CF1487G String Counting

You have $ c_1 $ letters 'a', $ c_2 $ letters 'b', ..., $ c_{26} $ letters 'z'. You want to build a beautiful string of length $ n $ from them (obviously, you cannot use the $ i $ -th letter more than $ c_i $ times). Each $ c_i $ is greater than $ \frac{n}{3} $ . A string is called beautiful if there are no palindromic contiguous substrings of odd length greater than $ 1 $ in it. For example, the string "abacaba" is not beautiful, it has several palindromic substrings of odd length greater than $ 1 $ (for example, "aca"). Another example: the string "abcaa" is beautiful. Calculate the number of different strings you can build, and print the answer modulo $ 998244353 $ .

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