There is a set of 1000 switches, each of which has four positions, called $$A, B, C$$, and $$D$$. When the position of any switch changes, it is only from $$A$$ to $$B$$, from $$B$$ to $$C$$, from $$C$$ to $$D$$, or from $$D$$ to $$A$$. Initially each switch is in position $$A$$. The switches are labeled with the 1000 different integers $$(2^{x})(3^{y})(5^{z})$$, where $$x, y$$, and $$z$$ take on the values $$0, 1, \ldots, 9$$. At step i of a 1000-step process, the $$i$$-th switch is advanced one step, and so are all the other switches whose labels divide the label on the $$i$$-th switch. After step 1000 has been completed, how many switches will be in position $$A$$?

(第十七届AIME1999 第7题)