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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author naruse
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        HonestOrUnkind2 solver = new HonestOrUnkind2();
        solver.solve(1, in, out);
        out.close();
    }

    static class HonestOrUnkind2 {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int a[][] = new int[n][n];
            for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) a[i][j] = -1;
            for (int i = 0; i < n; i++) {
                int k = in.nextInt();
                for (int j = 0; j < k; j++) {
                    int x = in.nextInt();
                    int y = in.nextInt();
                    x--;
                    a[i][x] = y;
                }
            }
            int ans = 0;
            for (int i = 0; i < (1 << n); i++) {
                boolean ok = true;
                for (int j = 0; j < n; j++) {
                    int now = (i >> j) % 2;
                    for (int k = 0; k < n; k++) {
                        if (a[j][k] == -1) continue;
                        if (now == 0) {
                            //
                        } else {
                            if (a[j][k] == 1 && (i >> k) % 2 == 0) {
                                ok = false;
                            } else if (a[j][k] == 0 && (i >> k) % 2 == 1) {
                                ok = false;
                            }
                        }
                    }
                    if (!ok) break;
                }
                if (ok) {
                    int cnt = 0;
                    for (int j = 0; j < n; j++) {
                        if ((i >> j) % 2 == 1) cnt++;
                    }
                    ans = Math.max(ans, cnt);
                }
            }
            out.println(ans);
        }

    }
}