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) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int[] A = new int[N];
        ArrayList<int[]> xx = new ArrayList<int[]>();
        ArrayList<int[]> yy = new ArrayList<int[]>();
        for (int i=0;i<N;i++) {
            A[i] = Integer.parseInt(sc.next());
            int[] x = new int[A[i]];
            int[] y = new int[A[i]];
            for (int j=0;j<A[i];j++) {
                x[j] = Integer.parseInt(sc.next())-1;
                y[j] = Integer.parseInt(sc.next());
            }
            xx.add(x);
            yy.add(y);
        }

        int ans = 0;
        loop:for (int i=0;i<1<<N;i++) {
            int[] array = new int[N];
            int tmp = i;
            int sum = 0;
            for (int j=0;j<N;j++) {
                if ((tmp&1)==1) {
                    array[j]=1;
                    sum++;
                }
                tmp=tmp>>1;
            }
            // System.out.println(sum);
            // System.out.println(Arrays.toString(array));
            for (int k=0;k<N;k++) {
                int[] xxx = xx.get(k);
                int[] yyy = yy.get(k);
                if (array[k]==0) {
                    for (int l=0;l<A[k];l++) {
                        if (array[xxx[l]]==yyy[l]) sum=0;
                    }
                } else { // array[k]=1
                    for (int l=0;l<A[k];l++) {
                        if (array[xxx[l]]!=yyy[l]) sum=0;
                    }
                }
            }
            ans = Math.max(ans, sum);
        }
        System.out.println(ans);
    }
}