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 Scala (2.11.7) (judge verdict: Runtime Error)

import java.util.Scanner

object Main extends App {

  val sc = new Scanner(System.in)
  val n = sc.nextInt
  val input: Array[Map[Int, Int]] = Array.fill(n) {
    Array.fill(sc.nextInt)(sc.nextInt - 1, sc.nextInt).toMap
  }

  var result = 0
  for (i <- 0 until (1 << n)) {

    val digits = i.toString.size
    val str = (0 until (n - digits)).map(_ => "0").mkString
    val c = (str + i.toBinaryString.toInt).reverse
    var isValid = true
    import scala.util.control.Breaks.{break, breakable}
    breakable {
      for (j <- 0 until n) {
        if (((i >> j) & 1) == 1) {
          val ok = input(j).forall { pair => c(pair._1).asDigit == pair._2 }
          if (!ok) {
            isValid = false
            break
          }
        }
      }
    }
    if (isValid) {
      result = Math.max(result, c.count(c => c.equals('1')))
    }

  }

  println(result)
}