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 <iostream>

#include <vector>
#include <map>
#include <algorithm>
#include <fstream>
#include<cstdio>
#include<iomanip>
#include<stack>
#include<queue>
#include<string>
#include <cstdlib>
#include <typeinfo>
#include <math.h>
#include <list>
#include <set>

#define REP(i, n) for(int i=0;i<n;i++)
#define REP2(i, s, n) for(int i=s;i<n;i++)
#define REP_1(i, n) for(int i=1;i<n+1;i++)
#define bitSearch(bit, n) for(int bit = 0; bit < (1 << n); bit++)
#define sz(x) int(x.size())
using namespace std;

template<class T>
void print(const T &value) {
    std::cout << value << std::endl;
}

void yesno(bool a) { if (a)cout << "yes" << endl; else cout << "no" << endl; }

void YesNo(bool a) { if (a)cout << "Yes" << endl; else cout << "No" << endl; }

void YESNO(bool a) { if (a)cout << "YES" << endl; else cout << "NO" << endl; }

typedef long long ll;
typedef unsigned long ul;
typedef long double ld;

template<class T>
inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}


ll INF = 1000001000;
ll mod = 1000000007;//10^9+7
ll power(ll x, ll n, ll mod) {//x^nをmodで割った余り
    ll res = 1;
    if (n > 0) {
        res = power(x, n / 2, mod);
        if (n % 2 == 0) res = (res * res) % mod;
        else res = (((res * res) % mod) * x) % mod;
    }
    return res;
}

int dx[8] = {-1, 0, 0, 1, -1, -1, 1, 1};
int dy[8] = {0, -1, 1, 0, -1, 1, -1, 1};

struct Edge {
    int to, cost;

    Edge(int to, int cost) : to(to), cost(cost) {};
};

using Graph = vector<vector<int>>;//隣接リスト:G[i]にはiと隣接する頂点が入るよ。
using GraphW = vector<vector<Edge>>;//重み付きの隣接リスト
using P = pair<int, int>;//BFSで利用。queueに入れる。
using lP = pair<ll, ll>;
using PP = pair<int, P>; //dijkstraで利用,priority_queueに入れる。
using p_queue = priority_queue<int, vector<int>, greater<int>>;//小さい順

class UnionFindTree {

public:
    UnionFindTree(int size) : memberSize(size) {
        par.resize(size * sizeof(ll));
        rnk.resize(size * sizeof(ll));
        diff_weight.resize(size * sizeof(ll));
        REP(i, size) {
            par[i] = i;
            rnk[i] = 0;
            diff_weight[i] = 0;
        }
    }

    int memberSize;

    vector<int> par;
    vector<int> rnk;
    vector<ll> diff_weight;

//n個のnodeで初期化する関数
    void init(ll n) {
        REP(i, n) {
            par[i] = i;
            rnk[i] = 1;
        }
    }

//木の根を求める。この際，親は根に更新される。
    int find(ll x) {
        if (par[x] == x) { return x; }
        else {
            int r = find(par[x]);
            diff_weight[x] += diff_weight[par[x]];
            return par[x] = r;
        }
    }

//xとyが同じ集合に属するか判定
    bool same(ll x, ll y) {
        return find(x) == find(y);
    }

//xとyの属する集合を融合
    void unite(ll x, ll y) {
        x = find(x);
        y = find(y);
        if (x == y) { return; }

        if (rnk[x] < rnk[y]) {
            par[x] = y;
        } else {
            par[y] = x;
            if (rnk[x] == rnk[y]) { rnk[x]++; }
        }
    }

    //xの重み
    ll weight(ll x) {
        find(x);
        return diff_weight[x];
    }

    ll diff(ll x, ll y) {
        return weight(y) - weight(x);
    }

    //重みごと更新。weight(y)-weight(x)=wとなるようにする
    void merge(int x, int y, int w) {
        w += weight(x);
        w -= weight(y);
        x = find(x);
        y = find(y);
        if (x == y) { return; }
        if (rnk[x] < rnk[y]) {
            par[x] = y;
            diff_weight[x] = -w;
        } else {
            par[y] = x;
            diff_weight[y] = w;
            if (rnk[x] == rnk[y]) { rnk[x]++; }
        }
    }
};

priority_queue<P, vector<P>, greater<P>> que;

struct Coordinate {
    int x, y;

    Coordinate(int y, int x) : y(y), x(x) {};
};

ll gcd(ll a, ll b) {
    if (a < b) {
        ll tmp = a;
        a = b;
        b = tmp;
    }
    ll r = a % b;
    while (r != 0) {
        a = b;
        b = r;
        r = a % b;
    }
    return b;
}


//番号ズレ注意！！
int main() {
    int ans = 0;
    int N;
    cin >> N;
    vector<int> hon[N], dis[N];
    REP(i, N) {
        int a;
        cin >> a;
        REP(j, a) {
            int x, y;
            cin >> x >> y;
            x--;
            if (y == 1) { hon[i].push_back(x); }
            else { dis[i].push_back(x); }
        }
    }
    REP(bit, 1 << N) {
        bool ok = true;
        int num = 0;
        REP(i, N) {
            if ((bit >> i) & 1) {
                int s = hon[i].size();
                REP(j, s) {
//                    cout << "bit:" << bit << " i,j: " << i << " " << j << " hon:" << hon[i][j] << endl;
                    if (((bit >> (hon[i][j]))&1) == 0) {
                        ok = false;
                        break;
                    }
                }
                int t = dis[i].size();
                REP(j, t) {
//                    cout << "bit:" << bit << " i,j: " << i << " " << j << " dis:" << dis[i][j]<<" real;"<<((bit >> (dis[i][j]))&1) << endl;
                    if (((bit >> (dis[i][j]))&1) == 1) {
//                        cout << "FALSE!! bit:" << bit << endl;
                        ok = false;
                        break;
                    }
                }
                num++;
            }
        }
        if (!ok)continue;
//        cout << "bit: " << bit << endl;
        chmax(ans, num);
    }
    print(ans);
}