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

fscanf(STDIN, "%d", $n);
$a_arr = [];
$x_arr = [];
$y_arr = [];
for ($i = 0; $i < $n; ++$i) {
    fscanf(STDIN, "%d", $a);
    $a_arr[] = $a;

    for ($j = 0; $j < $a; ++$j) {
        fscanf(STDIN, "%d %d", $x, $y);
        $x_arr[$i][] = $x;
        $y_arr[$i][] = $y;
    }
}

$max = 0;
for ($bit = 0; $bit < (1 << $n); ++$bit) {
    $honests = [];
    for ($i = 0; $i < $n; ++$i) {
        if ($bit & (1 << $i)) {
            $honests[] = $i;
        }
    }

    $flg = true;
    foreach ($honests as $honest) {
        for ($j = 0; $j < $a_arr[$honest]; ++$j) {
            if (
                ($y_arr[$honest][$j] == 1 && !in_array($x_arr[$honest][$j] - 1, $honests))
                || ($y_arr[$honest][$j] == 0 && in_array($x_arr[$honest][$j] - 1, $honests))
            ) {
                $flg = false;
                break 2;
            }
        }
    }

    if ($flg) {
        $max = max($max, count($honests));
    }
}

echo $max;