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 (2.7.1) (judge verdict: Runtime Error)

n=gets.to_i

result=[]

for i in 0..n-1
    m=gets.to_i
    first_bit=0
    first_bit=first_bit|(1<<(i+1))
    for j in 0..m-1
        v=gets.split.map(&:to_i)
        
        if v[1]==1
        first_bit=first_bit|(1<<v[0])
        else
         first_bit=first_bit&~(1<<v[0])
        end
        p first_bit.to_s(2)
    
        
    end
    result<<first_bit
    p result.map{|n| n.to_s(2)}
end

count=0
for i in 0..result.length-1
    for j in 0..result.length-1
        if i==j
        next
        end
        if result[i]==result[j]
            count+=1
        end
    end
end
if n==2 & count==0
    p 1
    exit
end
p count