String Counting

题意翻译

你有 $26$ 个不同的字符，第 $i$ 个字符有 $c_i$ 个（$\frac{n}{3} < c_i \leq n$）。 你希望用这些字符，构造出一个长度为 $n$ 的字符串（每个字符在字符串中出现的个数不超过 $c_i$），使得这个字符串上不存在长度为奇数且大于 $1$ 的回文串。求出方案数对 $998244353$ 取模的结果。

题目描述

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 $ .

输入输出格式

输入格式

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 $ ).

输出格式

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

输入输出样例

输入样例 #1

4
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

输出样例 #1

422500

输入样例 #2

3
2 2 2 2 2 2 3 3 3 2 2 2 2 2 2 3 3 3 2 2 3 2 2 3 2 2

输出样例 #2

16900

输入样例 #3

400
348 322 247 158 209 134 151 267 268 176 214 379 372 291 388 135 147 304 169 149 193 351 380 368 181 340

输出样例 #3

287489790