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: Runtime Error)

n = gets.to_i
a = [0, 1]
array = a.repeated_permutation(n).to_a

shogens = []
for i in 1..n
  shogen_ctn = gets.to_i
  for j in 1..shogen_ctn
    shogens.push(gets.split(" ").map(&:to_i))
  end
end

ctn = []
for i in 0..array.length-1
 # p array[i]
  #p shogens
  j = 0
  while j <= n-1
    if array[i][j] == 0 && shogens[j][1] == 0
      shogens[j][1] = 1
    elsif array[i][j] == 0 && shogens[j][1] == 1
      shogens[j][1] = 0
    end
    j += 1
  end
  new_shogens = shogens.sort
  k = 1
  while k <= n 
    if new_shogens.uniq.group_by{|item| item[0] == k}[true] != nil && new_shogens.uniq.group_by{|item| item[0] == k}[false] != nil
      if new_shogens.uniq.group_by{|item| item[0] == k}[true].length == 1 && new_shogens.uniq.group_by{|item| item[0] == k}[false].length == 1
        ctn << new_shogens.uniq.group_by{|item| item[0] == k}[true][0][1] + new_shogens.uniq.group_by{|item| item[0] == k}[false][0][1]
      end
    end
    k += 1
  end
end

if ctn == []
  puts 0
else
  puts ctn.max
end