Hexagon A B C D E F is divided into five rhombuses, \mathcal{P}, \mathcal{Q}, \mathcal{R}, \mathcal{S}, and \mathcal{T}, as shown. Rhombuses \mathcal{P}, \mathcal{Q}, \mathcal{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.
