# 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.

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