1433E · Two Round Dances

Problem: One day, $n$ people ($n$ is an even number) met on a plaza and made two round dances, each round dance consists of exactly $\frac{n}{2}$ people. Your task is to find the number of ways $n$ people can make two round dances if each round dance consists of exactly $\frac{n}{2}$ people. Each person should belong to exactly one of these two round dances.

Round dance is a dance circle consisting of $1$ or more people. Two round dances are indistinguishable (equal) if one can be transformed to another by choosing the first participant. For example, round dances $[1, 3, 4, 2]$, $[4, 2, 1, 3]$ and $[2, 1, 3, 4]$ are indistinguishable.

For example, if $n=2$ then the number of ways is $1$: one round dance consists of the first person and the second one of the second person.

For example, if $n=4$ then the number of ways is $3$. Possible options:

• one round dance — $[1,2]$, another — $[3,4]$;
• one round dance — $[2,4]$, another — $[3,1]$;
• one round dance — $[4,1]$, another — $[3,2]$.

Your task is to find the number of ways $n$ people can make two round dances if each round dance consists of exactly $\frac{n}{2}$ people.

Input Format: The input contains one integer $n$ ($2 \le n \le 20$), $n$ is an even number.

Output Format: Print one integer — the number of ways to make two round dances. It is guaranteed that the answer fits in the $64$-bit integer data type.