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>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <fstream>
#include <string.h>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <queue>
#include <math.h>
#define ff first
#define ss second
#define ll long long
using namespace std;
int a[16], x[16][16], y[16][16], honests[16];
int main () {
    ios::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
    int n;
    cin>>n;
    for(int i = 0; i < n; i++) {
        cin>>a[i];
        for(int j = 0; j < a[i]; j++) {
            cin>>x[i][j]>>y[i][j];
        }
    }
    int ans = 0;
    for(int mask = 1; mask < (1 << n); mask++) {
        int curans = 0;
        for(int i = 0; i < n; i++) {
            if(mask & (1 << i)) {
                honests[i] = 1;
                curans++;
                //cout<<i<<" ";
            }
        }
        bool p = 1;
        for(int i = 0; i < n; i++) {
            if(honests[i]) {
                for(int j = 0; j < a[i]; j++) {
                    if(y[i][j] == 0 && honests[x[i][j] - 1] == 1) {
                        p = 0;
                        break;
                    }
                    if(y[i][j] == 1 && honests[x[i][j] - 1] == 0) {
                        p = 0;
                        break;
                    }
                }
                if(p == 0)
                    break;
            }
        }
        //cout<<": "<<p<<endl;
        if(p == 1)
            ans = max(ans, curans);
        for(int i = 0; i < n; i++)
            honests[i] = 0;
    }
    cout<<ans;
}
/*
 9 2
 6 19 3 4 4 2 6 7 8
 1 7 21
 1 5 18
 1 3 14
 1 1 8
 0 8 38
 0 6 36
 0 4 32
 0 2 26
 */