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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func init() {
	const maxWord = (1 << 30)
	buf := []byte{}
	sc.Buffer(buf, maxWord)
	sc.Split(bufio.ScanWords)
}

func input() string {
	sc.Scan()
	return sc.Text()
}

func max(x, y int) int {
	if x > y {
		return x
	}
	return y
}

// Testimony x:person, y:is honest
type Testimony struct {
	x int
	y int
}

func makePattern(n, t int) []int {
	pattern := make([]int, n)
	for i := 0; i < n; i++ {
		pattern[i] = t & 1
		t = t >> 1
	}
	return pattern
}

func validate(n int, a, pattern []int, testimonies [][]Testimony) bool {
	for i := 0; i < n; i++ {
		if pattern[i] == 0 {
			continue
		}

		t := testimonies[i]
		for j := 0; j < a[i]; j++ {
			if t[j].y != pattern[t[j].x] {
				return false
			}
		}
	}
	return true
}

func main() {
	n, _ := strconv.Atoi(input())
	a := make([]int, n)
	testimonies := make([][]Testimony, n)
	for i := 0; i < n; i++ {
		a[i], _ = strconv.Atoi(input())
		t := make([]Testimony, a[i])
		for j := 0; j < a[i]; j++ {
			x, _ := strconv.Atoi(input())
			y, _ := strconv.Atoi(input())
			t[j] = Testimony{x - 1, y}
		}
		testimonies[i] = t
	}

	ans := 0
	patternNum := 1 << uint(n)
	for i := 1; i < patternNum; i++ {
		pattern := makePattern(n, i)
		if validate(n, a, pattern, testimonies) {
			sum := 0
			for j := 0; j < n; j++ {
				sum += pattern[j]
			}
			ans = max(ans, sum)
		}
	}
	fmt.Println(ans)
}