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: Accepted)

import java.io.*
import java.util.*

fun solve(N: Int, xy: Array<MutableList<Pair<Int, Int>>>) {
    fun isConsistent(flag: List<Int>): Boolean {
        // flag=1の人たちの証言が整合するか
        for (honest in flag.withIndex().filter{ it.value == 1 }.map{ it.index }) {
            for (statement in xy[honest]) {
                if (flag[statement.first - 1] != statement.second) return false
            }
        }
        return true
    }
    // println(xy.toList())
    // bit all search
    var ans = 0
    for (i in 0 until (1 shl N)) {
        val flags = (0 until N).map { (i shr it) and 1 }
        if (flags.sum() <= ans) continue
        if (isConsistent(flags)) { ans = flags.sum() }
    }
    println(ans)
    return
}

fun main(args: Array<String>) {
    fun StringArray(size: Int, init: (Int) -> String = { "\u0000" }): Array<String> {
        return Array<String>(size, init)
    }
    class Scanner(stream: InputStream) {
        private val reader = BufferedInputStream(stream).bufferedReader()
        private var st: StringTokenizer? = null
        fun next(): String {
            while (!(st?.hasMoreTokens() ?: false)) st = StringTokenizer(reader.readLine())
            return st!!.nextToken()
        }
    }
    val sc = Scanner(System.`in`)
    val N = sc.next().toInt()
    val xy = Array(N) { mutableListOf<Pair<Int, Int>>() }
    for (i in 0 until N) {
        val A = sc.next().toInt()
        repeat(A){
            val x = sc.next().toInt()
            val y = sc.next().toInt()
            xy[i].add(x to y)
        }
    }
    solve(N, xy)
}