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: Wrong Answer)

import copy

N = int(input())
X = []
for i in range(N):
  A = int(input())
  X.append([])
  for _ in range(A):
    X[i].append(list(map(int, input().split())))

print(X)

def rec(condition, i):
  if i==N:
    return condition.count(1)
  _X = X[i]
  _condition = copy.copy(condition)
  through_condition = copy.copy(condition)
  through_condition[i] = 0
  if condition[i]==0:
    return rec(copy.copy(through_condition), i+1)
  for x in _X:
    if _condition[ x[0]-1 ] == -1:
      _condition[ x[0]-1 ] = x[1]
    elif _condition[ x[0]-1 ] != x[1]:
      return 0 if _condition[i]==1 else rec(copy.copy(through_condition), i+1)
  _condition[i] = 1
  return max(rec(copy.copy(through_condition), i+1), rec(copy.copy(_condition), i+1))

print( rec([-1 for _ in range(N)], 0) )