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: Wrong Answer)

N = int(input())
info = [[] for _ in range(N)]
true =  [[] for _ in range(N)]

for i in range(N):
    for _ in range(int(input())):
        x, y = map(int, input().split())
        info[x - 1].append(y)
        if y == 1:
            true[x - 1].append(i)

flag = False
for i in info:
    if i.count(0) > 0:
        flag = True
if flag is False: # 不親切な人は一人もいない
    print(N)
    exit()

def detect_lier(j): # jを不親切な人とする
    if j in lier:
        return
    lier.append(j)
    for t in true[j]:
        detect_lier(t) # jを正直者だと言った人も不親切な人
    
    return lier

ans = False

for i in range(N):
    lier = []
    detect_lier(i)
    if ans is not False:
        ans = max(ans, N - len(set(lier)))
    else:
        ans = N - len(set(lier))

print(ans)