CF706C Hard problem

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|

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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 $ .