Contest Duration: - (local time) (300 minutes) Back to Home
J - Get Everything /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 制約

• 入力は全て整数
• 1 ≤ N ≤ 12
• 1 ≤ M ≤ 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

### 入力

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}}


### 入力例 1

2 3
10 1
1
15 1
2
30 2
1 2


### 出力例 1

25


1 と鍵 2 を購入すると、全ての宝箱を開けることが出来ます。このときの費用は 25 円であり、これが最小値です。

### 入力例 2

12 1
100000 1
2


### 出力例 2

-1


### 入力例 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


### 出力例 3

69942


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