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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    val n = readLine()?.toInt() ?: return
    val aa = 1.until(n + 1).map {
        val a = readLine()?.toInt() ?: return
        A(
            it,
            0.until(a).map {
                val (x, y) = readLine()?.split(" ")?.map(String::toInt) ?: return
                Testimony(x, y == 0)
            }
        )
    }
    val candidates = mutableListOf<BooleanArray>()
    generateCandidates(booleanArrayOf(), n, 0, candidates)

    val count = candidates.map { liars ->
        if (verify(n, aa, liars)) {
            liars.count { !it }
        } else {
            0
        }
    }.max()
    println(count.toString())
}

data class Testimony(val number: Int, val liar: Boolean)
data class A(
    val number: Int,
    val testimony: List<Testimony>
)

fun verify(n: Int, aa: List<A>, liars: BooleanArray): Boolean {
    aa.flatMap {
        val liar = liars[it.number - 1]
        if (liar) {
            it.testimony.map {
                Testimony(it.number, !it.liar)
            }
        } else {
            it.testimony
        }
    }.forEach {
        if (liars[it.number - 1] != it.liar) {
            return false
        }
    }
    return true
}

tailrec fun generateCandidates(array: BooleanArray, n: Int, index: Int, candidates: MutableList<BooleanArray>) {
    if (index == n) {
        candidates.add(array)
    } else {
        generateCandidates(array + booleanArrayOf(true), n, index + 1, candidates)
        generateCandidates(array + booleanArrayOf(false), n, index + 1, candidates)
    }
}