Abundances Of Absolutes

Algebra Level 3

$\mathcal A=\displaystyle\sum_{i=1}^{2016}\left|x-a_i\right|$

Let $a_1,a_2,a_3,\ldots ,a_{2016}$ form an increasing arithmetic progression (AP) which consists of only positive terms. Let the minimum value of $\mathcal A$ be $2016^2$ for real $x$ . Then find the sum of all possible values of the common difference of AP.

Notation: $| \cdot |$ denotes the absolute value function.