Beautiful dates

Vova considers a date written in the format DDMMYYYY to be beautiful if, when reversed, it still represents a valid calendar date. For example, September $1$, $2010$ ($01092010$) is beautiful, as reversing it gives February $1$, $9010$ ($01029010$), which is a valid date. However, April $3$, $1991$ ($03041991$) is not beautiful, because reversing it results in the non-existent $91$st month of the year $4030$. Vova wants to know how many such beautiful dates exist between his birthday and the day he started first grade, inclusive. Help him determine this number.