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 Python (3.4.3) (judge verdict: Wrong Answer)

N, M = list(map(int, input().split()))

data_list = []
for i in range(N):
    tmp_list = list(map(int, input().split()))[1:]
    data_list.append(set(tmp_list))

class UnionFind:
    def __init__(self, count):
        root = [0] * count
        for i in range(count):
            root[i] = i
        self.root = root
    def unite(self, a, b):
        root = self.root
        root[a] = b
    def find(self, a):
        r = self.root[a]
        if (a == r):
            return a
        else:
            r = self.find(r)
            self.root[a] = r
            return r

uf = UnionFind(N)

for i in range(N):
    for j in range(i + 1, N):
        if(len(data_list[i] & data_list[j]) > 0):
            uf.unite(i, j)


b = True
for i in range(N):
    for j in range(i + 1, N):
        if(not uf.find(i) == uf.find(j)):
            b = False
            break
    if(not b):
        break
    
print('YES' if b else 'NO')