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) {
        // C - HonestOrUnkind2

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt(); // 人数
        int[] a = new int[n]; // 証言数
        int[][] x = new int[n][n]; // 誰に対して？
        int[][] y = new int[n][n]; // 証言
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            for (int j = 0; j < a[i]; j++) {
                x[i][j] = sc.nextInt();
                y[i][j] = sc.nextInt();
            }
        }
        //        System.out.println("x=" + Arrays.deepToString(x));
        //        System.out.println("y=" + Arrays.deepToString(y));

        ArrayList<int[]> ptn = new ArrayList<>();
        for (int j = 0; j < 2; j++) {
            setPtn(0, j, new int[n], ptn);
        }

        int max = 0;
        int count = 0;
        for (int[] idx : ptn) {
            //            System.out.println("idx=" + Arrays.toString(idx));
            count = 0;
            for (int i = 0; i < n; i++) {
                //                System.out.println("idx[i]=" + idx[i] + " (i=" + i + ")");
                if (idx[i] == 0) { // 不親切な人のときバイパス
                    continue;
                }
                for (int j = 0; j < n; j++) {
                    //                    System.out.println("x[i][j]=" + x[i][j] + " (i=" + i + " ,j=" + j + ")");
                    //                    System.out.println("y[i][j]=" + y[i][j] + " (i=" + i + " ,j=" + j + ")");
                    if (x[i][j] == 0) {
//                        System.out.print("count:");
//                        System.out.println("idx=" + Arrays.toString(idx));
                        count++;
                        break;
                    } else {
                        //                        System.out.println("idx[x[i][j] - 1]=" + idx[x[i][j] - 1]);
                        if (idx[x[i][j] - 1] == y[i][j]) {
//                            System.out.println("x[i][j]=" + x[i][j] + " (i=" + i + " ,j=" + j + ")");
//                            System.out.println("y[i][j]=" + y[i][j] + " (i=" + i + " ,j=" + j + ")");
                        } else {
                            i = n;
                            count = 0;
                            break;
                        }
                    }
                }
            }
            if (max < count)
                max = count;
        }

        System.out.println(max);
    }

    static void setPtn(int d, int c, int[] idx, List<int[]> ptn) {
        idx[d] = c;
        if (idx.length - 1 > d) {
            for (int l = 0; l < 2; l++) {
                setPtn(d + 1, l, idx, ptn);
            }
        } else {
            int[] tmpidx = idx.clone();
            ptn.add(tmpidx);
        }
    }

}