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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class Program
{
    static void Main(string[] args)
    {
        var wrong_answer = new wrong_answer();
        wrong_answer.Solve();
    }
}

public class wrong_answer
{
    const int INF = 1 << 30;
    const long INFL = 1L << 60;
    const int MOD = 1000000007;
    const int MOD2 = 998244353;

    myinout IO = new myinout();
    Math2 mmath = new Math2();



    public void Solve()
    {
        //ここから
        var o = IO.intm;
        var n = o[0];
        var m = o[1];
        var a = new long[m];
        var b = new long[m];
        var c = new long[m];
        for (int i = 0; i < m; ++i)
        {
            var oo = IO.longm;
            a[i] = oo[0];
            b[i] = oo[1];
            c[i] = (int)IO.intm.Select(x => 1L << (x - 1)).Sum();
            IO.wri(a[i]);
        }

        var dp = new long[1 << n];
        for (int i = 1; i < (1 << n); ++i)
        {
            dp[i] = INFL;
        }

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

        if (dp[(1 << n) - 1] == INFL) IO.wri(-1);
        else IO.wri(dp[(1 << n) - 1]);




    }


}




//b-aで降順

public class Math2
{
    public long[] fact;
    public long[] invfact;
    public void factoricalmodset(long N, long MOD = 1000000007)
    {
        fact = new long[N + 1];
        invfact = new long[N + 1];
        fact[0] = 1;

        for (long i = 1; i <= N; ++i)
        {
            fact[i] = fact[i - 1] * i % MOD;
        }
        invfact[N] = pow(fact[N], MOD - 2);

        for (long i = N; i > 0; --i)
        {
            invfact[i - 1] = invfact[i] * i % MOD;
        }

    }

    public long nCr(long n, long r, long MOD = 1000000007)
    {
        return (fact[n] * invfact[r] % MOD * invfact[n - r] % MOD);
    }

    public long pow(long i, long n, long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }

    public long gcd(long i, long y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public long lcm(long i, long y)
    {
        return i * y / gcd(i, y);
    }

    public Dictionary<long, int> primefactorization(long N)
    {
        var ret = new Dictionary<long, int>();

        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;

        }
        if (N >= 2) ret[N] = 1;

        return ret;

    }

    public List<long> divisorenumrate(long N)
    {
        var ret = new List<long>();

        for (long i = 1; i * i <= N; ++i)
        {

            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }

        }

        return ret;

    }

    public void swap<T>(ref T a, ref T b)
    {
        var i = a;
        a = b;
        b = i;
    }

}

class myinout
{
    //in
    public string str => Console.ReadLine();

    public string[] strm => str.Split(' ');

    public long[] longm => strm.Select(long.Parse).ToArray();
    public int[] intm => strm.Select(int.Parse).ToArray();
    public char[] charm => str.ToArray();
    public long long1 => longm[0];
    public int int1 => intm[0];
    public char char1 => charm[0];

    //out
    public void wri<T>(T i)
    {
        Console.WriteLine(i);
    }

    public void yn(bool i)
    {
        if (i) wri("Yes");
        else wri("No");
    }

}