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.*;

class Main{
    static List<Map<Integer, Integer>> shougen = new ArrayList<>();
    static int res = 0;
    static int n = 0;
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();


        Integer[] a = new Integer[n];
        for(int i=0;i<n;i++){
            a[i] = -1;
            int shougen_num = sc.nextInt();
            Map<Integer, Integer> one_shougen = new HashMap<>();
            for(int j=0;j<shougen_num;j++){
                Integer key = sc.nextInt();
                Integer val = sc.nextInt();
                one_shougen.put(key-1, val);
            }
            shougen.add(one_shougen);
        }

        a[0] = 1;
        saiki(a, 0);
        a[0] = 0;
        saiki(a, 0);

        System.out.println(res);

    }

    static void saiki(Integer[] a, Integer number){
        if(number==a.length){
            int count = 0;
            for(int i=0;i<n;i++){
                if(a[i]==1)count++;
                // System.out.print(a[i] + " ");
            }
            if(res < count){
                res = count;
            }
            // System.out.println(count);
            return;
        }

        Map<Integer, Integer> one_shougen = new HashMap<>();
        one_shougen = shougen.get(number);        
        if(a[number]==1){
            for(Integer key : one_shougen.keySet()){
                Integer val = one_shougen.get(key);
                if(a[key]==-1){
                    a[key] = val;
                }
                else if(a[key]!=val){
                    return;
                }
            }
            saiki(a, number+1);
        }
        else if(a[number]==0){
            for(Integer key : one_shougen.keySet()){
                Integer val = one_shougen.get(key);
                // 証言を反転
                if(val==1){
                    val = 0;
                }
                else{
                    val = 1;
                }
                if(a[key]==-1){
                    a[key] = val;
                }
                else if(a[key]!=val){
                    return;
                }
            }
            saiki(a, number+1);
        }
        else{
            a[number] = 1;
            saiki(a, number);
            a[number] = 0;
            saiki(a, number);
        }
    }
}