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: Accepted)

N, M = map(int, input().split())
L = []
for i in range(N):
  Ls = list(map(int, input().split()))
  Ls.pop(0)
  Ls = [l-1 for l in Ls]
  L.append(Ls)
#print(L)
UF = list(range(N+M))
def par(m):
  s = []
  r = UF[m]
  while r != m:
    s.append(m)
    m = r
    r = UF[m]
  for i in s:
    UF[i] = r
  return r
def unite(m, n):
  i = par(m)
  j = par(n)
  UF[j] = i
for i in range(N):
  Ls = L[i]
  for l in Ls:
    unite(i, N+l)
    unite(N+l, i)
#print(UF)
#for i in range(N+M):
#  p = par(i)
#print(UF)
ok = True
for i in range(1, N):
  if par(i) != par(i-1):
    ok = False
    break
if ok:
  print("YES")
else:
  print("NO")