fast kuhn! TOP!

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

#define db(x) cerr<<#x<<" == "<<x<<endl
#define _ <<", "<<

mt19937_64 llrand(random_device{}());

const int INF = 0x3f3f3f3f;
const int N = 105, A = 11, M = 3 * N * (1<<A);

int n, cnt, mcnt, r[M];
map<string, int> m;
vector<int> a[N];

bitset<1005> val[M];
unordered_map<bitset<1005>, int> ms;

int b[M], x, vis[M], mat[M];
vector<int> g[M];

bool match(int u) {
  if (vis[u] == x) return 0;
  vis[u] = x;
  for (int v : g[u])
    if (!b[v] or match(b[v])) {
      b[v] = u;
      mat[u] = v;
      return 1;
    }
  return 0;
}

int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int x;
    char s[15];
    scanf("%d", &x);
    while (x--) {
      scanf("%s", s);
      if (!m.count(s)) m[s] = mcnt++;
      a[i].push_back(m[s]);
    }

    for (int j = 1; j < (1<<a[i].size()); j++) {
      bitset<1005> xx = 0;
      for (int k = 0; k < a[i].size(); k++) if ((1<<k)&j)
        xx.set(a[i][k]);

      if (!ms.count(xx)) {
        cnt++;
        val[cnt] = xx;
        ms[xx] = cnt;
        r[cnt] = i;
      }
    }
  }

  for (int i = 1; i <= cnt; i++) if (val[i].count() > 1) {
    for (int j = 0; j < a[r[i]].size(); j++) {
      auto xx = val[i];
      int bit = a[r[i]][j];
      if (!xx[bit]) continue;

      xx.reset(bit);

      g[ms[xx]].push_back(i + cnt);
    }
  }

  for (int i = 1; i <= cnt; i++) {
    //shuffle(g[i].begin(), g[i].end(), llrand); // Pior???
    random_shuffle(g[i].begin(), g[i].end());
  }

  int ans = cnt;

  // fast kuhn
  while (1) {
    int xx = 0;

    x++;
    for (int i = 1; i <= cnt; i++) if (!mat[i])
      xx += match(i);

    if (xx == 0) break;
    ans -= xx;
  }

  /*
  // kuhn normal
  for (int i = 1; i <= cnt; i++) {
    x++;
    ans -= match(i);
  }
  */

  printf("%d\n", ans);
  return 0;
}