Problem:
Score : 400 points

Problem Statement

On a planet far, far away, M languages are spoken. They are conveniently numbered 1 through M.

For CODE FESTIVAL 20XX held on this planet, N participants gathered from all over the planet.

The i-th (1≦i≦N) participant can speak K_i languages numbered L_{i,1}, L_{i,2}, ..., L_{i,{}K_i}.

Two participants A and B can communicate with each other if and only if one of the following conditions is satisfied:

There exists a language that both A and B can speak.

There exists a participant X that both A and B can communicate with.

Determine whether all N participants can communicate with all other participants.

Constraints

2≦N≦10^5

1≦M≦10^5

1≦K_i≦M

(The sum of all K_i)≦10^5

1≦L_{i,j}≦M

L_{i,1}, L_{i,2}, ..., L_{i,{}K_i} are pairwise distinct.

Partial Score

200 points will be awarded for passing the test set satisfying the following: N≦1000, M≦1000 and (The sum of all K_i)≦1000.

Additional 200 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N M
K_1 L_{1,1} L_{1,2} ... L_{1,{}K_1}
K_2 L_{2,1} L_{2,2} ... L_{2,{}K_2}
:
K_N L_{N,1} L_{N,2} ... L_{N,{}K_N}

Output

If all N participants can communicate with all other participants, print YES. Otherwise, print NO.

Sample Input 1

4 6
3 1 2 3
2 4 2
2 4 6
1 6

Sample Output 1

YES

Any two participants can communicate with each other, as follows:

Participants 1 and 2: both can speak language 2.

Participants 2 and 3: both can speak language 4.

Participants 1 and 3: both can communicate with participant 2.

Participants 3 and 4: both can speak language 6.

Participants 2 and 4: both can communicate with participant 3.

Participants 1 and 4: both can communicate with participant 2.

Note that there can be languages spoken by no participant.

Sample Input 2

4 4
2 1 2
2 1 2
1 3
2 4 3

Sample Output 2

NO

For example, participants 1 and 3 cannot communicate with each other.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
template<class T = int> using V  = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T, class H> void rsz(V<T> &v, H h) { v.resize(h); }
template<class T, class H, class... R> void rsz(V<T> &v, H h, R... r) { v.resize(h); for (auto&& i : v) rsz(i, r...); }
using P = pair<int, int>;
struct QF {
  V<> par; V< set<int> > chi;
  QF(int n) { par.resize(n); chi.resize(n); for (int i = 0; i < n; i++) par[i] = i, chi[i].insert(i); }
  bool same(int x, int y) { return par[x] == par[y]; }
  void _merge(int x, int y) { for (int i : chi[y]) par[i] = x; chi[x].insert(chi[y].begin(), chi[y].end()); chi[y].clear(); }
  void unite(int x, int y) { if (chi[par[x]].size() < chi[par[y]].size()) swap(x, y); if (!same(x, y)) _merge(par[x], par[y]); }
};

int main() {
  cin.tie(NULL); ios::sync_with_stdio(false);
  int n, m; cin >> n >> m;
  V<> k(n); VV<> l(n);
  for (int i = 0; i < n; i++) {
    cin >> k[i];
    l[i].resize(k[i]); for (int j = 0; j < k[i]; j++) cin >> l[i][j];
  }
  V<P> a;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < l[i].size(); j++) a.emplace_back(l[i][j], i);
  }
  sort(a.begin(), a.end());
  QF qf(n);
  for (int i = 0; i < a.size() - 1; i++) {
    if (a[i].first == a[i + 1].first) qf.unite(a[i].second, a[i + 1].second);
  }
  cout << (qf.chi[qf.par[0]].size() == n ? "YES" : "NO") << '\n';
}