Buying Sets

题面翻译

题意

有一个大小为 $n$ 的全集，每个元素是一个数，有 $n$ 个子集。题目保证任意 $k$ 个子集的并的大小 $\geqslant k$ 。

每个子集有一个可正可负的权值，你需要选出一些子集使得这些子集并的大小等于子集个数，且所选子集的权值和最小。可以为空集。

数据范围

$n \leqslant 300$

题目描述

The Hexadecimal virus loves playing with number sets — intersecting them, uniting them. One beautiful day she was surprised to find out that Scuzzy, her spherical pet cat, united all sets in one and ate the result! Something had to be done quickly and Hexadecimal rushed to the market.

The market has $n$ sets of numbers on sale. The virus wants to buy the following collection of sets: the number of sets in the collection should be exactly the same as the number of numbers in the union of all bought sets. Moreover, Hexadecimal wants to buy the cheapest suitable collection of set.

Yet nothing's so easy! As Mainframe is a kingdom of pure rivalry markets, we know that the union of any $k$ sets contains no less than $k$ distinct numbers (for every positive integer $k$ ).

Help the virus choose the suitable collection of sets. The collection can be empty.

输入格式

The first line contains the only number $n$ ( $1<=n<=300$ ) — the number of sets available in the market.

Next $n$ lines describe the goods: first we are given $m_{i}$ ( $1<=m_{i}<=n$ ) — the number of distinct numbers in the $i$ -th set, then follow $m_{i}$ numbers — the set's elements. We know that the set's elements are distinct positive integers and they do not exceed $n$ .

The last line contains $n$ integers whose absolute values do not exceed $10^{6}$ — the price of each set.

输出格式

Print a single number — the minimum price the virus will have to pay for such a collection of $k$ sets that union of the collection's sets would have exactly $k$ distinct numbers ().

样例 #1

样例输入 #1

3
1 1
2 2 3
1 3
10 20 -3

样例输出 #1

-3

样例 #2

样例输入 #2

5
2 1 2
2 2 3
2 3 4
2 4 5
2 5 1
1 -1 1 -1 1

样例输出 #2

0

样例 #3

样例输入 #3

5
2 1 2
2 2 3
2 3 4
2 4 5
2 5 1
-1 1 -1 1 -1

样例输出 #3

-1