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: Runtime Error)

#!/usr/bin/env python3]
import sys
sys.setrecursionlimit(2000)

N = int(input())
syogen = []
for i in range(N):
    N_a = int(input())
    syogen_a = []
    for _ in range(N_a):
        x, y = input().split()
        syogen_a.append([int(x) - 1, int(y)])
    syogen.append(syogen_a)


def syojiki(i):
    for x, y in syogen[i]:
        if y == 1:
            syojiki_list.append(x)
            if len(syojiki_list) >= N:
                return
            syojiki(x)


def check_syojiki(syojikitati):
    d = {}
    for s in range(N):
        if not (s in syojikitati):
            d[s] = 0

    for s in syojikitati:
        d[s] = 1
        for x, y in syogen[s]:
            if d[x] != y:
                return False
            else:
                d[x] = y
    return True


max_syojiki = 0

for i in range(2 ** N):
    d = {}
    syojiki_list = []
    for j in range(N):
        if (i >> j) & 1:
            syojiki_list.append(j)
            syojiki(j)
    syojiki_list = list(set(syojiki_list))
    if check_syojiki(syojiki_list):
        max_syojiki = max(max_syojiki, len(syojiki_list))

print(max_syojiki)