IMO Shortlist 2006 problem C2

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2. travnja 2012.
Let P be a regular 2006-gon. A diagonal is called good if its endpoints divide the boundary of P into two parts, each composed of an odd number of sides of P. The sides of P are also called good.
Suppose P has been dissected into triangles by 2003 diagonals, no two of which have a common point in the interior of P. Find the maximum number of isosceles triangles having two good sides that could appear in such a configuration.
Izvor: Međunarodna matematička olimpijada, shortlist 2006