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.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        try (BufferedReader in =
                new BufferedReader(new InputStreamReader(System.in))) {

            String line;
            line = in.readLine();

            int n = Integer.parseInt(line);

            int[][] sayTable = new int[n][];
            for (int i = 0; i < n; ++i) {
                line = in.readLine();
                int a = Integer.parseInt(line);
                sayTable[i] = new int[n];
                for (int j = 0; j < a; ++j) {
                    line = in.readLine();
                    String[] params = line.split(" ");
                    int x = Integer.parseInt(params[0]) - 1;
                    int y = Integer.parseInt(params[1]);
                    sayTable[i][x] = y + 1;
                }
            }
            int maxHonest = search(sayTable, new int[n], 0);
            System.out.println(maxHonest);
        }
    }

    public static int search(
            int[][] sayTable, int[] honest, int i) {

        if (i >= sayTable.length) {
            if (checkHonestAll(honest, sayTable)) {
                return (int) Arrays.stream(honest)
                        .filter(say -> say == 2)
                        .count();
            } else {
                return 0;
            }
        }

        int[] sayArray = sayTable[i];

        int count = 0;
        int h = honest[i];
        if ((h == 0 || h == 2) && checkHonest(honest, sayArray)) {
            int[] copyHonest = Arrays.copyOf(honest, honest.length);
            setHonest(copyHonest, sayArray);
            copyHonest[i] = 2;
            int c = search(sayTable, copyHonest, i + 1);
            if (count < c) {
                count = c;
            }
        }
        honest[i] = 1;
        int c = search(sayTable, honest, i + 1);
        if (count < c) {
            count = c;
        }
        return count;
    }

    public static boolean checkHonestAll(int[] honest, int[][] sayTable) {
        for (int j = 0; j < sayTable.length; ++j) {
            int[] sayArray = sayTable[j];
            for (int i = 0; i < sayArray.length; ++i) {
                int say = sayArray[i];
                if (say == 0) {
                    continue;
                }
                int h = honest[i];
                if (h == 0) {
                    continue;
                }
                if (h != say) {
                    return false;
                }
            }
            
        }
        return true;
    }
    
    public static boolean checkHonest(int[] honest, int[] sayArray) {
        for (int i = 0; i < sayArray.length; ++i) {
            int say = sayArray[i];
            if (say == 0) {
                continue;
            }
            int h = honest[i];
            if (h == 0) {
                continue;
            }
            if (h != say) {
                return false;
            }
        }
        return true;
    }

    public static void setHonest(int[] honest, int[] sayArray) {
        for (int i = 0; i < sayArray.length; ++i) {
            int say = sayArray[i];
            if (say == 1) {
                honest[i] = 1;
            } else if (say == 2) {
                honest[i] = 2;
            }
        }
    }

}