Write a C$++$ program that will implement the following tasks to help students understand how to use direct and indirect recursion. Make sure to use appropriate variable types and display the results clearly.

Direct Recursion:

a$)$ Implement a function named "countDown" that takes an integer parameter $"$n$".$

b$)$ Inside the function, display the value of $"$n$".$

c$)$ If $"$n$"$ is greater than zero, recursively call the "countDown" function with $"$n$-1"$ as the argument.

Indirect Recursion:

a$)$ Implement two functions named "foo" and "bar" that call each other in a recursive manner.

b$)$ The "foo" function should take an integer parameter $"$n$"$ and display the value of $"$n$".$

c$)$ If $"$n$"$ is greater than zero, recursively call the "bar" function with $"$n$-1"$ as the argument.

d$)$ The "bar" function should take an integer parameter $"$n$"$ and display the value of $"$n$".$

e$)$ If $"$n$"$ is greater than zero, recursively call the "foo" function with $"$n$-1"$ as the argument.

User Input:

a$)$ Inside the main function, prompt the user to enter an integer value "num".

b$)$ Read and store the input in a suitable variable.

Direct Recursion Execution:

a$)$ Call the "countDown" function and pass "num" as the argument.

b$)$ Observe the output and verify that the "countDown" function displays the countdown from "num" to zero.

Indirect Recursion Execution:

a$)$ Call the "foo" function and pass "num" as the argument.

b$)$ Observe the output and verify that the "foo" and "bar" functions display the alternating values from "num" to zero.

Note: You are encouraged to use appropriate variable names, comments, and proper indentation in your code for better readability.

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Submission Guidelines:

$$ Write a well$-$structured C$++$ program that implements the above tasks.

$$ Provide clear and concise comments to explain the purpose of each section of code.

$$ Test your program with different input values to ensure its correctness.