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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import math
from functools import reduce
from collections import deque
from itertools import combinations
import sys
sys.setrecursionlimit(10**7)

def s(generator, splitter, mapper):
    return [ mapper(s) for s in generator().split(splitter) ]

# スペース区切りの入力を読み込んで数値リストにして返します。
def get_nums_l():
    return [ int(s) for s in input().split(" ")]

# 改行区切りの入力をn行読み込んで数値リストにして返します。
def get_nums_n(n):
    return [ int(input()) for _ in range(n)]

def subsets(items):
    _subsets_=[]
    for i in range(len(items) + 1):
        for c in combinations(items, i):
            _subsets_.append(c)
    return _subsets_

INF = 999999999999999999999999

n,m = get_nums_l()

# ある扉の組み合わせを鍵1本で開けられる最小コストのリスト
keys = [INF] * (2 ** (n+2))

for _ in range(m):
    cost, b = get_nums_l()
    ccc = get_nums_l()

    # print(cost,b)


    for s in subsets(ccc):
        keyn = 0
        # print(s)
        for c in s:
            keyn += 2 ** c
        
        #print("keyn", keyn)
        if keys[keyn] > cost:
            keys[keyn] = cost

# print(keys)

# そもそも開けられない扉があったら無理
for i in range(1,n+1):
    if keys[2**i] == INF:
        print(-1)
        exit()

memo=[None] * (2 ** (n+2))

def solve(targets):

    lent = len(targets)
    
    # print(targets)

    if lent == 0:
        return 0

    if lent == 1:
        memo[2*list(targets)[0]] = keys[2*list(targets)[0]]
        # print(targets, keys[2**list(targets)[0]])
        return keys[2**list(targets)[0]]

    all_s = set(targets)

    keyn=0
    for c in targets:
        keyn += 2 ** c
    
    if memo[keyn]:
        return memo[keyn]

    _min = keys[keyn]

    for s in subsets(targets):
        if len(s) in (0, lent):
            continue
        rev = all_s.difference(s)
        cost = solve(s) + solve(rev)
        if _min > cost:
            _min = cost
    memo[keyn] = _min
    # print(targets, memo[keyn])
    return _min


ans = solve(set(range(1, n+1)))
# print(memo)
print(ans if ans < INF else -1)