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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;

namespace AtCoder
{
    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        class Man
        {
            public readonly int honest;
            public readonly int unkind;
            public Man(int[][] pairs)
            {
                foreach (int[] pair in pairs)
                {
                    switch (pair[1])
                    {
                    case 0: unkind |= 1 << (pair[0] - 1); break;
                    case 1: honest |= 1 << (pair[0] - 1); break;
                    }
                }
            }
        }

        static int CountBits(int n)
        {
            int cnt = 0;
            while (n > 0)
            {
                if ((n & 1) != 0) { ++cnt; }
                n >>= 1;
            }
            return cnt;
        }

        static bool Conceivable(int N, int bits, Man[] men)
        {
            for (int i = 0; i < N; ++i)
            {
                if ((bits & (1 << i)) != 0)
                {
                    if ((men[i].honest & ~bits) != 0) { return false; }
                    if ((men[i].unkind & bits) != 0) { return false; }
                }
            }
            return true;
        }

        static int Solve(int N, Man[] men)
        {
            int max = 0;
            for (int bits = 0; bits < 1 << N; ++bits)
            {
                if (Conceivable(N, bits, men)) { max = Math.Max(CountBits(bits), max); }
            }
            return max;
        }

        static void Main(string[] args)
        {
            int N = ReadInt();
            var men = new Man[N];
            for (int i = 0; i < N; ++i)
            {
                int A = ReadInt();
                var pairs = new int[A][];
                for (int j = 0; j < A; ++j) { pairs[j] = ReadInts(); }
                men[i] = new Man(pairs);
            }
            Console.WriteLine(Solve(N, men));
        }
    }
}