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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>

#define BUF_SIZE 40

int get_int(void) {
  int num;
#ifdef BUF_SIZE
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, stdin)) return 0;
  sscanf(line, "%d", &num);
#else
#error
#endif
  return num;
}

int get_int2(int *a1, int *a2) {
#ifdef BUF_SIZE
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, stdin)) return -1;
  sscanf(line, "%d %d", a1, a2);
#else
#error
#endif
  return 0;
}

void setbit(int *bits, int idx) {
    *bits |= (1<<idx);
}

char getbit(int *bits, int idx) {
    return (*bits) & (1<<idx);
}

#define MAX_NUM 15

int main(void) {
    int num = get_int();
    int i, j;
    int check[MAX_NUM] = {0};
    int opinion[MAX_NUM] = {0};
    for(i = 0; i < num; i++) {
        int es = get_int();
        for(j = 0; j < es; j++) {
            int idx, yn;
            // idx: 1-indexed number
            get_int2(&idx, &yn);
            setbit(&check[i], idx-1);
            if(yn) setbit(&opinion[i], idx-1);
        }
    }
#ifdef DEBUG
    for(i = 0; i < num; i++) {
        printf("check: %d; op: %d\n", check[i], opinion[i]);
    }
#endif

    int pattern;
    int max = 0;
    for(pattern = 0; pattern < (1<<num); pattern++) {
        int cnt = __builtin_popcount(pattern);
        if(cnt <= max) continue;
        // assume that cnt > max
        // do check
        for(i = 0; i < num; i++) {
            // if person i is dishonest, skip
            if(!(pattern & (1<<i))) continue;
            // if contradiction, set flag to be 0
            if(((check[i] & pattern) ^ opinion[i]) != 0) {
                cnt = 0;
                break;
            }
        }
        // update max
        max = cnt > max ? cnt : max;
    }
    printf("%d\n", max);
}