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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main()
{
    int people, i, testimonies, j, tot = 0;

    scanf("%d", &people);

    int honest[people];

    for(i = 0;  i < people; i++)
    {
        honest[i] = 0;
    }

    for(i = 0; i < people; i++)
    {
        scanf("%d", &testimonies);

        int x[testimonies], y[testimonies];

        for(j = 0; j < testimonies; j++)
        {
            scanf("%d %d", &x[j], &y[j]);
        }

        for(j = 0; j < testimonies; j++)
        {
            if(y[j] == 1 || (y[j] == y[j+1] && y[j] == 1))
            {
                honest[i] = 1;
            }
            else
            {
                honest[i] = 0;
                break;
            }
        }
    }

    for(i = 0; i < people; i++)
    {
        tot += honest[i];
    }

    printf("%d", tot);

    return 0;
}