A14124 | 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 $998244353$ .