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: Runtime Error)

#include<iostream>
#include<algorithm>
#include<iomanip>
#include<string>
#include<vector>

typedef unsigned long long ULL;
typedef long long LL;

using namespace std;

typedef struct{
    int A;
    int x[15];
    int y[15];
}DATA;

int process(DATA *data,int N,ULL type);
int Set(DATA *data, int *honest, bool *check,int pos);
int main(){
    int N;
    int A;
    int x,y;
    ULL i,j;
    DATA *data;
    int count=0;
    int ans;
    cin >> N;
    data = new DATA[N];
    for(i=0;i<N;i++){
        cin >> A;
        data[i].A = A;
        for(j=0;j<A;j++){
            cin >> x >> y;
            data[i].x[j] = x;
            data[i].y[j] = y;
        }
    }
    
    //cout << endl;
    ans = 0;
    for(i=0;i< ( 0x01 << ( N - 1 ));i++){
        count = process(data,N,i);
        if( count > ans){
            ans = count;
        }
    }
    cout << ans << endl;
    return 0;
}

int process(DATA *data,int N,ULL type){
    int i,j;
    int *honest;
    bool *check; 
    int count;
    int temp;

    honest = new int[N];
    check = new bool[N];
    for(i=0;i<N;i++){
        honest[i] = -1;
        check[i] = false;
    }
    for(i=0;i<N;i++){
        if( ((type >> i) & 0x01) == 0x01){
            temp = Set(data,honest,check,i);
            if( temp == -1){
                return -1;
            }
        }
    }
    count = 0;
    for(i=0;i<N;i++){
        if( honest[i] == 1){
            count++;
        }
    }

    return count;
}
int Set(DATA *data, int *honest, bool *check,int pos){
    int i,j;
    int x;
    int y;
    int temp;
    if( honest[pos] == 0){
        return -1;
    }
    honest[pos] = 1;
    check[pos] = true;
    for(i=0;i < data[pos].A;i++){
        x = data[pos].x[i] -1 ;
        y = data[pos].y[i];
        if( honest[x] == -1){
            honest[x] = y;            
        }else if(honest[x] != y){
            return -1;
        }
    }
    for(i=0;i<data[pos].A;i++){
        if( check[data[pos].x[i-1]] == false && data[pos].y[i] == 1){
            temp = Set(data,honest,check,data[pos].x[i]-1);
            if( temp == -1){
                return -1;
            }
        }
    }
    return 0;
}