It is observed that January 1, 2002 was the first "sum-day" of the 21st century, that is, when that date is written in the mm-dd-yy format, it becomes 01/01/02, and 1+1 = 2. More specifically, a "sum-day" is a date in which the month and the day add up to the year.

(i) Determine the total number of sum-days from January 1, 2002 to December 31, 2100 inclusively.

(ii) Determine the last sum-day in the period covered under (i).

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