$-.$ P$6\mathrm{.}1$ Write a program that initializes a list with ten random integers and then prints four lines of output, containing

Every element at an even index.

Every even element.

All elements in reverse order.

Only the first and last element.

P$6\mathrm{.}2$ Write a program that reads numbers and adds them to a list if they aren't already contained in the list. When the list contains ten numbers, the program displays the contents and quits.

$-"$ P$6\mathrm{.}3$ Write a program that adds all numbers from $2$ to $10,000$ to a list. Then remove the multiples of $2($but not $2),$ multiples of $3($but not $3),$ and so on$,$ up to the multiples of $100.$ Print the remaining values.

$-.$ P$6\mathrm{.}4$ Write list functions that carry out the following tasks for a list of integers. For each function, provide a test program.

a$.$ Swap the first and last elements in the list.

b$.$ Shift all elements by one to the right and move the last element into the first position. For example, $1491625$ would be transformed into $2514916.$

c$.$ Replace all even elements with $0.$

d$.$ Replace each element except the first and last by the larger of its two neighbors.

e$.$ Remove the middle element if the list length is odd, or the middle two elements if the length is even.

f$.$ Move all even elements to the front, otherwise preserving the order of the elements.