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)

import java.io.PrintWriter

fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ")
fun nextIntList() = nextList().map(String::toInt)
fun nextLongList() = nextList().map(String::toLong)
fun nextDoubleList() = nextList().map(String::toDouble)

val pw = PrintWriter(System.out)
fun print(s: Any = "") = pw.print(s)
fun println(s: Any = "") = pw.println(s)

fun main(args: Array<String>) {
    main()
    pw.flush()
}

fun main() {
    val N = nextInt()
    val inputs = Array(N) {
        val A = nextInt()
        Array(A) {
            val (x, y) = nextIntList()
            intArrayOf(x, y)
        }
    }
    val ans = f(0, inputs, IntArray(N + 1) { -1 }, 0)
    println(ans)
}

fun f(n: Int, data: Array<Array<IntArray>>, results: IntArray, cnt: Int): Int {
    if (n >= data.size) return cnt
    val type = results[n + 1]
    return when (type) {
        0 -> {
            f(n + 1, data, results, cnt)
        }
        1 -> {
            val updated_results = update(data[n], results)
            if (updated_results == null) {
                0
            } else {
                f(n + 1, data, updated_results, cnt + 1)
            }
        }
        else -> {
            val skip_results = results.clone()
            skip_results[n] = 0
            val updated_results = update(data[n], results)
            if (updated_results == null) {
                f(n + 1, data, skip_results, cnt)
            } else {
                Math.max(f(n + 1, data, updated_results, cnt + 1), f(n + 1, data, skip_results, cnt))
            }
        }
    }
}

fun update(data: Array<IntArray>, results: IntArray): IntArray? {
    val new_results = results.clone()
    for (d in data) {
        val (x, y) = d
        if (new_results[x] != -1 && new_results[x] != y) return null
        new_results[x] = y
    }
    return new_results
}