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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
from itertools import product
#from collections import defaultdict
input = sys.stdin.readline
def main():
    N = int( input())
    A = [[0]*N for _ in range(N)]
    C = [0]*N
    for i in range(N):
        C[i] = int( input())
        for _ in range(C[i]):
            x, y = map( int, input().split())
            A[i][x-1] = -1+y*2
    ans = 0
    T = [-1, 1]
    for P in product( range(-1, 2, 2), repeat = N):
        check = True
        for i in range(N):
            if P[i] == -1:
                continue
            for j in range(N):
                if A[i][j] == 0:
                    continue
                if A[i][j]*P[i] != P[j]:
                    check = False
                    break
        if check:
            if ans < (sum(P) + N)//2:
                ans = (sum(P) + N)//2
    print(ans)
if __name__ == '__main__':
    main()