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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
public class ABC147C {
    private static List<int> A = new List<int>();
    private static List<List<int>> x = new List<List<int>>();
    private static List<List<bool>> y = new List<List<bool>>();

    public static void Main() {
        int N, ans = 0;
        List<bool> isKind = new List<bool>();
        List<bool> isDefined = new List<bool>();
        N = int.Parse(Console.ReadLine());
        for (int i = 0; i < N; i++) {
            int A_i = int.Parse(Console.ReadLine());
            isKind.Add(false);
            isDefined.Add(false);
            x.Add(new List<int>());
            y.Add(new List<bool>());
            A.Add(A_i);
            for (int j = 0; j < A_i; j++) {
                string[] str = Console.ReadLine().Split(' ');
                x[i].Add(int.Parse(str[0]) - 1);
                y[i].Add(int.Parse(str[1]) == 1);
            }
        }
        
        ans = Calc(isDefined, isKind);

        Console.WriteLine(ans);
    }

    public static int Calc(List<bool> isDefined, List<bool> isKind) {
        int max = 0;
        for (int i = 0; i < isDefined.Count; i++) {
            if (isDefined[i]) continue;
            isDefined[i] = true;
            isKind[i] = true;
            int result = Check(i, isDefined, isKind, 1);
            if (result == 0) {
                isDefined[i] = false;
                isKind[i] = false;
                continue;
            }
            result += Calc(isDefined, isKind);
            if (max < result) max = result;
        }
        return max;
    }

    public static int Check(int p, List<bool> isDefined, List<bool> isKind, int ans) {
        for (int i = 0; i < A[p]; i++) {
            if (isDefined[x[p][i]]) {
                if (isKind[x[p][i]] != y[p][i]) return 0;
            } else {
                isDefined[x[p][i]] = true;
                isKind[x[p][i]] = y[p][i];
                if (y[p][i]) {
                    ans++;
                    int result = Check(x[p][i], isDefined, isKind, ans);
                    if (result == 0) {
                        isDefined[x[p][i]] = false;
                        return 0;
                    }
                }
            }
        }
        return ans;
    }
}