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 (2.4.0) (judge verdict: Runtime Error)

from collections import Counter, defaultdict
import sys
sys.setrecursionlimit(10 ** 5 + 10)
# input = sys.stdin.readline
from math import factorial
import heapq, bisect
import math
import itertools
import queue
from collections import deque
from fractions import Fraction


def ternary (n, k, length):
    if n == 0:
        nums = ['0' for i in range(length)]
        nums = ''.join(nums)
        return nums
    nums = ''
    while n:
        n, r = divmod(n, k)
        nums += str(r)
    nums = nums[::-1]
    nums = nums.zfill(length)
    return nums

def main():
    num = int(input())
    say_count = []
    say_data = []
    for i in range(num):
        aaa = int(input())
        say_count.append(aaa)
        data = [list(map(int, input().split())) for i in range(aaa)]
        say_data.append(data)


    ans = 0
    for i in range(2 ** num):
        bin_data = list(map(int, ternary(i, 2, num)))
        kari_ans = bin_data.count(1)

        people_flg = [-1 for i in range(num)]
        dame_flg = 0
        for j in range(num):
            if people_flg[j] == -1:
                people_flg[j] = bin_data[j]
            else:
                if people_flg[j] != bin_data[j]:
                    dame_flg = 1

            if people_flg[j] == 0:
                continue

            for k in range(say_count[j]):
                people, flg = [say_dataj][k]
                people -= 1
                if people_flg[people] == -1:
                    people_flg[people] = flg
                else:
                    if people_flg[people] != flg:
                        dame_flg = 1

            if dame_flg:
                break
        if dame_flg:
            continue
        ans = max(ans, kari_ans)

    print(ans)






if __name__ == '__main__':
    main()