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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
  static int[] par;
  static int[] rank;
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int m = sc.nextInt();
    par = new int[n];
    rank = new int[n];
    ArrayList[] list = new ArrayList[m];
    for(int i = 0; i < m; i++) {
      list[i] = new ArrayList<Integer>();
    }
    for(int i = 0; i < n; i++) {
      int k = sc.nextInt();
      for(int j = 0; j < k; j++) {
        int l = sc.nextInt() - 1;
        list[l].add(i);
      }
    }
    init(n);
    for(int i = 0; i < m; i++) {
      for(int j = 0; j < list[i].size() - 1; j++) {
        unite((int)list[i].get(j), (int)list[i].get(j + 1));
      }
    }
    String ans = "NO";
    HashSet<Integer> set = new HashSet<Integer>();
    for(int i = 0; i < n; i++) {
      set.add(find(i));
    }
    if(set.size() == 1) ans = "YES";
    System.out.println(ans);
  }
  static void init(int m) {
      for(int i = 0; i < m; i++) {
        par[i] = i;
        rank[i] = 0;
      }
    }
  static int find(int x) {
      if(par[x] == x) {
        return x;
      } else {
        return par[x] = find(par[x]);
      }
    }
  static void unite(int x, int y) {
      x = find(x);
      y = find(y);
      if(x != y) {
        if(rank[x] < rank[y]) {
          par[x] = y;
        } else {
          par[y] = x;
          if(rank[x] == rank[y]) {
            rank[x]++;
          }
        }
      }
    }
  static boolean same(int x, int y) {
      return find(x) == find(y);
    }
}