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
  list($n) = explode(" ", trim(fgets(STDIN)));

  $b = [];
  for ($i=0; $i<$n; $i++) {
    list($a[$i]) = explode(" ", trim(fgets(STDIN)));
    $b[$i] = [];
    for ($j=0; $j<$a[$i]; $j++){
      list($y, $z) = explode(" ", trim(fgets(STDIN)));
      $b[$i][$y] = $z;
    }
  }

  $max_honest_cnt = 0;

  // bit全探索 (2^n通り)
  for ($bit=0; $bit<(1<<$n); $bit++) {
    // 初期化
    $honest_cnt = 0;
    $valid = true;
    // 1～N番目までをチェック
    for ($i=1; $i<=$n; $i++) {
      // i番目が正直者の場合
      if($bit & (1<<($i-1))){
        $honest_cnt++;
//        if($bit === 7){
//          echo $honest_cnt.PHP_EOL;
//        }

        // i番目の証言で矛盾がないかチェック
        foreach($b[$i-1] as $key => $value){
          // 正直者が正直者リストの中にいない
          if($value == 1){
            if(!($bit & (1<<($key-1)))) {
              $valid = false;
              break;
            }
          }
          // 不親切が正直者リストの中にいる
          else {
            if($bit & (1<<($key-1))) {
              $valid = false; 
              break;
            }
          }
        }
        if(!$valid){
          break;
        }
      }
    }
    // 矛盾なし
    if($valid){
//      echo $bit.PHP_EOL;
      $max_honest_cnt = max($max_honest_cnt, $honest_cnt);
    }
  }

  echo $max_honest_cnt;