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)

from itertools import product

import numpy as np
n = int(input())
syougen = np.zeros([n, n])

for i in range(n):
    a = int(input())
    for _ in range(a):
        x, y =  list(map(int, input().split()))
        syougen[i, x-1] = 2 * y - 1

score = 0
for binary in product([1, 0], repeat=n):
    s = syougen.copy()
    s[np.array(binary) == 0] *= 0
    
    flag = True
    ma = np.max(s, axis = 0)
    mi = np.min(s, axis = 0)
    if np.max(ma - mi) == 2:
        flag = False
    if np.min(np.array(binary) - ma) == -1:
        flag = False
    if np.max(np.array(binary) -mi) == 2:
        flag = False
        
    if flag:
#         print(binary)
        if sum(binary) > score:
            score = sum(binary)
            break
print(score)