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There are three coplanar parallel lines. If any $p$ points are taken on each of the lines, then find the maximum number of triangles with the vertices of these points.

  1. $p^{2}(4p-3)$
  2. $p^{3}(4p-3)$
  3. $p(4p-3)$
  4. $p^{3}$
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