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 (3.8.2) (judge verdict: Accepted)

from collections import deque


def do_code():
    num = int(input())
    matrix = [[2] * (num + 1) for _ in range(num + 1)]
    honests = [set() for _ in range(num + 1)]
    unkinds = [set() for _ in range(num + 1)]
    # 人iは1〜Nのためインデックス0は使わずに1~Nで使うようにする
    for n in range(1, num + 1):
        u = set()
        h = set()
        ans = int(input())
        for a in range(ans):
            x, y = map(int, input().split(" "))
            if y == 1:
                h.add(x)
            else:
                u.add(x)
        honests[n] = h
        unkinds[n] = u
    count = 0
    for n in range(1, 2 ** num):
        honest_set = set()
        for j in range(num):
            t = 2 ** j
            if n & t == t:
                honest_set.add(j + 1)
        th = set()
        tu = set()
        queue = deque(honest_set)
        visited = set()
        while len(queue) > 0:
            t = queue.popleft()
            if t in visited:
                continue
            visited.add(t)
            queue.extend(honests[t])
            th |= honests[t]
            tu |= unkinds[t]
        if not th.isdisjoint(tu):
            # 正直者と仮定した人の証言を集めた場合にhonest && unkindな人がいる＝矛盾
            continue
        if not honest_set.isdisjoint(tu):
            continue
        honest = max(len(th), len(honest_set))
        count = max(count, honest)
    print(count)


if __name__ == '__main__':
    do_code()