A collection of 8 cubes consists of one cube with edge-length $$k$$ for each integer $$k, 1 \le k \le 8.$$ A tower is to be built using all 8 cubes according to the rules: Any cube may be the bottom cube in the tower. The cube immediately on top of a cube with edge-length $$k$$ must have edge-length at most $$k+2.$$ Let $$T$$ be the number of different towers than can be constructed. What is the remainder when $$T$$ is divided by 1000?

(第二十四届AIME1 2006 第11题)