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)

import sys

input = sys.stdin.readline


def main():
    N = int(input())
    xy = {i+1:[] for i in range(N)}
    
    for i in range(N):
        for j in range(int(input())):
            xy[i+1].append(tuple(map(int, input().split())))
            
    ans = 0
    nums = [2**i for i in range(N)]
    for i in range(1, 2**N):
        num = [idx+1 for idx, n in enumerate(nums) if i & n != 0]
        visited = [False] * (N+1)
        A = [None] * (N+1)
        
        f = True
        for i in num: A[i] = True
        
        while num:
            n = num.pop(0)
            if visited[n]: continue
            visited[n] = True
            
            for x, y in xy[n]:
                if A[x] is None: 
                    A[x] = y
                    if y and not visited[x]: num.append(x)
                    
                elif A[x] == y: continue
                else: f = False; break
            if not f: break
        if f: 
            ans = max(ans, sum([a for a in A if not a is None]))
            
    print(ans)

if __name__ == '__main__':
    main()