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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.regex.Pattern;

public class Main {
    public void solve(BufferedReader stdin, PrintWriter stdout) throws NumberFormatException, IOException {
        int[] first = toIntArray(stdin.readLine());
        int n = first[0]; // 宝箱の個数
        int m = first[1]; // 鍵の個数
        int[] a = new int[m]; // 鍵の値段
        int[] c = new int[m]; // 開けることができる宝箱をbitで表現したもの
        for (int i = 0; i < m; i++) {
            a[i] = toIntArray(stdin.readLine())[0]; // 鍵の値段
            for (int j : toIntArray(stdin.readLine())) {
                c[i] = c[i] | (1 << (j - 1));
            }
        }


        // dp[どこまで鍵を見たか][開けた宝箱(bit)] = コストの最小値
        int max = Arrays.stream(a).sum() + 1;
        int[][] dp = new int[m + 1][1 << n];
        for (int[] raw : dp) {
            Arrays.fill(raw, max);
        }
        dp[0][0] = 0;

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < 1 << n; j++) {
                dp[i + 1][j] = Math.min(dp[i + 1][j], dp[i][j]);
                dp[i + 1][j | c[i]] = Math.min(dp[i + 1][j | c[i]], dp[i][j] + a[i]);
            }
        }

        int ans = dp[m][(1 << n) - 1];
        if (ans == max) {
            stdout.println(-1);
        } else {
            stdout.println(ans);
        }
    }

    private Pattern space = Pattern.compile(" ");

    private int[] toIntArray(String line) {
        return space.splitAsStream(line).mapToInt(Integer::parseInt).toArray();
    }

    public static void main(String[] args) throws NumberFormatException, IOException {
        BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter stdout = new PrintWriter(System.out, false);
        new Main().solve(stdin, stdout);
        stdout.flush();
    }
}