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: Accepted)

import math
import sys

stdin = sys.stdin

ns = lambda: stdin.readline().rstrip()
ni = lambda: int(stdin.readline().rstrip())
nm = lambda: map(int, stdin.readline().split())
nl = lambda: list(map(int, stdin.readline().split()))
mod = 10**9 + 7 
sys.setrecursionlimit(1000010)

s = []
N = int(input())
A=[]
Rules=[]

def check():
    for i in range(len(Rules)):
        if s[i] != True:
            continue
        r = Rules[i]
        for rr in r:
            (x,y) = rr
            if y == 1:
                if s[x -1 ] == False:
                    return False
            else:
                if s[x-1] == True:
                    return False
            # print(rr)
    return True

for _ in range(N):
    a = ni()
    A.append(a)
    r = []
    for _ in range(a):
        rr = nl()
        r.append(rr)
    Rules.append(r)

# print(A,Rules)

l = 2 **N 
maxgood = 0
for i in range(1,l ):
    s=[]
    ix = i 
    good = 0
    for _ in range(N):
        if ix %2 != 0:
            good += 1
        s.append(ix%2 !=0 )
        ix = ix //2
    # print(good,s)
    if good > maxgood:
        if check():
            maxgood = good
print(maxgood)