Abundances Of Absolutes

Algebra Level 3

A=i=12016xai\mathcal A=\displaystyle\sum_{i=1}^{2016}\left|x-a_i\right|

Let a1,a2,a3,,a2016a_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 A\mathcal A be 201622016^2 for real xx. Then find the sum of all possible values of the common difference of AP.

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

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