$1.$ Write a Java program A$2$p$1.$java with a public class A$2$p$1$ and no named packages that accepts one command line argument a which is assumed to be positive integer at least $2.$ Calculate and print an integer list starting from a and ending until some integer appears a second time by iteratively applying a math function f to the value of a$.$ The math function f is defined as f$($x$)=(3$x$+1)/2$ if x is odd and f$($x$)=$x$/2$ if x is even. The iteration will stop when some value is reached twice. For example: When a is $6,$ the integer list should be $6,3,5,8,4,2,1,2$ and the length of this list is $8.$ The length of the list should also be printed. You program can, but does not have to$,$ store all elements of the list in memory at once. A sample run can look like the following $($those shown in blue color are typed by the user$)$:

$[$kwang@computer$][$~$/$temp$]$$java A$2$p$114$

Iterated list for $14$ is:

$14,7,11,17,26,13,20,10,5,8,4,2,1,2$

Length of the list: $14$

$2.$ Write a Java program A$2$p$2.$java with a public class A$2$p$2$ and no named packages that accepts a command line argument m that is assumed to be a multiple of $60($e$.$g$.60,120,$etc$).$ Generate a string of m random upper case English characters and store them in a char array. Design three additional methods other than the main method each of which is supposed to convert one$-$third of the m chars in your array in place into a backward$-$offset lower case version $($i$.$e$.$A$->$z$,$B$->$a$,$C$->$b$,...,$Y$->$x$,$Z$->$y$).$ Print out the string $($i$.$e$.$ all array elements$)$ both before and after conversion on two separate lines. You can choose which one$-$third of the array each of the three methods will convert, as long as their combined work converts all m chars in the array. Can you imagine how you would change your program if four additional methods should be created to do the conversion, each of which converts one$-$fourth of the m chars? What about five methods? Six methods? Just submit the three$-$method version. A sample run can be seen later.