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A=∑i=12016∣x−ai∣\mathcal A=\displaystyle\sum_{i=1}^{2016}\left|x-a_i\right|A=i=1∑2016∣x−ai∣
Let a1,a2,a3,…,a2016a_1,a_2,a_3,\ldots ,a_{2016}a1,a2,a3,…,a2016 form an increasing arithmetic progression (AP) which consists of only positive terms. Let the minimum value of A\mathcal AA be 201622016^220162 for real xxx. 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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