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: Accepted)

from sys import stdin, stdout # only need for big input

max_honest = 0
testomonies = []
state = []

def dfs(person):
    global max_honest
    if person >= len(state):
        correctState = True
        for p in range(len(state)):
            if state[p] == 1:
                for t in testomonies[p]:
                    x, y = t
                    if state[x] != y:
                        correctState = False
                        break
        if correctState:
            sum = 0
            for s in state:
                sum += s
            max_honest = max(max_honest, sum)
        return

    state[person] = 0
    dfs(person + 1)

    state[person] = 1 
    dfs(person + 1)
    

def solve():
    global state
    n = int(input())
    for _ in range(n):
        a = int(input())
        t = []
        for _ in range(a):
            x, y = [int(inp) for inp in input().split()]
            t.append((x - 1,y))
        testomonies.append(t)
    # print(testomonies)
    state = [-1] * n
    dfs(0)
    print(max_honest)


def main():
    solve()


if __name__ == "__main__":
    main()