Problem 2. Let P be a regular 2006-gon. A diagonal of P 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.
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