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will say that the lengths satisfy Pythagorus' Theorem up to epsilon if, for some small epsilon difference between e and a2 b2 is less than e. That is, > 0, the absolute The use of e allows us to specify a tolerance for the equality check. That is, we can tolerate (or accept) an error in the check that is smaller than e. Write a Java class, called Pythagorus, that has three methods: isPythagorusInt, isPythagorusDouble and main. The first method will test if three integers satisfy Pythagorus' Theorem, the second will test if three approximate real numbers satisfy Pythagorus' Theorem (up to e accuracy), and the last method will query a user for input to test numbers with the other two functions. The specifications for the first two methods are given below public static boolean isPythagorusInt(int a, int b, int c) /* Purpose: determine if a,b,c form a Pythagorean Triple where c is the hypotenuse * Input: a,b,c are each non-negative integers * Output : output true if c^2 = a^2 + b^2 output false if not public static boolean isPythagorusDouble (double a, double b, double c, double epsilon) *Purpose determine if a,b,c satisfy Pythagorus' Theorem up to epsilon * * Input: a,b,c are each non-negative doubles * Output : - outputs true if a,b,c satisfy Pyhtagorus' Theorem where c is the hypotenuse epsilon is a non-negative doubles up to the given epsilon - outputs false if not Note that this class must be a program so the main method must be public, static, return void have the right input argument type. The main method should repeatedly query the user for triples of numbers until they want to quit the program. First the user is asked if they want to enter integers, floating point numbers or quit the program If they choose to enter numbers they are then asked to enter a triple of numbers (one input; three numbers comma separated). The program will outout true or false for the given triple. This is repeated until the user decides to quit with the String "quit". Valid input for the first question are the strings "int", "float" and "quit". We will only test your code with these three strings (and various numbers)