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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