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.io.InputStream;
import java.io.PrintStream;
import java.util.*;
import java.util.Map.Entry;

public class Main {
    public static void main(String[] args) throws Exception {
        solve(System.in, System.out);
    }

    static void solve(InputStream is, PrintStream os) {
        // Your code here!
        Scanner scan = new Scanner(is);
        HashMap<Integer, HashMap<Integer, Integer>> map = new HashMap<>();
        int N = scan.nextInt();
        for(int i = 0; i < N; i++) {
            int A = scan.nextInt();
            HashMap<Integer, Integer> subMap = new HashMap<>();
            for(int j = 0; j < A; j++) {
                int x = scan.nextInt() - 1;
                int y = scan.nextInt();
                subMap.put(x,y);
            }
            map.put(i, subMap);
        }

        int ans = 0;
        long allPattern = (long)Math.pow(2.0, N);
        for(long i = 0; i < allPattern; i++) {
            boolean isAllTrue = true;
            int numOf1 = 0;
            for(int j = 0; j < N; j++) {
                long tmp = i;
                tmp >>= j;
                if((tmp & 1) == 1) {
                    numOf1++;
                    HashMap<Integer, Integer> subMap = map.get(j);
                    boolean isTrue = true;
                    for(Entry<Integer, Integer> entry :subMap.entrySet()) {
                        tmp = i;
                        tmp >>= entry.getKey();
                        if((tmp & 1) != entry.getValue()) {
                            isTrue = false;
                            break;
                        }
                    }
                    if(!isTrue) {
                        isAllTrue = false;
                        break;
                    }
                }
            }
            if(isAllTrue) {
                if(ans < numOf1)
                    ans = numOf1;
            }
        }

        os.println(ans);
    }

}