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 = readInt()
  val XY = (1..N).map {
    val A = readInt()
    (1..A).map { readInts() }
  }

  var max = 0
  for (i in 0 until N) {
    var TFN = arrayOfNulls<Boolean>(N)
    for (i in 0 until i) TFN[i] = false

    fun assume(n: Int, tf: Boolean): Boolean {
      if (TFN[n] != null) {
        return TFN[n] == tf
      }
      TFN[n] = tf
      if (tf) {
        XY[n].forEach {
          val x = it[0]
          val y = it[1] == 1
          if (!assume(x - 1, y)) return false
        }
      }
      return true
    }
    for (j in i until N) {
      val tmp = TFN.copyOf()
      if (assume(j, true)) {
        continue
      }
      TFN = tmp
      assume(j, false)
    }
    val sum = TFN.count { it == true }
    max = Math.max(max, sum)
  }

  println(max)
}

fun readString() = readLine()!!
fun readStrings() = readString().split(' ')
fun readInt() = readString().toInt()
fun readInts() = readStrings().map { it.toInt() }