Squared away

Geometry Level 5

Given is a square with sides of length 100.

Points \(P_1, \dots, P_{12}\) lie on the square in such a way, that the total pairwise distance between the points \[D = \sum_{i<j} d(P_i,P_j)\] is maximal.

How much is \(\lfloor D \rfloor\)? (I.e. \(D\) rounded down to the nearest smaller integer.)

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