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: Wrong Answer)



import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        PrintWriter out = new PrintWriter(System.out);
        FastScanner sc = new FastScanner();
        Strategy strategy = new MyStrategy();
        strategy.solve(out, sc);
        out.flush();
    }
}

class Key {
    private int cost;
    private boolean[] boxes;

    Key(int cost, int N) {
        this.cost = cost;
        this.boxes = new boolean[N];
        Arrays.fill(this.boxes, false);
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;
        Key key = (Key) o;
        return getCost() == key.getCost();
    }

    @Override
    public int hashCode() {
        return Objects.hash(getCost());
    }

    public void setCost(int cost) {
        this.cost = cost;
    }

    public void setBoxTrue(int i) {
        this.boxes[i] = true;
    }

    public int getCost() {
        return cost;
    }

    public boolean getBoxVal(int i) {
        return boxes[i];
    }
}

class MyStrategy implements Strategy {
    @Override
    public void solve(PrintWriter out, FastScanner sc) {
        int N = sc.nextInt();
        int M = sc.nextInt();
        PriorityQueue<Key> queue = new PriorityQueue<>(new Comparator<Key>() {
            @Override
            public int compare(Key o1, Key o2) {
                int c1 = o1.getCost();
                int c2 = o2.getCost();
                return Integer.compare(c1, c2);
            }
        });
        for (int i=0; i<M; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            Key key = new Key(a, N);
            for (int j=0; j<b; j++) {
                key.setBoxTrue(sc.nextInt()-1);
            }
            queue.add(key);
        }
        boolean[] boxes = new boolean[N];
        Arrays.fill(boxes, false);
        int sum = 0;
        while (true) {
            boolean canBreak = true;
            boolean added = false;
            Key key = queue.poll();
            if (key == null) {
                out.println(-1);
                return;
            }

            for (int i=0; i<N; i++) {
                if (!boxes[i] && key.getBoxVal(i)) {
                    boxes[i] = true;
                    if (!added) {
                        added = true;
                        sum += key.getCost();
                    }
                }

                if (!boxes[i]) {
                    canBreak = false;
                }
            }
            if (canBreak) {
                break;
            }
        }
        out.println(sum);
    }
}

interface Strategy {
    void solve(PrintWriter out, FastScanner sc);
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}