G. String Counting
time limit per test
10 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

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 $998244353$.

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 $998244353$.

Examples
Input
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

Output
422500

Input
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

Output
16900

Input
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

Output
287489790