  Let $s$ be West's deterministic stack-sorting map. A well-known result (West)
is that any length $n$ permutation can be sorted with $n-1$ iterations of $s.$
In 2020, Defant introduced the notion of highly-sorted permutations --
permutations in $s^t(S_n)$ for $t \lessapprox n-1.$ In 2023, Choi and Choi
extended this notion to generalized stack-sorting maps $s_{\sigma},$ where we
relax the condition of becoming sorted to the analogous condition of becoming
periodic with respect to $s_{\sigma}.$ In this work, we introduce the notion of
minimally-sorted permutations $\mathfrak{M}_n$ as an antithesis to Defant's
highly-sorted permutations, and show that $\text{ord}_{s_{123, 132}}(S_n) = 2
\lfloor \frac{n-1}{2} \rfloor,$ strengthening Berlow's 2021 classification of
periodic points.
