Absolute One-to-One Function

Let \(x_1, x_2, \ldots, x_{2017}\) be distinct real numbers. How many one-to-one functions

\[f:\{x_1, x_2, \ldots, x_{2017} \} \to \{x_1, x_2, \ldots, x_{2017} \}\]

satisfy

\[ | f(x_1) - x_1 |= | f(x_2) - x_2 | = \cdots = | f(x_{2017}) - x_{2017} | ? \]

\[\] Notation: \( | \cdot | \) denotes the absolute value function.

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