Question: Implement a simple Date class. You should be able to represent any date from January 1, 1800, to December 31, 2500; subtract two dates; increment a date by a number of days; and compare two dates using both equals and compareTo. A Date is represented internally as the number of days since some starting time, which, here, is the start of 1800. This makes all methods except for construction and toString trivial. The rule for leap years is a year is a leap year if it is divisible by 4 and not divisible by 100 unless it is also divisible by 400. Thus 1800, 1900, and 2100 are not leap years, but 2000 is. The constructor must check the validity of the date, as must toString. The Date could be bad if an increment or subtraction operator caused it to go out of range. Once you have decided on the specifications, you can do an implementation. The difficult part is converting between the internal and external representations of a date. What follows is a possible algorithm. Set up two arrays that are static fields. The first array, daysTillFirstOfMonth, will contain the number of days until the first of each month in a nonleap year. Thus it contains 0, 31, 59, 90, and so on. The second array, daysTillJan1, will contain the number of days until the first of each year, starting with firstYear. Thus it contains 0, 365, 730, 1095, 1460, 1826, and so on because 1800 is not a leap year, but 1804 is. You should have your program initialize this array once using a static initializer. You can then use the array to convert from the internal representation to the external representation.