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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

from collections import Counter, defaultdict
import sys
sys.setrecursionlimit(10 ** 5 + 10)
input = sys.stdin.readline
from math import factorial
import heapq, bisect
import math
import itertools
from copy import copy

import queue
from collections import deque



def divisor(n): #nの約数を全て求める
    i = 1
    table = set()
    while i * i <= n:
        if n%i == 0:
            table.add(i)
            table.add(n//i)
        i += 1
    return table

ans = 10 ** 10

def check(box_num, kagi_num, kagi_data, ind, now_data_kari, money, data):
    now_data = now_data_kari.copy()

    if ind == box_num:
        for i in range(box_num):
            if now_data[i] == 0:
                break
        else:
            global ans
            ans = min(ans, money)
        return


    if now_data[ind]:

        check(box_num, kagi_num, kagi_data, ind + 1, now_data, money, data)
        return

    for i in range(len(kagi_data[ind + 1])):
        aaa = kagi_data[ind + 1][i]
        now_data = now_data_kari.copy()
        for ele in data[aaa][1]:
            now_data[ele - 1] += 1
        check(box_num, kagi_num, kagi_data, ind + 1, now_data, money + data[aaa][0][0], data)



def main():
    box_num, kagi_num = map(int, input().split())

    data = [0 for i in range(kagi_num)]
    kari = set()

    kagi_data = defaultdict(set)

    for i in range(kagi_num):
        a = list(map(int, input().split()))
        b = list(map(int, input().split()))
        kari |= set(b)
        data[i] = [a, b]
        for ele in b:
            kagi_data[ele].add(i)

    for i in range(1, box_num + 1):
        kagi_data[i] = list(kagi_data[i])
        kagi_data[i].sort()

    if len(kari) != box_num:
        print(-1)
        sys.exit()

    # print(data)
    # print(kagi_data)

    now_data = [0 for i in range(box_num)]
    check(box_num, kagi_num, kagi_data, 0, now_data, 0, data)

    global ans
    print(ans)




# def test():
#     for i in :
#         print(i)

if __name__ == '__main__':
    main()
    # test()