String Counting
Description
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 $998244353$.
Input
The first line contains one integer $n$ ($3 \le n \le 400$).
The second line contains $26$ integers $c_1$, $c_2$, ..., $c_{26}$ ($\frac{n}{3} < c_i \le n$).
Output
Print one integer — the number of strings you can build, taken modulo $998244353$.
Samples
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
422500
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
16900
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
287489790