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)

def eval(i, tmp, a)
  if tmp[i] == 1
    a[i].each do |aa|
      index = aa[0] - 1
      if tmp[index] == nil
        tmp[index] =  aa[1]
        eval(index, tmp, a)
      elsif tmp[index] != aa[1]
        raise "mujun"
      end
    end
  else
    a[i].each do |aa|
      index = aa[0] - 1
      if tmp[index] == nil
        tmp[index] =  aa[1] == 0 ? 1: 0
        eval(index, tmp, a)
      elsif tmp[index] == aa[1]
        raise "mujun"
      end
    end
  end
end

n = gets.to_i

a = Array.new(n).map{|_| Array.new}

(0...n).each do |i|
  ai = gets.to_i
  (1..ai).each do |_|
    a[i] << gets.chomp.split.map(&:to_i)
  end
end

ans = 0
(0...n).each do |i|
  tmp = Array.new(n)
  tmp[i] = 1
  begin
    eval(i, tmp, a)
    honests = tmp.select{|i| i == 1}.length
    ans = [ans, honests].max
  rescue RuntimeError
  end
end

p ans