Construction of uncountably many non-isomorphic linear (total) orderings of natural numbers

I would like to find a way to construct uncountably many non-isomorphic linear (total) orderings of natural numbers (as stated in the title).

I've already constructed two non-isomorphic total orderings. They are $$ 1 < 2 < 3 <\ldots\\ 1 > 2 > 3 >\ldots $$ where "$<$" and "$>$" are strict total ordering relations.

Thanks in advance for your help.

HINT: If you just want "uncountably many", then it's easy to observe that each countable ordinal can be expressed as a linear order of $\Bbb N$.

However if you want $2^{\aleph_0}$ (which is the maximal number of orders), then given $A\subseteq\Bbb N$, it is possible to use $A$ to define a unique linear order which looks like copies of the rational numbers with finite intervals between them, whose size depends on $A$.