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 Ruby (2.3.3) (judge verdict: Accepted)

class UnionFindTree
    def initialize(n)
        @par=[*0...n]
        @rank=[0]*n
    end
    def root(x)
        x==@par[x] ? x : @par[x]=root(@par[x])
    end
    def unite(x, y)
        x=root(x);
        y=root(y);
        if @rank[x]<@rank[y]
            @par[x]=y;
        else
            @par[y]=x;
            @rank[x]+=1 if @rank[x]==@rank[y]
        end
    end
    def same?(x, y)
        root(x)==root(y)
    end
end


n, m=gets.split.map &:to_i
l=[]
n.times{|i| _, *l[i]=gets.split.map{|e|e.to_i-1} }

a=UnionFindTree.new(1e5)
l.each{|v| v.each{|x| a.unite(x, v[0])}}
puts (l.each_cons(2).all?{|x, y| a.same?(x[0], y[0])} ? :YES : :NO)