SIMPLE JAVA PROBLEM! Can you please provide me with BOTH an algorithm and working program. Also there needs to be a month class AND a monthDRiver

Month Class Write a class named Month. The class should have an int field named monthNumber that holds the number of the month. For example, January would be 1, February would be 2, and so forth. In addition, provide the following methods:

A no-arg constructor that sets the monthNumber field to 1.

A constructor that accepts the number of the month as an argument. It should set the monthNumber field to the value passed as the argument. If a value less than 1 or greater than 12 is passed, the constructor should set monthNumber to 1.

A constructor that accepts the name of the month, such as January or February as an argument. It should set the monthNumber field to the correct corresponding value.

A setMonthNumber method that accepts an int argument, which is assigned to the monthNumber field. If a value less than 1 or greater than 12 is passed, the method should set monthNumber to 1.

A getMonthNumber method that returns the value in the monthNumber field.

A getMonthName method that returns the name of the month. For example, if the monthNumber field contains 1, then this method should return January. A toString method that returns the same value as the getMonthName method.

An equals method that accepts a Month object as an argument. If the argument object holds the same data as the calling object, this method should return true. Otherwise, it should return false.

A greaterThan method that accepts a Month object as an argument. If the calling objects monthNumber field is greater than the arguments monthNumber field, this method should return true. Otherwise, it should return false.

A lessThan method that accepts a Month object as an argument. If the calling objects monthNumber field is less than the arguments monthNumber field, this method should return true. Otherwise, it should return false.