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 Julia (0.5.0) (judge verdict: Runtime Error)

struct UF
	n::Int
	pr::Array{Int}
	sz::Array{Int}
	UF(n)=new(n,1:n,ones(Int,n))
end
function find(UF,a)
	if UF.pr[a]==a
		a
	else
		UF.pr[a]=find(UF,UF.pr[a])
	end
end
same(UF,a,b)=find(UF,a)==find(UF,b)
function unite(UF,a,b)
	a=find(UF,a)
	b=find(UF,b)
	if a==b
		false
	else
		if UF.sz[a]<UF.sz[b]
			UF.pr[a]=b
			UF.sz[b]+=UF.sz[a]
		else
			UF.pr[b]=a
			UF.sz[a]+=UF.sz[b]
		end
		true
	end
end
size(UF,a)=UF.sz[find(UF,a)]
function main()
	N,M=map(x->parse(Int,x),split(readline()))
	pr=-ones(Int,M)
	uf=UF(N)
	for i=1:N
		L=map(x->parse(Int,x),split(readline()))
		shift!(L)
		for l=L
			if pr[l]<0
				pr[l]=i
			else
				unite(uf,pr[l],i)
			end
		end
	end
	for i=1:N
		if !same(uf,1,i)
			println("NO")
			exit()
		end
	end
	println("YES")
end
main()