Consider the rule $"$if n is even divide it by $2$ otherwise multiply by three and add $1."$ For example, if we apply the rule to $7$ then we would get the new value $22$ since $7$ is odd and $3*7+1=22.$ On the other hand, if we apply the rule to $22$ we get $11$ since $22$ is even and $22/2=11.$

The Collatz conjecture states that any sequence that starts with a positive integer formed by repeatedly applying the above rule will always reach the number $1.$ For example $7-->22-->11-->34-->17-->52-->13-->40-->20-->10-->5-->16-->8-->4-->2-->1.($ Once the number $1$ is reached, we'll stop since the following values would be $1-->4-->2-->1$ repeating infinitely.$)$ We'll call such a sequence, a Collatz sequence.

So far, the Collatz conjecture has not been proved or disproved, so it's useful to investigate the outcome for various starting values.

Write a program to generate Collatz sequences with a starting value given by the user, to be stored in a value of type unsigned int. $($That$\text{'}$s like an int but only stores positive integers.$)$ The program will output the values obtained until $1$ is reached $($Of course if the Collatz conjecture is false you could get an infinite loop!$)$ The length of the sequence will also be given. To avoid integer overflow, include a defined constant LIMIT in your program with the value one billion. If the next value generate exceeds LIMIT then you should stop the loop and print "Limit exceeded!"

The user can continue with more starting values until they decide to quit.

Below are some sample runs. Your output should match the sample run output EXACTLY when given the same input. Use a do$-$while loop for the outer loop $($to allow the user to enter more starting values$)$ and a while loop for the inner loop $($to generate the sequence$).$ No use of the keyword break is allowed.

For your submission, copy paste your code and at the bottom insert a screenshot of a sample run with inputs $27,837799$ and $0($to quit$).$