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)