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)

require 'set'
N = gets.to_i

tuples = N.times.flat_map.with_index(1) { |_, id|
  gets.to_i.times.map {
    other, b = gets.chomp.split(' ').map(&:to_i)
    [id, other, b]
  }
}

layers = Set.new
semi_layers = {}

tuples.each do |(id, other, b)|
  if b == 1 && tuples.include?([other, id, 0])
    layers << id
  end
end

tuples.each do |(id, other, b)|
  if b == 0 && !tuples.include?([other, id, 1])
    unless layers.include?(other)
      semi_layers[id] ||= Set.new
      semi_layers[id] << other
    end

    unless layers.include?(id)
      semi_layers[other] ||= Set.new
      semi_layers[other] << id
    end
  end
end

semi_layers.sort_by { |_, v| v.size }.reverse.each do |id, others|
  next unless semi_layers.has_key?(id)

  layers << id
  semi_layers.delete(id)

  others.each do |other|
    semi_layers.delete(other)
  end
end

puts N - layers.size