Hexagon $$ABCDEF$$ is divided into five rhombuses, $$\mathcal{P, Q, R, S,}$$ and $$\mathcal{T,}$$ as shown. Rhombuses $$\mathcal{P, Q, R,}$$ and $$\mathcal{S}$$ are congruent, and each has area $$\sqrt{2006}.$$ Let $$K$$ be the area of rhombus $$\mathcal{T}.$$ Given that $$K$$ is a positive integer, find the number of possible values for $$K.$$

(第二十四届AIME1 2006 第8题)