2013-02 Functional equation

Let \( \mathbb{Z}^+ \) be the set of positive integers. Suppose that \( f : \mathbb{Z}^+ \to \mathbb{Z}^+ \) satisfies the following conditions.

i) \( f(f(x)) = 5x \).

ii) If \( m \geq n \), then \( f(m) \geq f(n) \).

iii) \( f(1) \neq 2 \).

Find \( f(256) \).

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