CF1433E Two Round Dances

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.

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

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.