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 rep(i, n) for(ll i = 0; i < (n); ++i)
#define repA(i, a, n) for(int  i = a; i <= (n); ++i)
#define repD(i, a, n) for(ll i = a; i >= (n); --i)
#define trav(a, x) for(auto& a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int) (x).size()
#define fill(a) memset(a, 0, sizeof(a))
#define fst first
#define snd second
#define mp make_pair
#define pb push_back
#define endl '\n'
const long double PI = 3.141592653589793238462643383;
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<double> vd;
typedef vector<long long int> vll;
typedef vector<pii> vii;
long long int Ceil(int a, int b){
    if(a%b==0) return a/b;
    else return (a/b)+1;
}
ll p=1000000007;
int main() {

    cin.sync_with_stdio(0); cin.tie(0);
    cin.exceptions(cin.failbit);
    int ans=0;
    ll n;cin>>n;
    vector<pair<int,int> > v[n];
    rep(i,n){
        int y;cin>>y;
        vector<pair<int,int> > t(y);
        rep(i,y){
            int a,b;cin>>a>>b;a--;
            t[i]=mp(a,b);
        }
        v[i]=t;
    }
    int mask=pow(2,n);
    for(int i=0;i<mask;i++){
        int flag=1;
        int x=__builtin_popcount(i);
        for(int j=0;j<n;j++){
            if(i&(1<<j)){
                for(auto k : v[j]){

                    if(k.snd==1){
                        if((i&(1<<k.fst))==0){
                            flag=0;break;
                        }
                    }
                    else{
                        if((i&(1<<k.fst))!=0){
                            flag=0;break;
                        }
                    }
                }
            }
        }
        // if(flag)cout<<i<<endl;
        if(flag)ans=max(ans,x);
    }
    cout<<ans;
    return 0;
}