The formula for converting a Fahrenheit temperature \(F\) to the corresponding Celsius temperature \(C\) is \(C = \frac{5}{9}(F-32).\) An integer Fahrenheit temperature is converted to Celsius, rounded to the nearest integer, converted back to Fahrenheit, and again rounded to the nearest integer. For how many integer Fahrenheit temperatures between \(32\) and \(1000\) inclusive does the original temperature equal the final temperature?

(第二十五届AIME1 2007 第5题)