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)

#!/usr/bin/env ruby
# coding: utf-8

class Man
  @@db = []
  def self.db
    @@db
  end

  def initialize(i)
    @id = i
    @@db[i] = self
    @log = ARGF.gets.to_i.times.map do
      x, y = ARGF.gets.split.map(&:to_i)
      [x-1, y==1]
    end
    @check = nil
    @honor = nil
  end

  attr_reader :id, :log
  attr_accessor :check, :honor

  def self.count
    @@db.map {|p| p.ok }.inject(:+)
  end

  def ok
    $stderr.puts "XX check=#{self.honor}"
    return 0 if self.honor == false
    queue = [self]
    while man = queue.shift
      man.log.each do |log|
        $stderr.puts "XX check #{man.id}: #{log}"
        peer = Man.db[log[0]]
        if log[1]
          if peer.honor == false
            self.clear
            self.check = false
            self.honor = false
            $stderr.puts "XX peer NG1 #{[peer]}"
            return 0
          end
          if peer.honor == nil
            peer.check = true
            peer.honor = true
            queue.push(peer)
          end
        else
          if peer.honor == true
            self.clear
            self.check = false
            self.honor = false
            $stderr.puts "XX peer NG2 #{[peer]}"
            return 0
          end
          if peer.honor == nil
            peer.check = true
            peer.honor = false
          end
        end
        $stderr.puts "XX peer #{[peer]}"
      end
    end
    $stderr.puts "XX check #{Man.db}"
    reset
    $stderr.puts "XX check #{Man.db}"
    return 1
  end

  def clear
    @@db.each do |man|
      if man.check
        man.check = nil
        man.honor = nil
      end
    end
  end

  def reset
    @@db.each do |man|
      man.check = nil
    end
  end
end

ARGF.gets.to_i.times.each do |i|
  Man.new(i)
end

puts Man.count