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: Accepted)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    int N = scanner.nextInt();
    List<Statement>[] statements = new List[N];
    for (int i = 0; i < N; i++) {
      statements[i] = new ArrayList<>();
      int a = scanner.nextInt();
      for (int j = 0; j < a; j++) {
        int x = scanner.nextInt();
        int y = scanner.nextInt();
        statements[i].add(new Statement(x - 1, y == 1));
      }
    }

    int max = 0;
    loop:
    for (int i = 0; i < (1 << N); i++) {
      for (int j = 0; j < N; j++) {
        if (((1 << j) & i) != 0) {
          for (Statement s : statements[j]) {
            if (((1 << s.who) & i) == 0 && s.honest) continue loop;
            if (((1 << s.who) & i) != 0 && !s.honest) continue loop;
          }
        }
      }
      max = Math.max(max, Integer.bitCount(i));
    }
    System.out.println(max);
  }

  private static class Statement {
    final int who;
    final boolean honest;

    private Statement(int who, boolean honest) {
      this.who = who;
      this.honest = honest;
    }
  }
}