Let $G$ be a $p$-group. Show that the number of normal subgroups of $G$ that have order $p^s$ is $1$ $mod(p)$.

I think I have to use Sylow theorems and the fact that every subgroup of order $p^s$ is contained in a $p$-Sylow subgroup, but I don't know how to apply this.
I also thought about defining an action in the set of normal subgroups of $G$ of order $p^s$, but I couldn't think of one that is useful.

Any help will be very appreciated. Thanks!