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 = trim(fgets(STDIN));

for($i=1; $i<=$n; $i++){
  $a = trim(fgets(STDIN));
  for($j=1; $j<=$a; $j++){
    $tes = explode(' ', trim(fgets(STDIN)));
  	$t[$i][$j] = $tes;
  }
}

for($i=2**$n-1; $i>=0; $i--){
  
    $p = str_pad(decbin($i), $n, 0, STR_PAD_LEFT);
    
    $pt = array_count_values(str_split($p));
    isset($pt[1])? $pc = $pt[1] : $pc = 0;
      
    $hc = 0;
    for($j=1; $j<=$n; $j++){      
      $jj = $j-1;
      if ($p[$jj] == 1){        
        $tc = 0;        
        foreach($t[$j] as $k=>$v){
          $vp = $v[0]-1;
          $vv = $v[1];          
          if ($p[$vp] == $vv) $tc++;          
        }        
        if ($tc == count($t[$j])) $hc++;         
      }      
    }
  
    if ($hc == $pc) break;
    
}

echo $hc;

?>