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()
    fun toBinaryNumberCharArray(num: Long): String {
        return String.format("%${n}d", java.lang.Long.toBinaryString(num).toLong())
    }

    val axy = Array(n) { mutableListOf<Pair<Int, Int>>() }
    (0 until n).forEach {
        val a = readLine()!!.toInt()
        for (i in 1..a) {
            val (x, y) = readLine()!!.split(' ').map(String::toInt)
            axy[it].add(Pair(x, y))
        }
    }
    var flag = (1L shl n) - 1
    while (flag >= 0) {
        val sf = toBinaryNumberCharArray(flag)
        var index = 0
        var check = true
        for (c in sf) {
            if (c == '1') {
                val syo = axy[index]
                for (xy in syo) {
                    val (x, y) = xy
                    if (sf[x - 1].toString() != y.toString()) check = false
                }
            }
            index++
        }
        if (check) {
            println(sf.count { it == '1' })
            return
        }
        flag--
    }
    println(0)
}