Problem:
Score : 300 points

Problem Statement

There are N people numbered 1 to N. Each of them is either an honest person whose testimonies are always correct or an unkind person whose testimonies may be correct or not.

Person i gives A_i testimonies. The j-th testimony by Person i is represented by two integers x_{ij} and y_{ij}. If y_{ij} = 1, the testimony says Person x_{ij} is honest; if y_{ij} = 0, it says Person x_{ij} is unkind.

How many honest persons can be among those N people at most?

Constraints

All values in input are integers.

1 \leq N \leq 15

0 \leq A_i \leq N - 1

1 \leq x_{ij} \leq N

x_{ij} \neq i

x_{ij_1} \neq x_{ij_2} (j_1 \neq j_2)

y_{ij} = 0, 1

Input

Input is given from Standard Input in the following format:

N
A_1
x_{11} y_{11}
x_{12} y_{12}
:
x_{1A_1} y_{1A_1}
A_2
x_{21} y_{21}
x_{22} y_{22}
:
x_{2A_2} y_{2A_2}
:
A_N
x_{N1} y_{N1}
x_{N2} y_{N2}
:
x_{NA_N} y_{NA_N}

Output

Print the maximum possible number of honest persons among the N people.

Sample Input 1

3
1
2 1
1
1 1
1
2 0

Sample Output 1

2

If Person 1 and Person 2 are honest and Person 3 is unkind, we have two honest persons without inconsistencies, which is the maximum possible number of honest persons.

Sample Input 2

3
2
2 1
3 0
2
3 1
1 0
2
1 1
2 0

Sample Output 2

0

Assuming that one or more of them are honest immediately leads to a contradiction.

Sample Input 3

2
1
2 0
1
1 0

Sample Output 3

1

Solution in Ruby (2.3.3) (judge verdict: Accepted)

n = gets.chomp.to_i
  
ans = []

n.times do |i|
  ans_count = gets.chomp.to_i
  ans[i] = []
  ans_count.times do |j|
    x, y = gets.chomp.split().map(&:to_i)
    ans[i][j] = [x-1, y == 1]
  end
end

result = 0

catch :finish do
  [true, false].repeated_permutation(n) do |comb|
    catch :next_comb do
      n.times do |i|
        next unless comb[i]
        #i番目の人が正直なとき矛盾するかどうか
        ans[i].each do |an|
          #an[0]番目の人がan[1]だと言っている
          throw :next_comb if comb[an[0]] != an[1] #矛盾していたら終了
        end
      end
      result = comb.count {|c| c }
      throw :finish
    end
  end
end

puts result