Question 91
A subset $S$ of the set $M = \{1, 2, \dots, p-1\}$, where $p$ is a prime number of the kind $12n + 11$ is *essential*, if the product $\Pi_s$ of all elements of the subset is not less than the product $\overline{\Pi}_s$ of all other elements of the set. The difference $\Delta_s = \Pi_s - \overline{\Pi}_s$ is called the *deviation* of the subset $S$. Determine the least possible remainder of division by $p$ of the deviation of an essential subset, containing $\frac{p-1}{2}$ elements.