2007 AIME I Problem 5

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 and rounded to the nearest integer; the resulting integer Celsius temperature is converted back to Fahrenheit and rounded to the nearest integer. For how many integer Fahrenheit temperatures T with 32 \leq T \leq 1000 does the original temperature equal the final temperature?