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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
)

func countBits(n int) int {
	var cnt int
	for ; n > 0; n /= 2 {
		if n&1 == 1 {
			cnt += 1
		}
	}
	return cnt
}

func checkHonest(n, i int) bool {
	return n&(1<<uint(i)) > 0
}

const (
	NOT_HONEST = 0
	HONEST     = 1
)

func main() {
	var n int
	fmt.Scan(&n)

	xy := make([]map[int]int, n+1)
	for i := 0; i < n+1; i++ {
		xy[i] = map[int]int{}
	}
	var a, x, y int
	for i := 1; i < n+1; i++ {
		fmt.Scan(&a)
		for j := 0; j < a; j++ {
			fmt.Scan(&x, &y)
			xy[i][x] = y
		}
	}

	var max, bits int
	maxBits := 1 << uint(n)
	for ; bits < maxBits; bits++ {
		honestCount := countBits(bits)
		result := make([][]int, n+1)
		isCorrect := true
	LOOPA:
		for i := 1; i < n+1; i++ {
			isHonest := bits&(1<<uint(i-1)) > 0
			if !isHonest {
				continue
			}
			for k, v := range xy[i] {
				if (v == HONEST) && !checkHonest(bits, k-1) || (v == NOT_HONEST) && checkHonest(bits, k-1) {
					isCorrect = false
					break LOOPA
				}
				result[k] = append(result[k], v)
			}
		}
	LOOPB:
		for i := 1; i < n+1; i++ {
			if len(result[i]) < 1 {
				continue
			}
			for j := 1; j < len(result[i]); j++ {
				if result[i][j] != result[i][j-1] {
					isCorrect = false
					break LOOPB
				}
			}
		}
		if isCorrect && max < honestCount {
			max = honestCount
		}
	}
	fmt.Println(max)
}