A "sum digit-day" is a date in which the sum of the digits of the month and the day add up to the sum of the digits of the year in the mm-dd-yy format.

For example,12-18-84 is a sum digit-day as the respective sum of the digits of the month and the day add up to 12 which is equal to the sum of the digits of the year.

(i) Determine the total number of sum digit-days from January 1, 2002 to December 31, 2099 inclusively.

(ii) Determine the year(s) having the maximum number of sum digit- days in the period covered under (i).

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