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 $ .

The first line contains one integer $ n $ ( $ 3 \le n \le 400 $ ). The second line contains $ 26 $ integers $ c_1 $ , $ c_2 $ , ..., $ c_{26} $ ( $ \frac{n}{3} < c_i \le n $ ).

Print one integer — the number of strings you can build, taken modulo $ 998244353 $ .