An analogous day is a date expressed in the mm-dd-yyyy format, where: yyyy= mm*dd*(sod(mm)+sod(dd))

For example, 09-27-4374 is an analogous day since: sod(mm)+sod(dd)) = 18, so that: yyyy= 9*27*18= 4374.

(i) Determine the respective first and last analogous days in the period covering January 1, 2000 to December 31, 2100 inclusively.

(ii) Determine the total number of analogous days in the period covered under (i).

*** sod(x) refers to the sum of digits of x.