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

class Program
{
    static void Main(string[] args) {
#if DEBUG
        //MyDebugger.MakeTestCase("../TextFile2.txt"); return;
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }
    static XY[][] XYs;

    static object process(TextReader input) {
        var n = int.Parse(input.ReadLine());

        XYs = new XY[n][];
        for(int i=0; i<n; i++) {
            var a = int.Parse(input.ReadLine());
            XYs[i] = new XY[a];
            for(int j=0; j<a; j++) {
                var spl   = input.ReadLine().Split(' ');
                XYs[i][j] = new XY(
                    int.Parse(spl[0])-1,
                    int.Parse(spl[1]));
            }
        }

        List<string> ptn = new List<string>();
        ptn.Add("0");
        ptn.Add("1");

        for (int i=1; i<n; i++) {
            var ptn2 = new List<string>();
            foreach(var x in ptn) {
                ptn2.Add(x + "0");
                ptn2.Add(x + "1");
                ptn = ptn2;
            }
        }

        int count = 0;
        foreach(var x in ptn) {
            var cs = x.ToCharArray();
            if(isOk(XYs, cs)) {
                var co = cs.Count(y => y == '1');
                count = Math.Max(count, co);
            }
        }

        return count;
    }

    static bool isOk(XY[][] XYs, char[] tbl) {
        for (int i=0; i<tbl.Length; i++) {
            if (tbl[i] == '1') {
                foreach(var xy in XYs[i]) {
                    if (xy.y == 1 && tbl[xy.x]=='0') return false;
                    if (xy.y == 0 && tbl[xy.x]=='1') return false;
                }
            }
        }
        return true;
    }
}

class XY
{
    public int x;
    public int y;

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