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 int long long
#define REP(i, l, r) for (int i=(l); i<(r); ++i)
#define RREP(i, r, l) for (int i=(r); i>(l); --i)
#define popcount __builtin_popcountll

const int INF = 1LL<<60;
const int MOD = 1000000007;

template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> t) {
    return "(" + to_string(get<0>(t)) + ", " + to_string(get<1>(t)) + ", " + to_string(get<2>(t)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> t) {
    return "(" + to_string(get<0>(t)) + ", " + to_string(get<1>(t)) + ", " + to_string(get<2>(t)) + ", " + to_string(get<3>(t)) + ")";
}

template <typename A>
string to_string(vector<A> v) {
    bool first = true;
    string result = "[";
    for (A i : v) {
        if (!first) result += ", ";
        first = false;
        result += to_string(i); 
    }
    return result + "]";
}

template <typename A>
string to_string(A x[], int n) {
    string result = "{";
    REP(i, 0, n) {
        if (i!=0) result += ", ";
        result += to_string(x[i]); 
    }
    return result + "}";
}

string bin_string(int x) {
    const int d = 64;
    string result(d, ' ');
    RREP(i, d-1, -1) result[d-1-i] = '0'+((x&1LL<<i)!=0);
    return result;
}

vector<int> getZ(string s) {
    int n = s.size();
    vector<int> z(n);
    int x = 0, y = 0;
    REP(i, 1, n) {
        z[i] = max(0LL, min(z[i-x], y-i+1));
        while (i+z[i] < n && s[z[i]] == s[i+z[i]]) {
            x = i;
            y = i+z[i];
            ++z[i];
        }
    }
    return z;
}

int powa(int base, int exp) {
    if (exp<=0) return 1;
    if (base<=0) return 0;
    int val = powa(base, exp>>1);
    val = val*val % MOD;
    if (exp&1) {
        val = val*base % MOD;
    }
    return val;
}

signed main() {
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    
    int n;
    cin >> n;
    vector<pair<int,int>> claims[n];
    REP(i, 0, n) {
        int a;
        cin >> a;
        REP(j, 0, a) {
            int x,y;
            cin >> x >> y;
            claims[i].push_back({x-1, y});
        }
    }

    int res=-1;
    REP(s, 0, 1<<n) {
        bool contra = false;
        REP(h, 0, n) {
            if (s&1<<h) {
                for (auto pr : claims[h]) {
                    int x, y;
                    tie(x, y) = pr;
                    if (((s&1<<x)!=0) != y) {
                        contra = true;
                        break;
                    }
                }
                if (contra) break;
            }
        }
        if (!contra) res = max(res, (int)popcount(s));
    }
    cout << res;
}