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: Wrong Answer)

<?php
$n = (int)trim(fgets(STDIN));

$comments = [];
for ($i=1; $i <= $n; $i++) { 
	$comments[$i] = [];
	$a = (int)trim(fgets(STDIN));
	for ($j=0; $j < $a; $j++) { 
		$input = explode(' ', trim(fgets(STDIN)));
		$x = (int)$input[0];
		$y = (int)$input[1];
		$comments[$i][] = [$x, $y];
	}
}
// 人nが正直者だとして、矛盾しない人々の集合をそれぞれ求める
$persons = [];
$honset_sums = [];
for ($i=1; $i <= $n; $i++) { 

	$persons[$i] = [];
	$honset_sums[$i] = 0;
	$my_honest_cmt = 0;

	$list = [];
	foreach ($comments[$i] as $cmt) {
		$list[$cmt[0]] = $cmt[1];
		$my_honest_cmt += $cmt[1];
	}
	for ($j=1; $j <= $n; $j++) { 
		$no_diff = true;
		if ($i == $j || (isset($list[$j]) && $list[$j] == 0)) {
			continue;
		}
		foreach ($comments[$j] as $cmt) {
			if (isset($list[$cmt[0]]) && $list[$cmt[0]] != $cmt[1]) {
				$no_diff = false;
				break;
			}
		}
		if ($no_diff) {
			$persons[$i][] = $j;
			foreach ($comments[$j] as $cmt) {
				$list[$cmt[0]] = $cmt[1];
			}
		}
	}
	if ((isset($list[$i]) && $list[$i] == 0) || count($persons[$i]) == 0) {
		$honset_sums[$i] = 0;
		//正直者に関する証言がない場合、自分は正直者として扱う
		if ($my_honest_cmt == 0) {
			$honset_sums[$i] = 1;
		}
	} else {
		foreach ($list as $k => $v) {
			// echo $i . ": " . $k . " => " . $v . PHP_EOL;
			$honset_sums[$i] += $v;
		}
		if (!isset($list[$i])) {
			$honset_sums[$i] += 1;
		}
	}
	// var_dump($persons[$i]);
	// var_dump($list);
}

echo max($honset_sums);