Super Lucky Tickets

For a spaceship to take off, each crew member needs a ticket. Each ticket has a sequence of $n$ digits, where $n$ is a positive even number.

Daniil calls a ticket super-lucky if both of the following properties hold:

• The sum of the first $\frac{n}{2}$ digits equals the sum of the last $\frac{n}{2}$ digits.
• The sum of the digits at even positions equals the sum of the digits at odd positions.

Help Daniil count the number of distinct super-lucky tickets modulo $998\,244\,353$.

The first line contains one number $n$, the length of a ticket ($2 \le n \le 200\,000$). It is guaranteed that $n$ is even.

Print the number of super-lucky tickets of length $n$ modulo $998\,244\,353$.