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)

import numpy as np

N = int(input())
A = [0]*N
X = np.zeros([N,N],dtype=int)
Y = np.zeros([N,N],dtype=int)

for n in range(N):
    A[n] = int(input())
    for a in range(A[n]):
        X[n][a], Y[n][a] = list(map(int,input().split()))

def counter( x ):
    if x == 0:
        return 0
    return counter( x >> 1 ) + (x & 1)

ans = 0
       
for bits in range( 1, 1<<N ):
    ok = True
    for i in range( 0, N ):
        if not ( bits & (1 << i) ):
            continue
        for j in range( 0, A[i] ):
            if (( bits >> (X[i][j]-1) ) & 1) ^ Y[i][j]:
                ok = False
    if ok:
        ans = max( ans, counter(bits) )
        
print(ans)