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 $f(256)$.