2. Let $P$ be a regular 2006-gon. If an end of a diagonal of $P$ divides the boundary of $P$ into two parts, each containing an odd number of sides of $P$, then the diagonal is called a "good edge". It is stipulated that each side of $P$ is a good edge.

Given 2003 non-intersecting diagonals inside $P$ that partition $P$ into several triangles, how many isosceles triangles with two good edges can there be in this partition?
2. If an isosceles triangle has two good sides, it is briefly referred to as a "good triangle". Let $\triangle A B C$ be a good triangle, and $A B, B C$ be the good sides. Then, there are an odd number of edges between points $A$ and $B$; the same applies to $B$ and $C$. We say these edges belong to the good $\triangle A B C$.

Thus, in each of these two groups, at least one edge does not belong to any other good triangle. This is because the good triangles with three vertices between $A$ and $B$ have two equal-length sides, thus, there are an even number of edges belonging to it. Apart from all the edges belonging to any other good triangle, there must be one edge left that does not belong to any other good triangle. We designate such two edges (one in each group) to correspond to $\triangle A B C$.

For each good triangle, designate a pair of edges, with no two triangles sharing the designated edges. Thus, it follows that under this partition, there are at most 1003 good triangles, and it is easy to draw a partition that achieves this value.