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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        Map<Integer, Person> m = new HashMap<>();

        for (int i = 0; i < n; i++) {
            m.put(i + 1, new Person());
        }

        for (int i = 0; i < n; i++) {
            int q = sc.nextInt();
            for (int j = 0; j < q; j++) {
                int key = sc.nextInt();
                int isHonest = sc.nextInt();
                Person person = m.getOrDefault(key, new Person());
                if (isHonest == 1) {
                    person.isHonest = true;
                }
                if (isHonest == 0) {
                    person.isLier = false;
                }

                m.put(key, person);
            }
        }

        int ans = 0;
        int tmp = 0;
        for (Entry<Integer, Person> e : m.entrySet()) {
            Boolean isH = e.getValue().isHonest;
            Boolean isL = e.getValue().isLier;
            if (null == isH && null == isL) {
                ans++;
            } else if (null == isH && false == isL) {
                tmp++;
            } else if (true == isH && null == isL) {
                ans++;
            } else if (true == isH && false == isL) {
                continue;
            }
        }

        System.out.println(ans + tmp / 2);
    }

    static class Person {
        Boolean isHonest;
        Boolean isLier;

        @Override
        public String toString() {
            return this.isHonest + ":" + this.isLier;
        }
    }
}