk(i)) {
        v.push_back(tot[i]);
      }
    }
  vector<int> res(m + 1);
  uad(res[0], 1);
  for (auto x : v) {
    if (x <= m) usu(res[x], 1);
  }
  res = pinv(res);
  printf("%d\n", res[m]);
  return 0;
}

```