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;

#define REP(i,n) for(ll i=0; i<(ll)(n); i++)
#define FOR(i,n,m) for (ll i=n; i<(ll)(m); i++)
#define pb push_back
#define INF 1000000007LL
#define all(a) (a).begin(),(a).end()

typedef long long ll;
typedef pair<int,int> p;

int dy[4]={-1,1,0,0};
int dx[4]={0,0,1,-1};

#define MAX_N 100010


int d[MAX_N*2];
int renum[MAX_N];

struct edge {int to, cost;};
vector<edge> G[MAX_N*2];
int V;

void dijkstra(int s){
    priority_queue<p,vector<p>, greater<p> > que;
    fill(d,d+V, INF);
    d[s]=0;
    que.push(p(0,s));
    while(!que.empty()){
        p pi = que.top(); que.pop();
        int v = pi.second;
        if(d[v] < pi.first) continue;
        REP(i,G[v].size()){
            edge e = G[v][i];
            if(d[e.to] > d[v] + e.cost){
                d[e.to] = d[v] + e.cost;
                que.push(p(d[e.to],e.to));
            }
        }
    }
}
int N,M;
int main(){
    ios::sync_with_stdio(false);
    cin >> N >> M;
    V = N+M;
    
    int ln_cur = N;
    REP(i,N) {
        int k;
        cin >> k;
        REP(j,k) {
            int ln;
            cin >> ln;
            if (renum[ln] < N) {
                renum[ln] = ln_cur;
                ln_cur++;
            }
            G[i].pb((edge){renum[ln],1});
            G[renum[ln]].pb((edge){(int)i,1});
        }
    }

    dijkstra(0);
    // たどり着けない奴がいたら即アウト
    int max_dis = 0;
    int max_dis_p = -1;
    REP(i,N) {
        if (d[i] == INF) {
            cout << "NO" << endl;
            return 0;
        }
        if (max_dis < d[i]) {
            max_dis = 1;
            max_dis_p = i;
        }
    }
    dijkstra(max_dis_p);
    max_dis = 0;
    max_dis_p = -1;
    REP(i,N) {
        if (d[i] == INF) {
            cout << "NO" << endl;
            return 0;
        }
        if (max_dis < d[i]) {
            max_dis = 1;
            max_dis_p = i;
        }
    }
    if (max_dis > 4) {
        cout << "NO" << endl;
        return 0;
    }
    else {
        cout << "YES" << endl;
    }
    
    return 0;
}