A Hailstone series is defined as follows: start with any integer value greater than $0,$ say x$.$ If x is even, then the next value in the series is x$/2$; if x is odd, then the next value in the series is $3$x $+1.$ Now apply the same rules to create the next value in the series, and so on$.$ The name Hailstone comes from the property that the values in such a series alternate between going up and down $($up for odd values and down for even values.$)$

For instance, here is the Hailstone series generated from starting value $17$:

$17,52,26,13,40,20,10,5,16,8,4,2,1$

Note that if a Hailstone series ever reaches the value $1,$ then the next value generated is $4,$ the next is $2,$ and the next is $1$ again. Thus, when a Hailstone series reaches $1,$ then it has converged in the sense that the rest of the series is $4,2,1,4,2,1,....$

The Hailstone series is the subject of a long$-$standing mathematical open question: given an arbitrary positive integer as a starting value, will the resulting Hailstone series converge as just described? For all positive integers of size at most $1\mathrm{.}2$x$1012,$ it is known that the series does converge. To date, however, there is no formal proof that all such series must converge. $($There is an interesting and readable article about the Hailstone series in the January $1984$ issue of Scientific American $.)$

For this assignment, you will write a program that allows users to enter a starting value from which the program computes and outputs the corresponding Hailstone series $($stopping with $1$ if it ever reaches $1).$ After the initial program works, there are a number of other requirements to change it slightly, one step at a time, as explained below.