#include <bits/stdc++.h>
using namespace std;
const int MOD = 998244353;
const int MAXN = 6E5;
const int BLOCK = 550;
int par[MAXN];
int sz[MAXN];
vector<int> a[MAXN];
vector<int> who_[MAXN];
bool isBad[MAXN];
vector<int> objects;
int dp[MAXN + 1];
int freq[BLOCK];
vector<int> adjList[MAXN];
int inDeg[MAXN];
int outDeg[MAXN];
int getRoot(int x) {
  if (par[x] != x) par[x] = getRoot(par[x]);
  return par[x];
}
bool mge(int x, int y) {
  x = getRoot(x);
  y = getRoot(y);
  if (x == y) return false;
  if (sz[x] < sz[y]) swap(x, y);
  par[y] = x;
  sz[x] += sz[y];
  for (int z : who_[y]) who_[x].push_back(z);
  return true;
}
void add(int &x, int y) {
  x += y;
  if (x >= MOD) x -= MOD;
}
int solve(int n) {
  vector<int> big;
  for (int num : objects) {
    if (num >= BLOCK)
      big.push_back(num);
    else
      freq[num]++;
  }
  dp[0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int b : big)
      if (i - b >= 0) add(dp[i], dp[i - b]);
    for (int j = 1; j < BLOCK; j++)
      if (i - j >= 0) add(dp[i], (int)((long long)freq[j] * dp[i - j] % MOD));
  }
  return dp[n];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  for (int i = 0; i < MAXN; i++) {
    par[i] = i;
    sz[i] = 1;
  }
  int n, m, k;
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++) {
    int c;
    cin >> c;
    a[i] = vector<int>(c);
    set<int> seen;
    for (int j = 0; j < c; j++) {
      cin >> a[i][j];
      a[i][j]--;
      if (seen.count(a[i][j])) isBad[i] = true;
      seen.insert(a[i][j]);
      if (j) {
        adjList[a[i][j - 1]].push_back(a[i][j]);
        outDeg[a[i][j - 1]]++;
        inDeg[a[i][j]]++;
      }
    }
  }
  for (int i = 0; i < k; i++) {
    a[n + i] = {i};
  }
  n += k;
  for (int i = 0; i < n; i++) {
    int num = a[i][0];
    who_[getRoot(num)].push_back(i);
    for (int j : a[i]) {
      mge(j, num);
    }
  }
  for (int i = 0; i < k; i++) {
    if (getRoot(i) != i) continue;
    int r = getRoot(i);
    bool valid = true;
    set<int> nums;
    for (int ind : who_[r]) {
      if (isBad[ind]) valid = false;
      for (int x : a[ind]) nums.insert(x);
    }
    if (!valid) continue;
    int sources = 0;
    int sinks = 0;
    for (int x : nums) {
      if (!inDeg[x]) sources++;
      if (!outDeg[x]) sinks++;
      if (outDeg[x]) {
        for (int y : adjList[x])
          if (y != adjList[x].back()) valid = false;
      }
    }
    if (sources != 1 || sinks != 1) valid = false;
    if (!valid) continue;
    objects.push_back(sz[r]);
  }
  int ans = solve(m);
  cout << ans << "\n";
  return 0;
}

### Prompt

Develop a solution in Cpp 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;
const int MOD = 998244353;
const int MAXN = 6E5;
const int BLOCK = 550;
int par[MAXN];
int sz[MAXN];
vector<int> a[MAXN];
vector<int> who_[MAXN];
bool isBad[MAXN];
vector<int> objects;
int dp[MAXN + 1];
int freq[BLOCK];
vector<int> adjList[MAXN];
int inDeg[MAXN];
int outDeg[MAXN];
int getRoot(int x) {
  if (par[x] != x) par[x] = getRoot(par[x]);
  return par[x];
}
bool mge(int x, int y) {
  x = getRoot(x);
  y = getRoot(y);
  if (x == y) return false;
  if (sz[x] < sz[y]) swap(x, y);
  par[y] = x;
  sz[x] += sz[y];
  for (int z : who_[y]) who_[x].push_back(z);
  return true;
}
void add(int &x, int y) {
  x += y;
  if (x >= MOD) x -= MOD;
}
int solve(int n) {
  vector<int> big;
  for (int num : objects) {
    if (num >= BLOCK)
      big.push_back(num);
    else
      freq[num]++;
  }
  dp[0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int b : big)
      if (i - b >= 0) add(dp[i], dp[i - b]);
    for (int j = 1; j < BLOCK; j++)
      if (i - j >= 0) add(dp[i], (int)((long long)freq[j] * dp[i - j] % MOD));
  }
  return dp[n];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  for (int i = 0; i < MAXN; i++) {
    par[i] = i;
    sz[i] = 1;
  }
  int n, m, k;
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++) {
    int c;
    cin >> c;
    a[i] = vector<int>(c);
    set<int> seen;
    for (int j = 0; j < c; j++) {
      cin >> a[i][j];
      a[i][j]--;
      if (seen.count(a[i][j])) isBad[i] = true;
      seen.insert(a[i][j]);
      if (j) {
        adjList[a[i][j - 1]].push_back(a[i][j]);
        outDeg[a[i][j - 1]]++;
        inDeg[a[i][j]]++;
      }
    }
  }
  for (int i = 0; i < k; i++) {
    a[n + i] = {i};
  }
  n += k;
  for (int i = 0; i < n; i++) {
    int num = a[i][0];
    who_[getRoot(num)].push_back(i);
    for (int j : a[i]) {
      mge(j, num);
    }
  }
  for (int i = 0; i < k; i++) {
    if (getRoot(i) != i) continue;
    int r = getRoot(i);
    bool valid = true;
    set<int> nums;
    for (int ind : who_[r]) {
      if (isBad[ind]) valid = false;
      for (int x : a[ind]) nums.insert(x);
    }
    if (!valid) continue;
    int sources = 0;
    int sinks = 0;
    for (int x : nums) {
      if (!inDeg[x]) sources++;
      if (!outDeg[x]) sinks++;
      if (outDeg[x]) {
        for (int y : adjList[x])
          if (y != adjList[x].back()) valid = false;
      }
    }
    if (sources != 1 || sinks != 1) valid = false;
    if (!valid) continue;
    objects.push_back(sz[r]);
  }
  int ans = solve(m);
  cout << ans << "\n";
  return 0;
}

```