# Functional Modulus

Algebra Level 5

$|f(x_{1})-x_{1}|=|f(x_{2})-x_{2}|=|f(x_{3})-x_{3}|=\ldots=|f(x_{n})-x_{n}|$

Let $$n$$ be an odd positive integer and let $$x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, \ldots, x_{n}$$ be distinct real numbers. Find the total number of one-to-one functions $$f: (x_{1}, x_{2}, x_{3},\ldots, x_{n}) \rightarrow (x_{1}, x_{2}, x_{3}, \ldots , x_{n})$$ such that the equation above is satisfied.

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