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.*;

public class Main {
    static int n;
    static int [][] all;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        all = new int[n][n];
        for (int i = 0; i < n; i++) {
            int a = sc.nextInt();
            Arrays.fill(all[i], -1);
            for (int j = 0; j < a; j++) {
                all[i][sc.nextInt() - 1] = sc.nextInt();
            }
        }
        int[] arr = new int[n];
        Arrays.fill(arr, -1);
        System.out.println(search(0, arr));
    }
    
    static int search(int idx, int[] arr) {
        if (idx >= n) {
            return 0;
        }
        int ans = Integer.MIN_VALUE;
        if (arr[idx] != 1) {
            int[] next = (int[])(arr.clone());
            next[idx] = 0;
            ans = search(idx + 1, next);
        }
        if (arr[idx] != 0) {
            int[] next = (int[])(arr.clone());
            next[idx] = 1;
            boolean flag = true;
            for (int i = 0; i < n; i++) {
                int x = all[idx][i];
                if (x != -1) {
                    if (next[i] != -1 && next[i] != x) {
                        flag = false;
                        break;
                    }
                    next[i] = x;
                }
            }
            if (flag) {
                ans = Math.max(ans, search(idx + 1, next) + 1);
            }
        }
        return ans;
        
    }
}