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 $998244353$.

见题面 Input 部分

见题面 Output 部分