Find all functions $\displaystyle f: \mathbb{N^{*}} \rightarrow \mathbb{N^{*}}$ which satisfy the following conditions

$\displaystyle i)$ $\displaystyle f$ is strictly increasing;

$\displaystyle ii)$ $\displaystyle f(f(n))= 4n+9$ for all $\displaystyle n \in \mathbb{N^{*}};$

$\displaystyle iii)$ $\displaystyle f(f(n)-n)=2n+9$ for all $\displaystyle n \in \mathbb{N^{*}}$.