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)

fun main(args : Array<String>) {
    val n = readLine()!!.toInt()
    val aa = Array(n){ mutableListOf<Pair<Int, Int>>() }

    repeat(n) { aIdx ->
        val a = readLine()!!.toInt()
        repeat(a) {
            val (x, y) = readLine()!!.split(" ").map { it.toInt() }
            aa[aIdx].add(Pair(x, y))
        }
    }

    var max = 0
    for (i in 0 until 1.shl(n)) {
        var failed = false

        inner@for (j in aa.indices) {
            val shouldSkip = ((i.shr(j) and 1) == 0)
            if (shouldSkip) continue@inner

            for (k in aa[j]) {
                val target = (i.shr(k.first-1) and 1)
                if (target != k.second) {
                    failed = true
                    break@inner
                }
            }
        }

        if (!failed) {
            max = Math.max(max, Integer.bitCount(i))
        }
    }

    println(max)
}