The 58th question: Given that $p$ is an odd prime, if a natural number $x$ satisfies that for any natural number $t, p \nmid\left(x-t^{2}\right)$, then $x$ is called a quadratic non-residue modulo $p$. Let the set $A=\{a \mid a \in Z, 1 \leq a<p, a$ and $4-$ $\mathrm{a}$ are both quadratic non-residues modulo $\mathrm{p}\}$. Find the remainder of the product of all elements in $\mathrm{A}$ divided by $\mathrm{p}$.