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.*;

public class Main {

    static class Pair {
        int x, y;

        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }

    // Count number of 1's
    public static int countSetBits(int n) {
        int count = 0;
        while (n > 0) {
            count += n & 1;
            n >>= 1;
        }
        return count;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<List<Pair>> li = new ArrayList<>();
        for (int i = 0; i < n; ++i) li.add(new ArrayList<>());
        for (int i = 0; i < n; ++i) {
            int a = sc.nextInt();
            for (int j = 0; j < a; ++j) {
                li.get(i).add(new Pair(sc.nextInt() - 1, sc.nextInt()));
            }
        }

        int res = 0;
        for (int bit = 0; bit < (1<<n); ++bit) {
            boolean flag = true;
            for (int i = 0; i < n; ++i) {
                if ((bit & (1<<i)) == 0) continue;

                for (Pair p : li.get(i)) {
                    if (p.y == 1 && (bit & (1<<p.x)) == 0) flag = false;
                    if (p.y == 0 && (bit & (1<<p.x)) != 0) flag = false;
                }
            }
            if (flag) {
                res = Math.max(res, countSetBits(bit));
            }
        }

        System.out.println(res);
    }
}