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: Wrong Answer)

N = gets.to_i
# 人ごとの証言の数
a = []
# 証言
s = {}
N.times do |i|
  a[i] = gets.to_i
  # 人iの証言
  s[i+1] = []
  a[i].times do |j|
    # 人iのj番目の証言
    s[i+1][j] = gets.split.map(&:to_i)
  end
end

ans = 0
(1<<N).times do |i|
  # puts "i=#{i.to_s(2)}"
  cnt = 0
  # 一人ずつ矛盾がないかチェック
  continue = false
  s.each do |key, t|
    t.each do |u|
      # 矛盾が生じていないかチェック
      # keyは証言している人, u[0]は証言されている人
      # puts "証言：人#{u[0]}=#{u[1]==i[key-1] ? 1 : 0}"
      if not i[u[0]-1] == (u[1]==i[key-1] ? 1 : 0)
        # 矛盾があった場合，次のiにいく
        # puts "矛盾\n"
        continue = true
        break
      end
    end
    if continue
      break
    end
  end
  # 矛盾がなかった場合
  if continue == false
    cnt = i.to_s(2).count('1')
    ans = [cnt, ans].max
    # puts "#{ans}\n"
  end
end

puts ans