How many morphism $\mathbb{F}_q\to \mathbb{F}_{q^n}$

Question

Sorry for my bad English.

Let $q$ be prime $p$ power, and $n>0$ be integer, and $\mathbb{F}_q$, $\mathbb{F}_{q^n}$ be finite fields.

Now how many morphisms of field $\mathbb{F}_q\to \mathbb{F}_{q^n}$?

Since ${\rm Aut}(\mathbb{F}_q)={\rm Gal}(\mathbb{F}_q /\mathbb{F}_p)\cong \mathbb{Z}/n\mathbb{Z}$, I think $\#{\rm Mor}(\mathbb{F}_q, \mathbb{F}_{q^n})\ge n.$