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 Python (3.4.3) (judge verdict: Accepted)

n = int(input())
comments = {}

for i in range(1, n+1):
    ni = int(input())
    comments[i] = [tuple(map(int, input().split())) for _ in range(ni)]

nhonests = [0]

for ibin in (format(i, "b") for i in range(2**n, 2**(n+1))):
    ni_lie, ni = 0, 1
    
    while (not ni_lie) and ni < n+1:        
        for ci in comments[ni]:            
            if int(ibin[ni]) and ci[1] ^ int(ibin[ci[0]]):
                ni_lie += 1
            ### print(ibin, ni, int(ibin[ni]), end=" ") ###
            ### print((ci[0], ci[1]), ci[0], int(ibin[ci[0]]), end=" ") ###
            ### print((ni_lie,)) ###
            
        ni += 1
        
    if not ni_lie:
        nhonests.append(ibin.count("1") - 1)
        ### print(ibin) ###
        
print(max(nhonests))