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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[][] x = new int[n][n];
        int[][] y = new int[n][n];
        
        for (int i = 0; i < n; i++) {
            int a = sc.nextInt();
            for (int j = 0; j < a; j++) {
                x[i][j] = sc.nextInt() - 1;
                y[i][j] = sc.nextInt();
            }
            x[i][a] = 999;
            y[i][a] = 999;
        }
        
        int[] answer = new int[n];
        int max = 0;
        
        for (int i = 0; i < n; i++) {
            answer[i] = 9;
        }
        
        answer[0] = 1;
        int ans1 = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (x[i][j] == 999) break;
                
                if (answer[i] == 1) {
                    if (answer[x[i][j]] == 9) {
                        answer[x[i][j]] = y[i][j];
                    } else if (answer[x[i][j]] != y[i][j]) {
                        ans1 = -1;
                        break;
                    }
                    answer[x[i][j]] = y[i][j];
                } else if (answer[i] == 9) {
                    if (answer[x[i][j]] == 9) {
                        answer[i] = 1;
                        answer[x[i][j]] = y[i][j];
                    } else if (answer[x[i][j]] != y[i][j]) {
                        answer[i] = 0;
                    } else {
                        answer[i] = 1;
                    }
                } else {
                    if (answer[x[i][j]] == 9) {
                        answer[x[i][j]] = 1 - y[i][j];
                    } else if (answer[x[i][j]] == y[i][j]) {
                        ans1 = -1;
                        break;
                    }
                    answer[x[i][j]] = 1 - y[i][j];
                }
            }
            
            if (ans1 == -1) {
                break;
            }
        }
        
        if (ans1 != -1) {
            for (int i = 0; i < n; i++) {
                if (answer[i] == 1) {
                    ans1++;
                }
            }
        }
        
        for (int i = 0; i < n; i++) {
            answer[i] = 9;
        }
        answer[0] = 0;
        int ans2 = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (x[i][j] == 999) break;
                
                if (answer[i] == 1) {
                    if (answer[x[i][j]] == 9) {
                        answer[x[i][j]] = y[i][j];
                    } else if (answer[x[i][j]] != y[i][j]) {
                        ans2 = -1;
                        break;
                    }
                    answer[x[i][j]] = y[i][j];
                } else if (answer[i] == 9) {
                    if (answer[x[i][j]] == 9) {
                        answer[i] = 1;
                        answer[x[i][j]] = y[i][j];
                    } else if (answer[x[i][j]] != y[i][j]) {
                        answer[i] = 0;
                    } else {
                        answer[i] = 1;
                    }
                } else {
                    if (answer[x[i][j]] == 9) {
                        answer[x[i][j]] = 1 - y[i][j];
                    } else if (answer[x[i][j]] == y[i][j]) {
                        ans2 = -1;
                        break;
                    }
                    answer[x[i][j]] = 1 - y[i][j];
                }
            }
            
            if (ans2 == -1) {
                break;
            }
        }
        
        if (ans2 != -1) {
            for (int i = 0; i < n; i++) {
                if (answer[i] == 1) {
                    ans2++;
                }
            }
        }
        
        if (ans1 == -1 || ans2 == -1) {
            System.out.println(0);
        } else {
            System.out.println(Math.max(ans1, ans2));
        }
    }
}