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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$n = intval(fgets(STDIN));
for($i = 0; $i < $n; $i++){
  $a[$i] = intval(fgets(STDIN));
  for($j = 0; $j < $a[$i]; $j++){
    fscanf(STDIN, '%d%d', $b, $c);
    $map[$i][$b-1] = $c; 
  }
}
$max = 0;
for($i = 0, $I = 2**$n; $i < $I; $i++){
  $bits = sprintf('%0'.$n.'b', $i);
  foreach($map as $from => $row){
    if($bits[$from] === '1'){ 
      foreach($row as $to => $v){
        if($bits[$to] != $v){ 
          continue 3;
        }
      }
    }
  }
  $sum = 0;
  for($j = 0; $j < $n; $j++){
    $sum+=$bits[$j];
  }
  $max = max($max, $sum);
}
echo $max;