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 1.1.14) (judge verdict: Wrong Answer)

(defun make-init-array (i n)
  (let ((result (make-array n :initial-element -1)))
    (setf (aref result i) 1)
    result))

(defun solve-1 (i n infos array)
  (if (= (aref array i) -1)
      (let ((array2 (copy-seq array)))
        (setf (aref array2 i) 1)
        (handler-case (progn (solve-1 i n infos array2)
                             (setf array array2))
          (error () (setf (aref array i) 0))))
      (let ((honestp (= (aref array i) 1))
            (says (nth i infos)))
        (loop for (x . y) in says
              do (cond
                   ((= (aref array (1- x)) -1)
                    (setf (aref array (1- x))
                          (if honestp
                              y
                              (if (= y 0) 1 0)))
                    (solve-1 (1- x) n infos array))
                   ((= (aref array (1- x)) (if honestp y (if (= y 0) 1 0))))
                   (t
                    (error "Conflict"))))))
  (let ((next (position-if (lambda (x) (= x -1)) array)))
    (if next
        (solve-1 next n infos array)
        array)))

(defun solve (n infos)
  (loop for i from 0 below n
        for result = (handler-case (solve-1 i n infos (make-init-array i n))
                       (error () nil))
        maximize (if result
                     (count 1 result :test #'=)
                     0)))

#-swank
(let* ((n (read))
       (infos (loop repeat n
                    collect (let ((m (read)))
                              (loop repeat m
                                    collect (cons (read) (read)))))))
  (format t "~S~%" (solve n infos)))