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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var allWords = new List<(int person, int word)>[N];

            for (var i = 0; i < N; i++)
            {
                var a = int.Parse(Console.ReadLine());
                allWords[i] = new List<(int, int)>();
                for (var j = 0; j < a; j++)
                {
                    var inputs = Console.ReadLine().Split(' ');
                    var x = int.Parse(inputs[0]) - 1;
                    var y = int.Parse(inputs[1]);
                    allWords[i].Add((x, y));
                }
            }

            var ans = 0;

            // a << n で2^n乗を計算することですべてのパターンをチェック
            for (var bits = 0; bits < 1 << N; bits++)
            {
                var hasNoContradiction = true;
                var honestCount = 0; // 正直者カウント

                for (int i = 0; i < N; i++)
                {
                    // i番目の人が不親切な人(0)の場合は、次の番号の人へ
                    if (((bits >> i) & 1) == 0) continue;

                    honestCount++;

                    // i番目の人の証言に矛盾がないか確認
                    for (var j = 0; j < allWords[i].Count; j++)
                    {
                        // 現在調査しているパターン(bits)から証言に出てきた人が正直者か不親切な人かの値 != 証言から正直者か不親切な人かの値
                        if ((bits >> (allWords[i][j].person) & 1) != allWords[i][j].word)
                        {
                            hasNoContradiction = false;
                        }
                    }
                }

                if (hasNoContradiction)
                {
                    ans = Math.Max(ans, honestCount);
                }
            }

            Console.WriteLine(ans);

        }
    }
}