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 Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(let* ((n (read))
       (m (make-array `(,(1+ n))))
       (ans 0))
  (loop :for i :from 1 :to n
        :do (setf (aref m i) (make-hash-table :size n)))
  (loop :for i :from 1 :to n
        :for a := (read)
        :do (loop :for j :from 1 :to a
                  :for x := (read)
                  :for y := (read)
                  :do (setf (gethash x (aref m i)) y))
        :do (setf (gethash i (aref m i)) 1))

  (loop :for c :from 0 :to (1- (expt 2 n))
        :do (loop :named main
                  :with acc := 0
                  :for i :from 1 :to n
                  :if (/= 0 (logand (expt 2 (1- i)) c))
                  :do (progn
                        (maphash (lambda (j val)
                                   (unless (funcall (if (= val 1) #'/= #'=) 0 (logand (expt 2 (1- j)) c))
                                     (return-from main)))
                                   (aref m i))
                        (incf acc))
                  :finally (setf ans (max acc ans))))
  (format t "~A~%" ans))