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: Wrong Answer)

s = gets.chomp.split(' ')
N = s[0].to_i #N人
M = s[1].to_i #M種類の言語

ary = [nil]
#格納
for i in 1..N
  ary << gets.chomp.split(' ').map { |e| e.to_i }
end
#puts ary.to_s

hantei = []
#人同士の共通の言語があるか
for i in 1..N
  hantei[i] = []
  for j in 1..N
    hantei[i][j] = false
    if i==j
      next
    else
      #別人なので検証する
      #puts i.to_s + ':' + j.to_s
      catch :escape do
        #puts ary[i].to_s
        #puts ary[j].to_s
        for k in 1..ary[i][0]
          for m in 1..ary[j][0]
            if ary[i][k] == ary[j][m]
              hantei[i][j] = true #共通言語を話せる
              throw :escape
            end
          end
        end
      end
    end
  end
end
#人同士をとりもつ人がいるか
for i in 1..N
  for j in 1..N
    if i==j
      next
    end
    #第３者
    for k in 1..N
      if i==k || j==k
        next
      end

      if hantei[i][k] && hantei[j][k]
        hantei[i][j] = true
      end
    end
  end
end
catch :escape2 do
  for i in 1..N
    for j in 1..N
      if i==j
        next
      end
      if hantei[i][j] == false
        puts 'NO'
        throw :escape2
      end
    end
  end
  puts 'YES'
end