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)