Two Round Dances

One day $n$ people ($n$ is even) met on a plaza and made two round dances. Find the number of ways $n$ people can make two round dances if each round dance consists of exactly $n/2$ 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.

Input

One even integer $n(2\le n\le 20)$.

Output

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

Examples

For example, for $n=4$ the number of ways is $3$:

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

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

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