A day on the calendar (usual Gregorian calendar used in the USA) can be represented as a tuple with three Int values (month,day,year) where the year is a positive integer, 1 <= month <= 12, and 1 <= day <= days_in_month. Here days_in_month is the number of days in the the given month (i.e. 28, 29, 30, or 31) for the given year.

Develop a Boolean Haskell function validDay d that takes a date tuple d and returns True if and only if d represents a valid date.

For example, validDay (8,20,2018) and validDay(2,29,2016} yield True and validDay (2,29,2017) and validDay(0,0,0) yield False.

Note: The Gregorian calendar was introduced by Pope Gregory of the Roman Catholic Church in October 1582. It replaced the Julian calendar system, which had been instituted in the Roman Empire by Julius Caesar in 46 BC. The goal of the change was to align the calendar year with the astronomical year.

Some countries adopted the Gregorian calendar at that time. Other countries adopted it later. Some countries may never have adopted it officially.

However, the Gregorian calendar system became the common calendar used worldwide for most civil matters. The proleptic Gregorian calendar extends the calendar backward in time from 1582. The year 1 BC becomes year 0, 2 BC becomes year -1, etc. The proleptic Gregorian calendar underlies the ISO 8601 standard used for dates and times in software systems.