CF543C Remembering Strings

You have multiset of $ n $ strings of the same length, consisting of lowercase English letters. We will say that those strings are easy to remember if for each string there is some position $ i $ and some letter $ c $ of the English alphabet, such that this string is the only string in the multiset that has letter $ c $ in position $ i $ . For example, a multiset of strings {"abc", "aba", "adc", "ada"} are not easy to remember. And multiset {"abc", "ada", "ssa"} is easy to remember because: - the first string is the only string that has character $ c $ in position $ 3 $ ; - the second string is the only string that has character $ d $ in position $ 2 $ ; - the third string is the only string that has character $ s $ in position $ 2 $ . You want to change your multiset a little so that it is easy to remember. For $ a_{ij} $ coins, you can change character in the $ j $ -th position of the $ i $ -th string into any other lowercase letter of the English alphabet. Find what is the minimum sum you should pay in order to make the multiset of strings easy to remember.

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