Hard problem

题面翻译

一些由小写字母组成的字符串，你想把它们按照字典序排序，但是你不能改变它们的顺序，只能反转其中一些字符串。反转某一个字符串需要消耗对应的一些体力值。如果无论怎么翻转都不能使这些字符串按照字典序排序，输出 -1，否则输出最少需要消耗的体力值。

感谢 @Fuko_Ibuki 提供的翻译

题目描述

Vasiliy is fond of solving different tasks. Today he found one he wasn't able to solve himself, so he asks you to help.

Vasiliy is given $n$ strings consisting of lowercase English letters. He wants them to be sorted in lexicographical order (as in the dictionary), but he is not allowed to swap any of them. The only operation he is allowed to do is to reverse any of them (first character becomes last, second becomes one before last and so on).

To reverse the $i$ -th string Vasiliy has to spent $c_{i}$ units of energy. He is interested in the minimum amount of energy he has to spent in order to have strings sorted in lexicographical order.

String $A$ is lexicographically smaller than string $B$ if it is shorter than $B$ ( $|A|<|B|$ ) and is its prefix, or if none of them is a prefix of the other and at the first position where they differ character in $A$ is smaller than the character in $B$ .

For the purpose of this problem, two equal strings nearby do not break the condition of sequence being sorted lexicographically.

输入格式

The first line of the input contains a single integer $n$ ( $2<=n<=100000$ ) — the number of strings.

The second line contains $n$ integers $c_{i}$ ( $0<=c_{i}<=10^{9}$ ), the $i$ -th of them is equal to the amount of energy Vasiliy has to spent in order to reverse the $i$ -th string.

Then follow $n$ lines, each containing a string consisting of lowercase English letters. The total length of these strings doesn't exceed $100000$ .

输出格式

If it is impossible to reverse some of the strings such that they will be located in lexicographical order, print $-1$ . Otherwise, print the minimum total amount of energy Vasiliy has to spent.

样例 #1

样例输入 #1

2
1 2
ba
ac

样例输出 #1

1

样例 #2

样例输入 #2

3
1 3 1
aa
ba
ac

样例输出 #2

1

样例 #3

样例输入 #3

2
5 5
bbb
aaa

样例输出 #3

-1

样例 #4

样例输入 #4

2
3 3
aaa
aa

样例输出 #4

-1

提示

In the second sample one has to reverse string $2$ or string $3$ . To amount of energy required to reverse the string $3$ is smaller.

In the third sample, both strings do not change after reverse and they go in the wrong order, so the answer is $-1$ .

In the fourth sample, both strings consists of characters 'a' only, but in the sorted order string "aa" should go before string "aaa", thus the answer is $-1$ .