Circle the wagons

Geometry Level 5

Given a circle with a diameter of 100.

Twelve points \(P_1, \dots, P_{12}\) lies on a circle, in such a way that their total pairwise distance, \[D = \sum_{i < j} d(P_i, P_j)\] is maximal.

Give the value of \(\lfloor D \rfloor\). (I.e. rounded down to the nearest integer.)

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