Write a program that determines the day of the week for a given date. You
can invent your own complex algorithm that takes into account the special
leap year rules, and changes in calendars, but this is a case where it makes
sense to look for things that are familiar. Who else might need to compute
values from dates over a wide span of time? Historians work with dates, but
generally don't compute from them. Astronomers, however, need to know
the difference in time between orbital events in the solar system that span
hundreds of years. Consulting an astronomy text, you will find that there is a
standard way of representing a date, called the Julian Day Number (JDN).
This value is the number of days that have elapsed since January 1, 4713 B.C.
Given the JDN for a date, there is a simple formula that tells the day of the
week:

DayOfWeek = (JDN + 1) % 7

The result is in the range of 0 to 6, with 0 representing Sunday.

The only remaining problem is how to compute the JDN, which is not so
simple. The algorithm computes several intermediate results that are added
together to give the JDN. We look at the computation of each of these three
intermediate values in turn.

If the date comes from the Gregorian calendar (later than October 15,
1582), then compute intRes1 with the following formula; otherwise, let
intRes1 be zero.

intRes1 = 2 - year / 100 + year / 400 (integer division)

The second intermediate result is computed as follows:

intRes2 = static_cast<int>(365.25 * Year)

We compute the third intermediate value with this formula:

intRes3 = static_cast<int>(30.6001 * (month + 1))

Finally, the JDN is computed this way:

JDN = intRes1 + intRes2 + intRes3 + day + 1720994.5

Your program should make appropriate use of value-returning functions in
solving this problem. These formulas require nine significant digits; you may
have to use the integer type long and the floating-point type double. Your
program should prompt the user appropriately for input of the date; it should
also properly label the output. Use proper coding style with comments to
document the algorithm as needed.

Your program is to read from a file. The file consists of dates in the format:
mm  dd  yyyy