Problem:
Score : 500 points

Problem Statement

We have N locked treasure boxes, numbered 1 to N.

A shop sells M keys. The i-th key is sold for a_i yen (the currency of Japan), and it can unlock b_i of the boxes: Box c_{i1}, c_{i2}, ..., c_{i{b_i}}. Each key purchased can be used any number of times.

Find the minimum cost required to unlock all the treasure boxes. If it is impossible to unlock all of them, print -1.

Constraints

All values in input are integers.

1 \leq N \leq 12

1 \leq M \leq 10^3

1 \leq a_i \leq 10^5

1 \leq b_i \leq N

1 \leq c_{i1} < c_{i2} < ... < c_{i{b_i}} \leq N

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
c_{11} c_{12} ... c_{1{b_1}}
:
a_M b_M
c_{M1} c_{M2} ... c_{M{b_M}}

Output

Print the minimum cost required to unlock all the treasure boxes.
If it is impossible to unlock all of them, print -1.

Sample Input 1

2 3
10 1
1
15 1
2
30 2
1 2

Sample Output 1

25

We can unlock all the boxes by purchasing the first and second keys, at the cost of 25 yen, which is the minimum cost required.

Sample Input 2

12 1
100000 1
2

Sample Output 2

-1

We cannot unlock all the boxes.

Sample Input 3

4 6
67786 3
1 3 4
3497 1
2
44908 3
2 3 4
2156 3
2 3 4
26230 1
2
86918 1
3

Sample Output 3

69942

Solution in Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.{Map, Queue, PriorityQueue}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val N, M = in.next().toInt
  val a = new Array[Int](M+1)
  val b = new Array[Int](M+1)
  val c = Array.ofDim[Int](M+1, N+1)
  for (i <- 1 to M) {
    val _a, _b = in.next().toInt
    a(i) = _a; b(i) = _b
    for (k <- 1 to _b) {
      c(i)(k) = in.next().toInt
    }
  }


  //
  var hash = Map[List[Boolean], Int]() // (opened, price)
  val hoge = Array.fill[Boolean](N+1)(false)
  hoge(0) = true
  hash += hoge.toList -> 0


  for (i <- 1 to M) {
    val nextHash = hash.clone

    for ((opened, price) <- hash) {
      val hoge = opened.toArray
      for (k <- 1 to b(i)) {
        if(!hoge(c(i)(k)))
          hoge(c(i)(k)) = true
      }
      val key = hoge.toList

      if (!nextHash.contains(key)) {
        nextHash += (key -> (price + a(i)))
      }
      else {
        val nowPrice = price + a(i)

        if (nowPrice < nextHash(key)) {
          nextHash(key) = nowPrice
        }
      }
    }

    hash = nextHash
  }

  
  var ans = -1
  val k = List.fill[Boolean](N+1)(true)
  if(hash.contains(k))
    ans = hash(k)
  
  println(ans)
}


class InputReader(stream: InputStream) {
  private val reader = new BufferedReader(new InputStreamReader(stream))
  private var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}