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: Runtime Error)

package main;

import java.io.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        Solution solver = new Solution();
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        solver.solve(1, in, out);
        out.close();
    }

    private static class Solution {
        static int INF = (int) 1e8;
        int[][] mem;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            mem = new int[m][(1 << (n + 1)) + 9];
            for (int[] x : mem) Arrays.fill(x, -1);
            int[] cost = new int[m];
            int[] keyMask = new int[m];
            for (int i = 0; i < m; ++i) {
                cost[i] = in.nextInt();
                int keys = in.nextInt();
                int mask = 0;
                for (int j = 0; j < keys; ++j) {
                    int box = in.nextInt() - 1;
                    mask |= (1 << box);
                }
                keyMask[i] = mask;
            }
            int res = solve(0, 0, n, cost, keyMask);
            if (res >= INF) {
                out.println("-1");
            } else {
                out.println(res);
            }
        }

        private int solve(int idx, int mask, int n, int[] cost, int[] keyMask) {
            if (allOnes(mask, n)) {
                return 0;
            }
            if (idx >= cost.length) return INF;
            if (mem[idx][mask] != -1) return mem[idx][mask];
            int res = solve(idx + 1, mask, n, cost, keyMask);
            res = Math.min(res, cost[idx] + solve(idx + 1, mask | keyMask[idx], n, cost, keyMask));
            mem[idx][mask] = res;
            return res;
        }

        private boolean allOnes(int mask, int n) {
            for (int i = 0; i < n; ++i) {
                if ((mask & (1 << i)) == 0) return false;
            }
            return true;
        }


    }

    private static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 23434);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }

}