You have three compulsory problems and one optional problem for this lab. The optional problem is for your practice and will not be graded. However, it is recommended that if you have sufficient time then you must attempt the optional problem. The optional problem is relatively tough as compared to the other three problems.

1. (30 marks) Write a program that takes three numbers as input from the user and checks whether any combination of these form a Pythagorean triplet or not. A Pythagorean triplet is the one in which the sum of squares of two numbers is equal to the square of the third number. For example:

Input: 12,13,5
Output: Form a Pythagorean triplet.

Input: 16,18,20
Output: Do not form a Pythagorean triplet.

2. (40 marks) Write a program to assign a grade according to the marks received in an exam. Make use of the switch statement. Your program should take the marks as input from the user and print the appropriate grade.
More than 80 receives A grade
More than 65 receives B grade
More than 50 receives C grade
More than 30 receives D grade
Less than 30 receives Failed

3. (40 marks) Write a program to check whether a given number is an Armstrong number or not. An Armstrong number is the one in which the sum of cubes of its digit is equal to the number itself. Your program should take a number as input and output whether the given number is an Armstrong number or not. For example:

Input: 371 
Output: Armstrong Number (27+343+1=371)

Input: 153
Output: Armstrong Number (1+125+27=153)

Input: 42
Output: Not an Armstrong Number (64+8=72) 

Optional Problem:

An integer is called perfect square if it can be expressed as square of some integer. For example, 1, 4, 9, 16 are perfect squares, but 6, 30, 44 are not perfect square. We say than an integer is a square-free integer if it is not divisible by any perfect square number, except 1. For example, 30 is a square-free number since none of its divisors (other than 1), {2, 3, 5, 6, 10, 15, 30} is a perfect square. But 12 is a non-square-free number since its divisor 4 is a perfect square. Write a program to determine whether an integer is square-free.