order theory - $mathbb{N}timesmathbb{Q}$ isomorphic to $mathbb{Q}timesmathbb{N}$

Consider $\mathbb{N}\times\mathbb{Q}$ and $\mathbb{Q}\times\mathbb{N}$ both with the ordering given by $(a,b)\leq(c,d)$ iff ($a

Are $\mathbb{N}\times\mathbb{Q}$ and $\mathbb{Q}\times\mathbb{N}$ isomorphic as totally ordered sets?

I think that they aren't so, I need to find a function $f:\mathbb{Q}\times\mathbb{N}\to \mathbb{N}\times\mathbb{Q}$ in order to do that with the use of the following definition:

Definition of isomorphic: Let $(X,≤_X)$ and $(Y,≤_Y)$ be posets. $Y$ is isomorphic to $X$ as a poset if there exists an isomorphism $f:X→Y$ of posets.

By

$(a,b)\leq(c,d)$ iff $a

I meant the left lexicographic order