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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.*
import java.util.*
import java.lang.*
import java.lang.Math.*


fun minCost(D: Array<IntPair>, N: Int): Int {
    val M = D.size

    val dp = Array(M+1){IntArray(0b01 shl N){INF}}
    // dp[i][s] := [0,i) のカギで開放状態 s を作るための最小コスト
    dp[0][0] = 0
    for (i in 1 .. M) {
        dp[i][0] = 0
    }

    for (i in 1 .. M) {
        val ds = D[i-1].first
        val cost = D[i-1].second
        for (s in 0 until (0b01 shl N)) {
            dp[i][s] = min(dp[i][s], dp[i-1][s])

            dp[i][s or ds] = min(dp[i][s or ds], dp[i-1][s] + cost)
        }
    }

    val ans = dp[M][(0b01 shl N) - 1]
    return if (ans >= INF) -1 else ans
}

fun solve() {
    val (N, M) = rd.readIntArray()
    val A = IntArray(M); val B = IntArray(M)
    val C = Array(M){ArrayList<Int>()}
    for (i in 0 until M) {
        val (a, b) = rd.readIntArray()
        A[i] = a; B[i] = b
        C[i].addAll(rd.readIntArray().toList())
    }

    val D = Array(M){IntPair(0, INF)}
    for (i in 0 until M) {
        var s = 0
        for (c in C[i]) {
            s = s or (0b01 shl (c-1))
        }
        D[i] = IntPair(s, A[i])
    }

    val ans = minCost(D, N)

    print(ans)
}


//val rd = debug.Reader("abc", "142", "e", "sample-1")
val rd = Reader()


fun main(args: Array<String>) {
    try {
        var exception: Throwable? = null
        val sth = Thread(null, SolveThread(), "solveThread", 128 * 1024 * 1024)
        sth.setUncaughtExceptionHandler { _, e -> exception = e }
        sth.start(); sth.join()
        if (exception != null) throw exception!!
    } catch (e: Exception) { throw e }
}
const val MOD = 1_000_000_007L; const val INF = Int.MAX_VALUE/2; const val LINF = Long.MAX_VALUE/2
const val EPS = 1e-9; fun DBLEQ(a: Double, b: Double): Boolean {return abs(a - b) < EPS}
data class IntPair(val first: Int, val second: Int)
data class To(val idx: Int, val cost: Long)
fun <T>edge(V: Int): Array<ArrayList<T>> { return Array(V){ArrayList<T>()} }
val errPrintln: (Any) -> Unit = { msg -> System.err.println(msg) }
fun rAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("EAssert Error: $msg"); throw Error(msg) }
}
fun tAssert(exp: Boolean, lazyMsg: () -> String = {""}) {
    if (!exp) { val msg = lazyMsg(); errPrintln("TAssert Error: $msg"); Thread.sleep(3000) }
}
class SolveThread : Runnable {
    override fun run() { solve() }
}
class Reader {
    private val br = BufferedReader(InputStreamReader(System.`in`))
    val readString: () -> String = { br.readLine() }
    val readInt: () -> Int = { br.readLine().toInt() }
    val readLong: () -> Long = { br.readLine().toLong() }
    val readIntArray: () -> IntArray = { br.readLine().split(' ').map { it.toInt() }.toIntArray() }
    val readLongArray: () -> LongArray = { br.readLine().split(' ').map { it.toLong() }.toLongArray() }
    val readListInt: () -> List<Int> = { br.readLine().split(' ').map { it.toInt() } }
    val readListLong: () -> List<Long> = { br.readLine().split(' ').map { it.toLong() } }
}