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: Wrong Answer)

#include<bits/stdc++.h>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
using namespace std;
typedef long long ll;
vector<int> node[18];
vector<int> dis[18];
int vis[20];
int cnt=0;
vector<int> tmp;
int pre[18][18];
void dfs(int x)
{
    cnt++;
    vis[x]=1;
    tmp.push_back(x);
    for(int i=0;i<node[x].size();i++)
    {
        int y=node[x][i];
        if(vis[y]==0)
        {
            //vis[y]=1;
            dfs(y);
        }
    }
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int n;
    cin>>n;
    for(int i=1;i<=n;i++)
    {
        int t;
        cin>>t;
        while(t--)
        {
            int x,y;
            cin>>x>>y;
            if(y==1) node[i].push_back(x);
            else dis[i].push_back(x);
            pre[i][x]=y;
        }
    }
    int ans=0;
    for(int i=1;i<=n;i++)
    {
        cnt=0;
        memset(vis,0,sizeof vis);
        dfs(i);
        //cout<<cnt<<" cnt"<<endl;
        bool chk=0;
        for(int j=1;j<=n;j++)
        {
            if(vis[j]==1)
            {
                for(int k=0;k<dis[j].size();k++)
                {
                    int nw=dis[j][k];
                    if(vis[nw]==1)
                    {
                        chk=1;
                        break;
                    }
                }
            }
            if(chk==1)
            {
                break;
            }
        }
        if(chk==0) ans=max(ans,cnt);
    }
    cout<<ans<<endl;
    return 0;
}