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: Wrong Answer)

package main

import "fmt"

type person struct {
	m map[int]int
}

func isok(persons []person, v []bool, i int) bool {
	p := &persons[i]
	pv := v[i]
	for j := 0; j < i; j++ {
		q := &persons[j]
		qv := v[j]

		for pp, pm := range p.m {
			for qp, qm := range q.m {
				if pp != qp {
					continue
				}
				if pm == qm {
					continue
				}
				if pv && qv {
					return false
				}
			}
		}

	}
	return true
}

func resolve(persons []person, v []bool, i int) int {
	if i == len(v) {
		ans := 0
		for _, b := range v {
			if b {
				ans++
			}
		}
		return ans
	}

	v[i] = true
	ans0 := 0
	if isok(persons, v, i) {
		ans0 = resolve(persons, v, i+1)
	}

	v[i] = false
	ans1 := 0
	if isok(persons, v, i) {
		ans1 = resolve(persons, v, i+1)
	}

	if ans0 > ans1 {
		return ans0
	}
	return ans1
}

func main() {
	var np int
	fmt.Scanf("%d\n", &np)

	persons := make([]person, np, np)
	for i := 0; i < np; i++ {
		var nm int
		fmt.Scanf("%d\n", &nm)
		person := &persons[i]
		person.m = make(map[int]int)
		for j := 0; j < nm; j++ {
			var p, m int
			fmt.Scanf("%d %d\n", &p, &m)
			person.m[p] = m
		}
	}

	v := make([]bool, np, np)
	fmt.Print(resolve(persons, v, 0))
}