SILK-ROAD 2006 Problem 3

A subset $S$ of the set $M=\{1,2,.....,p-1\}$ ,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 $\bar{{\Pi}_s}$ of all other elements of the set.The difference $\bigtriangleup_s=\Pi_s-\bar{{\Pi}_s}$ is called the deviation of the subset $S$ .Define the least possible remainder of division by $p$ of the deviation of an essential subset,containing $\frac{p-1}{2}$ elements.