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: Time Limit Exceeded)

N = int(input())

state = [[-1] * N for i in range(N)]
for index in range(N):
    Ai = int(input())
    for naka in range(Ai):
        x, y = map(int, input().split()) 
        state[index][x - 1] = y
        # state[index][naka] = [x, y]


# print(state)


maxx = 0
for index in range(2 ** N):
    # print(index)
    person = index
    tempM = 0
    Ai = 0
    ok = 1
    while person > 0:
        if person % 2 == 1:
            tempM += 1
            for i in range(N):
                if state[Ai][i] != -1:
                    # print(str(Ai) + " " + str(i))
                    # print(str(state[Ai][i]) + " " + str((index // (2 ** i)) % 2))
                    # print()
                    if state[Ai][i] != (index // (2 ** i)) % 2:
                        ok = 0
                
        
        person //= 2
        Ai += 1
    
    if ok == 1:
        maxx = max(maxx, tempM)

print(maxx)