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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

int count_bits(uint32_t bits) {
    int count = 0;
    uint32_t b = bits;
    while (b != 0) {
        int a = (b & 1);
        if (a == 1) {
            count++;
        }

        b >>= 1;
    }

    return count;
}

int main() {
    int N;
    std::cin >> N;

    int A[N+1];
    int x[N+1][N+1];
    int y[N+1][N+1];
    for (int i = 1; i <= N; ++i) {
        std::cin >> A[i];
        for (int j = 1; j <= A[i]; ++j) {
            std::cin >> x[i][j] >> y[i][j];
        }
    }

    int h[N + 1];
    int max = 0;
    for (uint32_t bits = 0; bits < (1u << N); ++bits) {
        for (int i = 1; i <= N; ++i) {
            h[i] = ((bits >> (i - 1)) & 1u);
        }

        bool flag = true;
        for (int i = 1; i <= N; ++i) {
            for (int j = 1; j <= A[i]; ++j) {
                if (h[i] == 1 && h[x[i][j]] != y[i][j]) {
                    flag = false;
                    break;
                }
            }

            if (flag == false) {
                break;
            }
        }

        if (flag) {
            max = std::max(max, count_bits(bits));
        }
    }

    std::cout << max << std::endl;

    return 0;
}