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>
using namespace std;

#define dump(x) cout << (x) << endl
#define Int int64_t
#define fi first
#define se second
 
Int INF = 1e18;
Int mod = 1e9+7;
//Int mod = 998244353;

int main() {
    Int n;
    cin >> n;
    vector<vector<pair<Int, Int>>> a(n);
    for (Int i = 0; i < n; i++) {
        Int x;
        cin >> x;
        vector<pair<Int, Int>> v(x);
        for (Int j = 0; j < x; j++) {
            cin >> v[j].fi >> v[j].se;
            v[j].fi--;
        }
        a[i] = v;
    }
    Int res = 0;
    for (Int bit = 0; bit < (1<<n); bit++) {
        bool check = true;
        for (Int i = 0; i < n; i++) {
            for (Int j = 0; j < a[i].size(); j++) {
                if ((bit & (1<<i)) and ((bit & (1<<a[i][j].fi)) != (a[i][j].se<<a[i][j].fi))) {
                    if (check) {
                       // cout << i << " " << bit << endl;
                    }
                    check = false;
                }
            }
        }
        if (check) {
            //dump(bit);
            Int cnt = 0;
            for (Int i = 0; i < n; i++) {
                if (bit & (1<<i)) {
                    cnt++;
                }
            }
            res = max(res, cnt);
        }
    }
    dump(res);
    return 0;
}