FUNCTION INPUT/OUTPUT

Hints: What month would you be in during the 66th day of the year? What days of the year are in October?
 
I think the OP didn't give us a complete image of the problem. It states that the input numbers (domain) can be any integer in [1,365]. Is the answer supposed to be a well defined function? Or are we supposed to notice some other property of the integers given that we can extrapolate to come to a unique answer for the pre-image of October?
 
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