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 (7.3.0) (judge verdict: Wrong Answer)

N = int(input())

S_list = [[] for _ in range(N)]
for i in range(N):
    A = int(input())
    if A == 0:
        S_list.append([])
    else:
        for a in range(A):
            S_list[i].append(list(map(int, input().split())))
ans = 0
for i in range(1 << N):
    A_list = [0 for _ in range(N)]
    for j in range(N):
        if (i >> j) & 1 == 1:
            A_list[j] = 1

    bool = True
    for a in range(len(A_list)):
        if S_list[a] == []:
            continue
        for s in range(len(S_list[a])):
            if A_list[a] == 0:
                if A_list[S_list[a][s][0]-1] == S_list[a][s][1]:
                    bool = False
                    break
            else:
                if A_list[S_list[a][s][0]-1] != S_list[a][s][1]:
                    bool = False
                    break
    if bool:
        ans = max(ans, sum(A_list))
print(ans)