For positive integers $$n,$$ let $$\tau (n)$$ denote the number of positive integer divisors of $$n,$$ including 1 and $$n.$$ For example, $$\tau (1)=1$$ and $$\tau(6) =4.$$ Define $$S(n)$$ by $$S(n)=\tau(1)+ \tau(2) + \cdots + \tau(n).$$ Let $$a$$ denote the number of positive integers $$n \leq 2005$$ with $$S(n)$$ odd, and let $$b$$ denote the number of positive integers $$n \leq 2005$$ with $$S(n)$$ even. Find $$|a-b|.$$

(第二十三届AIME1 2005 第12题)