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.*;
import java.io.*;
public class Main {
    static int[][] A;
    public static void main(String[] args) throws Exception {
        InputStreamReader r = new InputStreamReader(System.in);
        int N = nextInt(r);
        A = new int[N][N];
        for (int i = 0; i < N; i++) {
            int Ai = nextInt(r);
            for (int j = 0; j < Ai; j++) {
                int x = nextInt(r);
                int y = nextInt(r);
                A[i][x-1] = y == 1 ? 1 : -1;
            }
        }

        int ans = 0;
        int pow = pow(N);
        for (int i = 0; i < pow; i++) {
            int[] d = set(N, i);
            boolean ok = true;
            ok = check(N, d);
            ok = check(N, d);
            if (ok) {
                int c = 0;
                for (int j = 0; j < N; j++) {
                    if (d[j] == 1) {
                        c++;
                    }
                }
                ans = Math.max(ans, c);
            }
        }
        System.out.println(ans);
    }

    public static int nextInt(InputStreamReader r) throws Exception {
        String str = "";
        while (true) {
            int c = r.read();
            if (c == 32 || c == 10 || c == -1) {
                break;
            }
            str += (char)c;
        }
        return Integer.parseInt(str);
    }

    public static int pow(int N) {
        return N == 0 ? 1 : 2 * pow(N-1);
    }

    public static int[] set(int N, int i) {
        int[] res = new int[N];
        for (int j = 0; j < N; j++) {
            res[j] = i % 2 == 1 ? 1 : 0;
            i = i / 2;
        }
        return res;
    }

    public static boolean check(int N, int[] d) {
        for (int j = 0; j < N; j++) {
            if (d[j] == 1) {
                for (int k = 0; k < N; k++) {
                    if (A[j][k] == 1) {
                        if (d[k] == -1) {
                            return false;
                        } else {
                            d[k] = A[j][k];
                        }
                    }
                    if (A[j][k] == -1) {
                        if (d[k] == 1) {
                            return false;
                        } else {
                            d[k] = A[j][k];
                        }
                    }
                }
            }
        }
        return true;
    }
}