Write a program that reads a string from the keyboard and tests whether it contains a valid date. Display the date and a message that indicates whether it is valid. If it is not valid, also display a message explaining why it is not valid.

The input date will have the format mm/dd/yyyy. A valid month value mm must be from 1 to 12 (January is 1). The day value dd must be from 1 to a value that is appropriate for the given month. September, April, June, and November each have 30 days. February has 28 days except for leap years when it has 29. The remaining months all have 31 days each. A leap year is any year that is divisible by 4 but not divisible by 100 unless it is also divisible by 400.